HCM 2020 PDF

THE NATIONAL ACADEMIES PRESS
This PDF is available at http://nap.edu/25963 SHARE

   
Highway Capacity Manual Methodologies for Corridors

Involving Freeways and Surface Streets (2020)
DETAILS
390 pages | 8.5 x 11 | PAPERBACK

ISBN 978-0-309-68426-2 | DOI 10.17226/25963
CONTRIBUTORS
GET THIS BOOK University of Florida Transportation Institute, Cambridge Systematics, and Alex
Skabardonis; National Cooperative Highway Research Program; Transportation
Research Board; National Academies of Sciences, Engineering, and Medicine
FIND RELATED TITLES
SUGGESTED CITATION
National Academies of Sciences, Engineering, and Medicine 2020. Highway

Capacity Manual Methodologies for Corridors Involving Freeways and Surface
Streets. Washington, DC: The National Academies Press.
https://doi.org/10.17226/25963.

Visit the National Academies Press at NAP.edu and login or register to get:
– Access to free PDF downloads of thousands of scientiﬁc reports

– 10% off the price of print titles
– Email or social media notiﬁcations of new titles related to your interests
– Special offers and discounts

Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the National Academies Press.
(Request Permission) Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences.
Copyright © National Academy of Sciences. All rights reserved.

Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets
NCHRP
Web-Only Document 290:
Highway Capacity Manual Methodologies for Corridors

Involving Freeways and Surface Streets
University of Florida Transportation Institute

Gainesville, FL
Cambridge Systematics
Gainesville, FL
Alex Skabardonis
Consultant
Berkeley, CA
Contractor’s Final Report for NCHRP Project 15-57

Submitted June 2020
NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM

Systematic, well-designed, and implementable research is the most effective way to solve many problems facing state departments of
transportation (DOTs) administrators and engineers. Often, highway problems are of local or regional interest and can best be studied by
state DOTs individually or in cooperation with their state universities and others. However, the accelerating growth of highway
transportation results in increasingly complex problems of wide interest to highway authorities. These problems are best studied through a
coordinated program of cooperative research.
Recognizing this need, the leadership of the American Association of State Highway and Transportation Officials (AASHTO) in 1962
initiated an objective national highway research program using modern scientific techniques—the National Cooperative Highway Research
Program (NCHRP). NCHRP is supported on a continuing basis by funds from participating member states of AASHTO and receives the
full cooperation and support of the Federal Highway Administration (FHWA), United States Department of Transportation, under
Agreement No. 693JJ31950003.
COPYRIGHT INFORMATION
Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who
own the copyright to any previously published or copyrighted material used herein.
Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit
purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FTA,
GHSA, NHTSA, or TDC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this
document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced
material. For other uses of the material, request permission from CRP.
DISCLAIMER
The opinions and conclusions expressed or implied in this report are those of the researchers who performed the research. They are not
necessarily those of the Transportation Research Board; the National Academies of Sciences, Engineering, and Medicine; the FHWA; or
the program sponsors.
The information contained in this document was taken directly from the submission of the author(s). This material has not been edited
by TRB.
Copyright National Academy of Sciences. All rights reserved.

The National Academy of Sciences was established in 1863 by an Act of Congress, signed by President Lincoln, as a private, non-
governmental institution to advise the nation on issues related to science and technology. Members are elected by their peers for
outstanding contributions to research. Dr. Marcia McNutt is president.
The National Academy of Engineering was established in 1964 under the charter of the National Academy of Sciences to bring the
practices of engineering to advising the nation. Members are elected by their peers for extraordinary contributions to engineering.
Dr. John L. Anderson is president.
The National Academy of Medicine (formerly the Institute of Medicine) was established in 1970 under the charter of the National
Academy of Sciences to advise the nation on medical and health issues. Members are elected by their peers for distinguished contributions
to medicine and health. Dr. Victor J. Dzau is president.
The three Academies work together as the National Academies of Sciences, Engineering, and Medicine to provide independent,
objective analysis and advice to the nation and conduct other activities to solve complex problems and inform public policy decisions.
The National Academies also encourage education and research, recognize outstanding contributions to knowledge, and increase
public understanding in matters of science, engineering, and medicine.
Learn more about the National Academies of Sciences, Engineering, and Medicine at www.national-academies.org.
The Transportation Research Board is one of seven major programs of the National Academies of Sciences, Engineering, and Medicine.
The mission of the Transportation Research Board is to provide leadership in transportation improvements and innovation through
trusted, timely, impartial, and evidence-based information exchange, research, and advice regarding all modes of transportation. The
Board’s varied activities annually engage about 8,000 engineers, scientists, and other transportation researchers and practitioners from
the public and private sectors and academia, all of whom contribute their expertise in the public interest. The program is supported by
state transportation departments, federal agencies including the component administrations of the U.S. Department of Transportation,
and other organizations and individuals interested in the development of transportation.
Learn more about the Transportation Research Board at www.TRB.org.

COOPERATI VE RESEAR CH PROGRAMS
CRP STAFF FOR NCHRP WEB-ONLY DOCUMENT 290

Christopher J. Hedges, Director, Cooperative Research Programs
Lori L. Sundstrom, Deputy Director, Cooperative Research Programs
B. Ray Derr, Senior Program Officer
Anthony Avery, Senior Program Assistant
Eileen P. Delaney, Director of Publications
Natalie Barnes, Associate Director of Publications
Jennifer Correro, Assistant Editor
NCHRP PROJECT 15-57 PANEL

Field of Design—General Design
Andrew C. Mao, Texas Department of Transportation, Houston, TX (Chair)
Montasir M. Abbas, Virginia Polytechnic Institute and State University, Blacksburg, VA
Vicki Sue Haskell, Wisconsin Department of Transportation, Madison, WI
John Hourdos, University of Minnesota, Twin Cities, Minneapolis, MN
Marcus H. Januario, Shive-Hattery, Cedar Rapids, IA
Sanhita Lahiri, Virginia Department of Transportation, Richmond, VA
Errol Stoute, Jr., Maryland State Highway Administration, Hanover, MD
Peter A. Terry, Benchmark Civil Engineering Services, Inc., Allentown, PA
John H. Thai, City of Anaheim, Anaheim, CA
James D. Colyar, FHWA Liaison
Richard A. Cunard, TRB Liaison
ACKNOWLEDGMENT
The research reported herein was performed under NCHRP Project 15-57 by the University of Florida
Transportation Institute (UFTI). UFTI was the contractor for this study, with Cambridge Systematics
and Dr. Alexander Skabardonis as subcontractors. Dr. Lily Elefteriadou, Director at UFTI, was the
Principal Investigator. The other authors of this report are Fabio Sasahara, Graduate Research Assistant
at UFTI; Luan Carvalho, Graduate Research Assistant at UFTI; Tanay Datta Chowdhury, Graduate
Research Assistant at UFTI; Marilo Martin Gasulla, Graduate Research Assistant at UFTI; Richard
Margiotta, PhD, Principal at Cambridge Systematics and Alexander Skabardonis, PhD, Professor at
University of California Berkeley. The authors are thankful to the valuable contributions from the
members from the NCHRP Panel and from the Highway Capacity and Quality of Service Committee
for providing valuable feedback and facilitating contacts with public agencies for the data collection
task. The authors also thank the following public agency staff members who assisted with the site
identification and data collection: Daniel Buidens, Florida DOT; Rodney Carrero-Villa, Florida DOT;
Vicki Haskell, Wisconsin DOT; Brian Kary, Minnesota DOT; Sanhita Lahiri, Virginia DOT; David
Miranda, Georgia DOT; Rina Patolilic, Louisiana DOT; and Peter Vega, Florida DOT. Finally, the
authors acknowledge the valuable contribution of the following student assistants who contributed to
data analysis and reduction: Valerie Bonar, Christian Breau, Michael Hunter, Corbin Kramer, Brandon
Lahore, Sophia Semensky, and Hope Sotolongo-Miranda.

TABLE OF CONTENTS
SUMMARY ............................................................................................................................................... 1
1. INTRODUCTION ............................................................................................................................. 3
2. LITERATURE REVIEW ................................................................................................................ 4
3. CRITICAL REVIEW OF THE HCM .......................................................................................... 8
4. PERFORMANCE MEASURES ..................................................................................................12
5. QUEUE SPILLBACK INTO FREEWAYS ..............................................................................14
6. QUEUE SPILLBACK INTO URBAN STREETS ...................................................................27
7. LANE-BY-LANE SPEED AND FLOW ESTIMATION
METHODS FOR FREEWAYS ....................................................................................................35
8. SYSTEM ANALYSIS .....................................................................................................................41
9. SOFTWARE IMPLEMENTATION ..........................................................................................43
10. CONCLUSIONS AND RECOMMENDATIONS ....................................................................43
REFERENCES .......................................................................................................................................45
APPENDIX A. CHAPTER 38: SYSTEM ANALYSES .......................................................... 47

APPENDIX B. OFF-RAMP QUEUE SPILLBACK.............................................................. 232
APPENDIX C. FREEWAY OFF-RAMP – QUEUE SPILLBACK ANALYSIS................ 245
APPENDIX D. ON-RAMP QUEUE SPILLBACK CHECK................................................ 293
APPENDIX E. ON-RAMP QUEUE SPILLBACK ANALYSIS .......................................... 304
APPENDIX F. FREEWAY FACILITIES LANE-BY-LANE ANALYSIS ......................... 351
APPENDIX G. GLOSSARY .................................................................................................... 378
- iv -

LIST OF FIGURES
Figure 1 – HCM service measures by system element and mode .................................................. 8

Figure 2 – Schematic of a diverge influence area (HCM) .............................................................. 9
Figure 3 – Recommended performance measure framework for
different evaluation purposes ..................................................................................................... 13
Figure 4 – Data collection framework for queue spillback into freeway facilities ....................... 15
Figure 5 – Survey for off-ramp queue spillback study sites – outcome by state .......................... 16
Figure 6 – Miami, FL – I-95 SB to SW 25th Rd. .......................................................................... 17
Figure 7 – Tampa, FL – I-275 NB to SR-60 ................................................................................. 17
Figure 8 – Norfolk, VA – I-64 WB to Northampton Blvd ........................................................... 18
Figure 9 – Centreville, VA – I-66 WB to SR-28 (Sully Rd) ........................................................ 18
Figure 10 – Centreville, VA – I-66 EB to SR-28 (Sully Rd)........................................................ 18
Figure 11 – Minneapolis, MN – I-35W SB to 35th St. ................................................................. 18
Figure 12 – Atlanta, GA – I-285 NB to I-20................................................................................. 19
Figure 13 – Miami, FL – I-75 SB to SR 826 ................................................................................ 19
Figure 14 – Atlanta, GA – I-285 NB to GA-141 .......................................................................... 19
Figure 15 – Sacramento, CA – SR-99 NB to SR-50..................................................................... 19
Figure 16 – Back-of-queue length measurement – off-ramp queue spillback .............................. 20
Figure 17 – Sample of data illustrating queue spillback:
(a) queue length and (b) speeds by lane ..................................................................................... 21
Figure 18 – Unbalanced lane usage at the off-ramp: (a) right lane and (b) left lane .................... 22
Figure 19 – Effects of queue spillback across freeway lanes at three locations
upstream of the exit experiencing spillback (I-275 EB – Tampa, FL) ...................................... 22
Figure 20 – Blockage of one (a) or two (b) mainline lanes due to off-ramp queue spillback ...... 23
Figure 21 – Example of a forced merging maneuver for a vehicle attempting to
join the off-ramp queue .............................................................................................................. 24
Figure 22 – Micro-simulated off-ramp queue spillback (I-105@Bellflower
Interchange – Los Angeles, CA) ................................................................................................ 24
Figure 23 – Procedure for identifying spillback occurrence at an off-ramp/weaving segment .... 25
Figure 24 – Expanded link-node structure to evaluate the off-ramp segment .............................. 26
Figure 25 – Data collection framework for queue spillback into urban streets
(signalized intersection) ............................................................................................................. 27
Figure 26 – I-285 NB @ South Cobb Dr. and affected movements by on-ramp queue spillback:
(a) NB-Th/R and (b) SB-L ......................................................................................................... 30
Figure 27 – I-285W SB @ Cobb Pwky Dr. and affected movements by on-ramp
queue spillback: (a) NB-L and (b) SB-Th/R .............................................................................. 31
Figure 28 – I-285W NB @Cobb Pkwy Dr. with NB-R movement affected by
on-ramp queue spillback ............................................................................................................ 31
Figure 29 – Friars Rd. @ I-15 NB with WB-R movement affected by on-ramp
queue spillback........................................................................................................................... 32
Figure 30 – Partial blockage of northbound through movement by vehicles
trapped inside the intersection box ............................................................................................ 33
Figure 31 – Procedure for identifying spillback occurrence at an on-ramp ................................. 35
-v-

Figure 32 – Comparison of lane flow distribution on two different 2-lane segments:

(a) Minneapolis, MN and (b) Salt Lake City, UT ...................................................................... 37
Figure 33 – Comparison of lane flow distribution on two different 3-lane
segments: (a) Tampa, FL and (b) St. Paul, MN ......................................................................... 38
Figure 34 – Comparison of lane flow distribution on two different 4-lane
segments: (a) Salt Lake City, UT and (b) Tampa, FL ............................................................... 39
Figure 35 – Field data and predicted speed-flow curve for (a) lane 1 and
(b) lane 2 (CA-1 NB – Santa Cruz, CA) .................................................................................... 41
Figure 36 – Origins and destinations for a sample network (Gainesville, FL) ............................. 42
- vi -

Summary
The procedures detailed in the 6th Edition of the Highway Capacity Manual (HCM) estimate capacity
and several operational measures, including those determining Level of Service (LOS), for freeway
facilities as well as surface streets. However, the HCM lacks a methodology for evaluating the operational
performance of networks involving freeway-urban street interactions. The current HCM methods focus on
operational analysis of individual segments or sections, which may not correspond to the traveler’s
experience of an entire trip which traverses multiple different types of facilities. These methods do not
consider cases in which spillback occurs from one type of facility to another, or across an entire origin-
destination route, which is necessary for evaluation of network performance.
The objective of this research project is to develop materials for the HCM in order to modify the
freeway analysis methods and the urban street methods so that the effects of operations from one facility to
the other can be evaluated. This report summarizes the entire research effort and provides the proposed new
HCM Chapter (Chapter 38) in Appendix A- Chapter 38 - System Analysis. The new methods produced can
be used to evaluate operations along networks that include both freeways and urban streets. The methods
can also evaluate the impact of spillback into freeways and into urban streets from downstream facilities.
In summary, the following were accomplished:
Selection of appropriate performance measures: Travel time was selected as the performance measure
to evaluate highway systems. Travel time measures are already used in the HCM to evaluate urban streets
facilities. For freeway facilities, we developed additional models and methods to evaluate freeway
performance by lane, as spillback affects each lane of the freeway differently. In addition, a trip-based
performance measurement framework was developed to provide travel time estimates for given O-Ds
within a highway network. O-D measures reflect traveler experience and are well aligned with recently
available data collection methods which track individual trips. These new measures are intended to
complement segment-based measures provided in other HCM chapters.
Evaluation of queue spillback into freeways: Queue spillback into the freeway occurs due to insufficient
capacity in at least one element of the off-ramp: either the ramp proper, or the downstream ramp terminal.
The blockage of one or more freeway lanes adversely affects performance, and the extent of the blockage
effects depend on various factors including the design of the facility, the cause of the blockage, and the
length of the queue. Video and detector data from several locations were obtained, and used along with
microsimulation to develop the methodological framework. The methodology developed is based on the
calculation of demand and capacity at the downstream ramp terminal using the respective Interrupted Flow
methods. It expands the Oversaturated Segment Evaluation for freeway facilities (HCM Chapter 25) and
accounts for spillback and its effects by lane along the freeway mainline.
Evaluation of queue spillback into urban streets: Queue spillback into urban streets occurs due to
insufficient discharge capacity into the freeway merge. It may occur due to oversaturated conditions at the
merge segment or the presence of ramp metering. Video and detector data from several locations were
collected to understand how intersections are affected by on-ramp queue spillback. Microsimulation was
used to complement the evaluation of signalized ramp terminals and to analyze systems with unsignalized
intersections. The proposed methodology integrates the Interrupted Flow methodologies with the Freeway
Facilities procedure to account for constraints of the on-ramp capacity. Several adjustments were developed
to estimate the impacts of queue spillback from an on-ramp into upstream signalized and unsignalized
intersections, including roundabouts.
-1-

Lane by lane performance measures for freeways: Freeway speeds can vary widely depending on the
lane used, and each O-D is likely to use a specific lane or set of lanes along each segment. Spillback affects
each freeway lane differently, and its effects depend on the site design and the length of the queue. This
project developed models that estimate speeds and flows by lane. Detector data were collected from a
variety of locations around the US, and analytical models were developed to predict the lane flow
distribution and lane speed. These models considered a variety of factors including v/c ratio, presence of
nearby ramps, heavy vehicle percent, and grade. Regression models built from the field data demonstrated
that FFS and capacity values for each lane can be obtained as a percentage of the segment average with
satisfactory results.
Development of an O-D analysis framework: A new methodology was developed to estimate travel
times by O-D within a highway system. This methodology combines the tools of several HCM chapters
within the Uninterrupted Flow and Interrupted Flow volumes. It also builds on the research previously
described to evaluate queue spillback and system effects.
The limitations of the methods include the following:
Queue spillback into freeways:

• Overlapping bottlenecks cannot be addressed as they require iterative processes;
• Managed lanes are not addressed by the methodology.
Queue spillback into urban streets:

• Roundabouts with two lanes cannot be addressed;
• The procedures do not specifically address alternative intersection designs, such as SPUI, DDI;
however, the analyst may estimate capacities and queue lengths associated with a variety of
facilities and implement the methods described here for a variety of configurations;
• Indirect impacts of queue spillback, such as turn bay overflow are not addressed by this
methodology;
• The procedure relies on accurate estimates of the capacity of the merge obtained using the
Oversaturated Segment Evaluation (HCM Chapter 25); however the estimation of this capacity
is listed as a limitation of Chapter 25.
Freeway lane by lane analysis:

• Flow distribution models were not developed for segments with 5+ lanes. For these cases, using
equal distributions of flows and speeds are recommended.
System Analysis
• HCM Travel time reliability methodologies for Freeways (Chapter 11) and Urban Streets
(Chapter 17) have significant differences in their procedures. Therefore this project made no
attempt to incorporate reliability analysis in the new procedures.
In the future, it would be useful to develop a LOS framework for the travel time performance measures
yielded by this methodology to evaluate highway systems. Similar to other performance measures used in
the HCM, communicating the values of performance measures to a lay audience may be challenging, while
LOS may be a more useful construct.
-2-

1. Introduction
Background
The procedures detailed in the 6th Edition of the Highway Capacity Manual (HCM) estimate capacity
and several operational measures, including those determining Level of Service (LOS), for freeway
facilities as well as surface streets. However, the HCM lacks a methodology for evaluating the operational
performance of networks involving freeway-urban street interactions. The current HCM methods focus on
operational analysis of individual segments or sections, which may not correspond to the traveler’s
experience of an entire trip which traverses multiple different types of facilities. These methods do not
consider cases in which spillback occurs from one type of facility to another, or across an entire origin-
destination route, which is necessary for evaluation of network performance. Currently, the procedure for
evaluating Signalized Intersections (HCM 2016 Chapters 19 and 31) predicts the average expected queue
length at an approach given various combinations of geometric- or traffic-related inputs. Similarly, the
Freeway Facilities procedure (HCM 2016 Chapters 10 and 25) estimates the maximum expected queue
length at an on-ramp in the case of oversaturated conditions on the freeway mainline. However, the effects
of these queues as they propagate upstream – onto a freeway mainline or a surface street intersection – are
not considered.
Research Objectives and Report Organization

The objective of this research project is to develop materials for the HCM in order to modify the freeway
analysis methods and the urban street methods so that the effects of operations from one facility to the other
can be evaluated. This report summarizes the entire research effort and provides the proposed new HCM
Chapter (Chapter 38) in Appendix A - Chapter 38 - System Analysis.
Section 2 of this report provides the literature review conducted at the beginning of the project, while
Section 3 summarizes the results of a critical review of existing HCM methods. Section 4 discusses the
proposed performance measurement framework for the systems-based approach. Section 5 provides an
overview of the methodology developed for evaluating queue spillback from off-ramps into freeways,
including a review of the relevant data collection. Similarly, Section 6 discusses the data collection and
procedures to evaluate queue spillback into urban streets. Section 7 presents the models developed to
estimate lane-by-lane speeds and flows for freeway segments. Section 8 summarizes the methodology
developed to estimate travel times for origin-destination pairs within freeway-urban streets networks. These
travel times are estimated based on the research described in Sections 5, 6 and 7. Section 9 discusses the
computational software engine which replicates the methods developed. Section 10 provides the project’s
conclusions and recommendations. Several appendices are also provided which detail various aspects of
the research:
Appendix A - Chapter 38 - System Analysis (This appendix provides the new HCM Chapter 38, which is
recommended for inclusion in the HCM 6th Edition.)
Appendix B - Off-ramp Queue Spillback Check
Appendix C - Off-ramp Queue Spillback Analysis
Appendix D - On-ramp Queue Spillback Check
Appendix E - On-Ramp Queue Spillback Analysis
Appendix F – Freeway Facilities Lane-by-lane Analysis
Appendix G - Glossary
-3-

2. Literature Review
A review of the literature regarding operational effects of freeway-urban street interactions yielded a
limited number of publications. Although much of the published research on this topic does not directly
address performance measures in a manner consistent with HCM procedures, the concepts and framework
presented in the research are useful in developing the necessary procedural adjustments. For example,
previous research has quantified the delay incurred to freeway mainline vehicles as a result of off-ramp
queue spillback, but the HCM Freeway Facilities procedure does not estimate delay explicitly. Rather,
average travel speed is estimated, and the difference between that and the freeway’s free-flow speed can be
used to estimate delay.
This section first presents an overview of the literature found related to performance measures for
networks, followed by an overview related to the effects of oversaturation on freeway performance. The
last subsection discusses literature related to the effects of oversaturation on surface street performance.
Performance Measurement
A literature review on recent developments regarding performance measures yielded a range of different
approaches for the subject. Dong et al. (2016) propose a travel-time reliability prediction framework for
evaluating service quality on urban streets. According to the authors, “from a driver’s perspective, travel
time and its reliability are considered more intuitive measures of service quality than the levels of service
defined in the Transportation Research Board’s 2010 Highway Capacity Manual”. The proposed
framework, which takes into consideration the weather conditions on travel-time classification, was tested
on a freeway network in Iowa using probe vehicle data (it was also compared to VISSIM simulations with
similar results) with good results in representing field conditions for small networks. The work did not
consider lane-changing behavior and the percent of heavy vehicles in the analysis.
Friedrich (2016) presented an approach for evaluating entire multimodal journeys based on O-D points,
based on the German Guideline for Integrated Network Planning (RIN, 2008). In this framework typical
performance indicators include direct speed (direct distance over time, where direct distance is defined as
the straight-line distance) trip time ratio of public transport/car, and number of transfers. For each one of
the performance indicators, the evaluation outputs are presented as LOS ranges from A to F, similar to the
HCM, as the author states that results in this format are very easy to understand for decision makers.
Arun et al. (2016) present an operational analysis approach focused on the variability of driver
characteristics. The authors indicate that they had difficulties in implementing HCM methods in India due
to the diverse driver behavior and characteristics. According to the authors, the simple use of adjustment
factors is not adequate for representing the heterogeneity in Indian traffic conditions. Therefore, they
explored the possibility of adopting different sets of performance measures to better suit different locations,
and highlighted the strengths and limitations of each one.
In summary, the research team did not find any research directly pertaining to the HCM and systems
analysis. Most research on highway system performance prior to the start of this project had addressed
multimodal trips (for which performance measures are needed to address specific questions such as transit
to private automobile trip times), and performance measurement under varying driver populations.
Spillback Effects from Urban Streets to Freeways

A review of the literature regarding operational effects of freeway-urban street interactions yielded a
limited number of publications. Although much of the research published prior to this project on this topic
does not directly address performance measures in a manner consistent with HCM procedures, the concepts
and framework presented were useful in developing the necessary procedural adjustments. For example,
previous research quantified the delay incurred to freeway mainline vehicles as a result of off-ramp queue
-4-

spillback, but the HCM Freeway Facilities procedure does not account for this delay caused by queue
spillback into the mainline. Rather, average travel speed is estimated and the difference between that and
the freeway’s free-flow speed can be used to estimate delay.
In a study performed to compare field observations against this theory, Daganzo and Munoz (2000)
confirmed that off-ramp queues spilling over onto the freeway mainline indeed cause a significant reduction
in discharge flows downstream of the exit. During the queued steady state, an average discharge rate of
4,520 vehicles per hour on a three-lane freeway mainline (a 37.2% reduction from the HCM “base” capacity
of 7,200 vehicles per hour, according to the Basic Freeway Segments procedure) was observed. Note that
this rate should be compared to the “discharge capacity” of a mainline section, and the current version of
the HCM uses a generic capacity value, which does not consider the two-capacity phenomenon.
The proportion of exiting vehicles on the freeway also proved to have a significant effect on capacity: on
average, discharge rates increased from 4,520 to 5,720 vehicles per hour (26.5% increase) when the
proportion of exiting vehicles decreased from 29% to 24%, even though the actual number of exiting
vehicles remained constant. In a separate observation, vehicles were found to transition from free-flow
speeds to “queueing speeds” approximately 1 kilometer, or 3,280 feet, upstream of the queue. It was also
observed that drivers tend to adopt larger headway spacings over time “en masse”, and the authors indicated
that this happened likely because once the length and severity of the queue was collectively realized, driver
aggression as a whole subsided.
In a separate paper based on the data obtained in the previously described study, Munoz & Daganzo
(2002) focused instead on the “behavior” of the queue. It was found that the variation in speeds across
mainline lanes is greatest closest to the diverge point, whereas occupancy detectors positioned further
upstream indicated less variation. Specifically, lanes closer to the off-ramp queue were more affected in
terms of speed reduction, whereas the leftmost lane(s) showed very little difference between the presence
of a queue and free-flow conditions. Additionally, non-exiting vehicles in the vicinity of the off-ramp queue
“traveled more cautiously, with slightly wider but predictable spacings … and [that] more lane changes can
be expected.” In terms of capacity reduction, an average discharge flow of 1,500 veh/h/ln was recorded
immediately beyond the diverge point – 25% lower than that which this particular freeway’s geometric
conditions (as estimated by the authors) could potentially accommodate.
A similar study by Cassidy et al (2002) found that, in general, longer exit queues from the over-saturated
off-ramp were accompanied by lower discharge rates for the non-exiting vehicles, although no exact
measure of correlation between the two was established. The authors also note that exiting drivers
sometimes obstructed non-exiting vehicles by attempting to force their way into the queue rather than wait
for their turn. The authors do not discuss the possible correlation between queue length and forced queue
entries. The presence of a queue also affected the non-exiting vehicles’ average speed: upon the onset of
queueing at an off-ramp, non-exiting vehicles reduced their speed across all lanes, reaching speeds as low
as 25 kilometers per hour (15.5 miles per hour) before returning to free-flow speed downstream of the
diverge point.
Traffic operations during an incident may be similar to operations when a queue is present and thus we
briefly review here studies related to the capacity and traffic operational quality during incidents. In a
comprehensive comparison between various incident-related studies in the literature, Lu & Elefteriadou
(2013) present sets of capacity “adjustment factors” based on various conditions. In a regression analysis
developed based on past studies, capacity additions (denoted by a “plus” sign) and reductions (denoted by
a “minus” sign) were found to be dependent on congestion occurrence (+320 veh/h), number of lanes
(+1,213 veh/h/ln) and the number of lanes/shoulder affected (–1,948 veh/h, –1,116 veh/h and –182 veh/h
for shoulder, 1 lane and 2 lanes blocked, respectively). A similar regression structure could conceivably be
developed for queueing-related capacity reduction, albeit one that incorporates the probability of further
lane blockage in consideration of the queue length variability as well as driver variability (and particularly
the probability of forced lane changes into the queue.)
-5-

Based on the review of the literature, we can conclude that estimating operational measures in the case
of spillback from an off-ramp analytically is challenging, as it is very difficult to anticipate the wide variety
of driver actions. The following trends and observations documented in previous research are used in this
research to develop the framework of the proposed methodologies:
• Discharge flows along the mainline are affected by the presence of an off-ramp queue, with one
study observing 4,520 vehicles per hour on a three-lane freeway mainline (≈ 1,500 veh/h/ln.)
• Discharge rates along the mainline increase with decreasing off-ramp flows; they were also found
to increase with decreasing queue lengths, which are correlated with off-ramp demands.
• Rightmost lanes are more affected in terms of speed reduction, whereas the leftmost lane(s) show
very little difference between the presence of a queue and free-flow conditions.
• Exiting drivers sometimes obstruct through lanes by attempting to force their way into the queue.
However, research has not established any quantitative measures for the probability of such
blockage and its potential association with the off-ramp queue length.
• The presence of a queue at the off-ramp reduces the mainline vehicles’ speed with values
observed as low as 25 kilometers per hour (15.5 mi/h)
If the off-ramp queue blocks the right-most lane and is relatively short, non-exiting mainline drivers may
be willing to remain in the queued lane – albeit at a significantly reduced travel speed – and accept a small
amount of delay.
An FHWA-sponsored study (Saxton DTFH61-12-D-00020, Task Order 15: Highway Capacity Manual
(HCM) Systems Analysis Methodology) conducted by UF (PI: L. Elefteriadou) developed preliminary
procedures for conducting network analysis. However, the scope of that project did not include data
collection. The report proposed a series of modifications to the HCM in order to address spillback
conditions, and the research team used some of the findings and recommendations from that report in
crafting the data collection effort for this project.
Spillback Effects from Freeways to Urban Streets

Limited research has been reported to address freeway spillback onto signalized intersections. The HCM
Merge/Diverge Segments methodology determines whether volume exceeds capacity at any critical points
along the segment, and estimates the maximum expected queue along each on-ramp. However, the method
does not consider the effects the resultant queue may have on the upstream surface street. The HCM Ramp
Terminals and Alternative Intersections procedure includes an adjustment to consider spillback from the
downstream intersection to the upstream in the form of additional lost time. This lost time is estimated for
each upstream movement as a function of the downstream queue length and storage availability. A similar
logic can be applied in the case of spillback from the on-ramp to a local signalized intersection, as it results
in additional lost time for some/all the signal phases that serve traffic movements destined for the on-ramp.
Tian et al (2004) analyzed the effects of ramp metering spillback onto a diamond interchange using the
simulator DRIVE. Capacity reduction and delay increase were found upstream from the ramp meters due
to discharging flow reductions resulting from queue spillback and intersection blockage. The authors
estimated the delay incurred by the affected movements with a theoretical plot of demand over time.
For freeways without ramp metering, the queue discharge rate depends on freeway merge operations.
While arrival rates at the back of the on-ramp queue are an input to HCM procedures, departure rates into
the mainline during congested conditions are currently not available, and no guidance was found in the
literature to provide such estimates. This is a critical aspect of evaluating spillback conditions at a merge
ramp, as the discharge rate of the on-ramp traffic onto the freeway is a key parameter to calculate the queue
length along the ramp over time.
-6-

In conclusion, there are tools available to estimate the lost time incurred at the upstream intersections as
a function of a downstream queue length and storage availability. Still, extensive field observations are
necessary to document discharge rates at congested on-ramps and based on these estimate the resultant
queue length along the on-ramp.
-7-

3. Critical Review of the HCM
This section presents a critical review of the methods in the Highway Capacity Manual 6th Edition,
highlighting strengths and identifying weaknesses related to the evaluation of trips using freeways and
surface streets.
Overview of Performance Measures and Service Measures for HCM Analyses

The HCM uses the service measures shown in Figure 1 for each type of facility. As shown, the HCM
also provides for each facility a systems performance measure that can be converted to travel time. An
HCM procedure that includes freeways, highways, and urban streets simultaneously needs to have a
common set of performance measures, and ultimately, a common service measure. Other performance
measures unique to each facility type may be useful for a variety of purposes, but in order to consider all
facilities as an integrated system, a common and consistently used measure is essential.
Source: Highway Capacity Manual 6th edition - Exhibit 2-2

Figure 1 – HCM service measures by system element and mode
A detailed discussion on performance measures and the proposed trip-based evaluation framework is
presented in Section 4 – Discussion on Performance Measures.
Freeway Facilities
This subsection presents and discusses specific issues related to HCM freeway facilities analysis that
pertain to systems analysis.
Performance measurement: Freeway analysis is based on tools that estimate the operational
performance of each type of segment. The freeway systems analysis method evaluates operations in time
and space considering, to some degree, interactions (queue effects) between consecutive segments.
Operational performance is determined based on density and speed along each segment. In the case of
-8-

ramps, performance measures are estimated separately for the influence area (consisting of the two
rightmost lanes, and for a length of 1,500 ft.) and the remaining leftmost lanes. Based on these methods,
one can derive travel time for each segment and stitch together the travel time for the entire facility.
However, the quality of a particular trip from an origin to a destination cannot be obtained, because the
method does not provide operational performance by lane. In the field, speed can vary widely depending
on the lane used, and each origin-destination (O-D) is likely to use a specific lane or set of lanes along each
segment. For example, travelers exiting at a congested off-ramp will experience a much different travel
time than those using the left most lanes of the same segment. Currently, LOS for the facility is estimated
as a function of the LOS for each segment, and does not consider the quality of the trip from a traveler’s
perspective. However, travelers experience travel time over the entire system, as well as based on their O-
D. A performance measurement scheme for the entire system should also consider the origins and
destinations of the travelers within each segment.
Furthermore, five of the six LOS ranges exist where speeds are relatively high (above approximately 50
mi/h) and only one LOS range is used to define the congested regime, which is of the highest interest in
large urbanized areas. Many congestion management techniques will improve congestion (e.g., delay) but
the facility will still be classified as LOS F under the current framework.
Spillback from a downstream facility: The HCM addresses queue spillback only when it is fully
contained within the boundaries of a freeway facility. Spillback onto the freeway may occur either due to
inadequate capacity of the ramp proper, or due to inadequate capacity at the ramp terminal (typically the
signal at the downstream interchange). The capacity of the ramp proper is defined as the off-ramp’s
maximum allowable hourly flow rate based on its geometric characteristics (number of lanes, free-flow
speed, etc.). The capacity of the ramp terminal is defined as the capacity of the signalized or unsignalized
approach to the surface street. The current procedures in HCM provide guidance on estimating queue
storage ratio on ramp terminals, but do not directly address situations when ramps have queue-to-storage
ratio > 1.0 (LOS F at diverge ramps).
Influence area for merge and diverge areas: Currently, the HCM methodology for merge and diverge
areas focuses on predicting performance within a 1,500 ft. influence area and for the two rightmost lanes.
Figure 2 provides a schematic of the diverge influence area, according to the HCM. When spillback occurs,
it is likely that queue length extends upstream beyond 1,500 ft. Thus, the influence area of the junction may
be significantly longer. Also, the influence area may vary by time period depending on the demand-to-
capacity ratio and its variability. Lastly, the effects of spillback may affect additional lanes, as through
vehicles attempt to avoid the spillback and they increasingly use the leftmost lanes to maintain their speed.
The current freeway systems analysis framework, which uses a constant area (longitudinal distance and
cross section) to define this influence area, must be revised to consider spillback effects.
Source: Highway Capacity Manual 6th Ed. - Exhibit 14-7

Figure 2 – Schematic of a diverge influence area (HCM)
-9-

Impacts of spillback on weaving segments: Similar considerations to those described above are also
relevant for weaving segments. Along weaves, the on-ramp that is part of the weave may be affected in
different ways based on whether the spillback reaches its gore point or not. The area available to the two
weaving traffic streams would be reduced as a function of spillback. When longer queues prevail, the
upstream on-ramp may be entirely blocked, and it is possible that in this case the on-ramp and off-ramp
function independently, as there is no space available for weaving maneuvers.
Capacity constraints and speed reduction due to spillback: Spillback along the mainline results in
blockage of one or more lanes. Thus, capacity is reduced during such conditions, and the capacity reduction
depends on the frequency and duration of lane blockage. Also, lanes adjacent to those blocked are likely to
have reduced operating speeds. Those effects and their impact on the overall capacity and quality of service
must be addressed.
Ramp throughput during congested conditions: In order to consider the effects of an on-ramp queue to
upstream surface streets, it is necessary to estimate the queue length as a function of demand and capacity.
However, when the freeway mainline is congested, it is not clear what the capacity of the ramp is. In other
words, the HCM does not provide the actual relative contributions of the ramp demand vs. the mainline
demand at the merge during congested conditions; it assumes that the merge operates as a “zipper”, with
equal contributions from the shoulder lane and the on-ramp. However, the resulting ramp flow may be a
function of geometry, the extent and duration of congestion on the mainline, or prevailing driver behavior
in the region. The ramp capacity may be higher for weaving segments with lower freeway to off-ramp
demands and a longer weaving length. Estimating this discharge rate is necessary in order to estimate the
resulting queue length along the on-ramp. In cases where ramp metering is present, the discharge rate can
be determined and used to obtain the mainline input flow as defined by the HCM for oversaturated freeway
segments in Chapter 25.
Spillback effects along the mainline: Revised analyses should also consider the effects of spillback to
upstream segments, including basic freeway segments. For example, current procedures determine whether
the subject diverge ramp operates as an isolated ramp, considering the respective freeway and ramp
demands. These procedures should be revised to consider that the area of influence may vary as a function
of queue length and other factors related to spillback (for example the number of lanes blocked and their
respective frequency). Additionally, the lanes of the upstream segments may be differently affected,
depending on the spillback queue length.
Urban Streets
This subsection presents and discusses specific issues related to HCM urban streets analysis that pertain
to systems analysis.
Performance measurement. The urban streets methodology considers a variety of different facilities,
including street segments, signalized intersections, interchange ramps terminals (IRT), two-way stop-
controlled intersections (TWSC), all-way stop-controlled intersections (AWSC) and roundabouts. Each one
of these facilities have an associated MOE; intersections use control delay, while segments use travel speed.
Thus, development of a performance measurement framework for this group of facilities is easier, as these
existing measures can be converted to travel time.
Spillback from a downstream facility onto a signalized IRT. The connection between freeways and
urban streets is typically at an IRT. The HCM does not currently address spillback from freeways into
IRTs, however, the IRT methodology does address spillback from one signalized intersection to the other.
- 10 -

The procedure includes an adjustment to consider spillback from the downstream intersection to the
upstream in the form of additional lost time. This lost time is estimated for each upstream movement as a
function of the downstream queue length and storage availability. Similarly, the HCM Urban Streets
methodology provides an adjustment to the saturation flow rate to account for spillback effects. It is not
clear whether one approach may be preferable than the other. However, we recommend that the HCM
provides a consistent approach for addressing spillback onto signalized intersections and interchanges,
whether the queue is originating from a downstream intersection or from a freeway on-ramp.
Spillback from a downstream facility onto a roundabout IRT. Roundabouts are especially sensitive to
queue spillback, since it can result in complete gridlock for all movements. The current roundabouts
procedure does not evaluate roundabouts considering spillback.
Evaluation of actuated control for an intersection/interchange with spillback. The current signalized
methodology analysis framework considers both pre-timed and actuated control. In the case of pre-timed
control, signal control is an input, and the effective green can be adjusted to account for spillback. However,
in the case of actuated control, the signal phase duration is variable. This creates the following issues when
spillback occurs: a) the phase duration estimation would be impacted and thus the methodology needs to
be adjusted accordingly; and b) actuated control results in variable effective greens and thus variable
arrivals to the downstream ramp. These variable arrivals would result in variable queues at the ramp, which
will in turn affect the phase duration at the signal. This creates an iterative process which an HCM-type
analysis cannot address. This research project uses suitable assumptions and simplifications to provide a
reasonable framework for systems analysis, and uses equivalent pre-timed control to estimate phase
durations.
Queue length at the ramp receiving traffic from an intersection/interchange. Any type of queueing
analysis depends on the arrival patterns and the service patterns. In the case of a ramp junction receiving
traffic from an upstream intersection, the queue is calculated as a function of: a) the arrival patterns
upstream of the ramp - these are a function of the type of control, as well as the arrivals from each incoming
traffic stream; b) the departure rate at the ramp into the mainline - this is equal to the arrivals when
conditions are undersaturated. However, for oversaturated conditions, it is not clear what the discharge rate
is, and how it varies within an analysis period.
- 11 -

4. Performance Measures
This project develops trip-based (or O-D based) travel time measures in addition to the traditional facility-
based measures used in the HCM. Performance measures that relate to the trips taken by travelers are
considered the best approach, for the following reasons:
• Trips relate more directly to the traveler experience – they are how travelers actually experience
the system. Facility- and segment-based measures are still useful in this context because they
help practitioners identify and treat specific problems, such as bottlenecks.
• Each O-D within a freeway and urban street system uses a specific lane or set of lanes. Under
congested conditions, each lane across the facility may be operating very differently, and thus
evaluating the performance of the O-D would take into account the specific lane usage for those
trips.
• Measuring performance at the trip level is much more revealing for advanced operations
strategies, such as Active Traffic and Demand Management (ATDM) and Integrated Corridor
Management (ICM). Many components of these strategies seek to influence demand and to
balance demand with available capacity. Understanding what effect strategies have on trips is
important for selecting and modifying these strategies.
• Moving to trip-based measures is a logical step in the evolution of the HCM. The discipline of
performance measurement is moving in the direction of trip-based measures. As additional data
become available over the next several years to track the movement of individuals (hand-held
devices) and vehicles (connected vehicles, and eventually, automated vehicles), development of
trip-based measures from direct measurements will be enabled. Currently, it is possible to derive
trip-based measures synthetically, but when direct measurements become available, we expect a
rapid increase in the interest for trip-based measures.
• Trip-based measures are the basis for measuring accessibility. A logical extension of trip-based
measures, which are based on travel between specific origins and destinations, is the
measurement of accessibility. Accessibility is defined by two components: 1) the presence of
opportunities; and 2) the ease with which those opportunities can be obtained or “reached.”
Accessibility can be improved by improving the movement between opportunities or by moving
opportunities closer to travelers. Because it considers not only the performance of trips on the
system but also how trips interact with the entire built environment, accessibility is a key
indicator of the quality of life for a transportation agency’s customers.
Figure 3 shows the strategy behind selecting performance measures for the project. Both facility and trip
measures are recommended. Trip-based travel time measures are the most direct indicators of the traveler
experience but facility-based travel time measures also are useful for analysts to understand since many
improvement strategies are facility oriented. Other facility-based measures not defined in terms of travel
time are also recommended. These measures describe how the system is performing and are useful for
diagnosing problems. All three types of measures are needed to provide a complete picture of performance.
- 12 -

Type of Measures Key Features
• Traveler Focus
Trip-Based Measures
• Multiple Facilities
• Multiple Modes
Travel Time • Precursor to Accessibility
Outcome Measures
• Individual Facilities
Facility-Based Measures
• Bottleneck/Problem Identification
• Individual Facilities
Facility-Based Output Measures
• Vehicle-Oriented
• Non-travel time measures
• Help to Explain Outcomes
Segment d/c
Lane-to-Lane Speed Variability
VMT/PMT
Queue Statistics
Figure 3 – Recommended performance measure framework for different evaluation purposes
- 13 -

5. Queue Spillback into Freeways
Queue spillback into freeway facilities occurs due to insufficient capacity in at least one element of the
off-ramp, namely the ramp proper or the downstream ramp terminal. The impact of the spillback on the
freeway mainline can be restricted to the exit area or can extend for miles, depending on a series of factors.
This section summarizes the data collection and analysis process for developing the methodology to
evaluate queue spillback into freeways. Field data and simulation were used to develop the procedure,
which is presented in Appendix B - Off-ramp Queue Spillback Check and Appendix C - Off-ramp – Queue
Spillback Analysis.
Data Collection
Data collection (Task 6) is a critical part in the development of analytical procedures to evaluate the
interactions between freeway and urban street facilities. The research team used a combination of field data
and simulation modeling in order to comprehensively evaluate a variety of designs and traffic conditions
that can be found throughout the U.S. The use of simulated data to complement field data was made
necessary for two important reasons:
1. The number of feasible traffic, control, and highway design characteristics available is extremely
high, making a pure field data collection approach unrealistic.
2. Simulation allows us to isolate the effects of a specific variable (for example, the length of the
acceleration lane) on traffic operations. Field data are subject to day-to-day noise in traffic
attributes (because of fluctuations in demand, weather, incidents, special events, etc.) that make it
difficult to isolate the effects of a single variable.
Even though microsimulation cannot and should not replace field data collection, it can very effectively
supplement field data. Properly calibrated simulation models can replicate driver behavior and
aggressiveness based on simple observations of gap acceptance, headway distributions, number of lane
changes per mile, etc.
This section describes the data collection for each of the three major components, including: data
requirements, dataset description, data reduction efforts, agencies contacted and application of
microsimulation.
Data Requirements
The process of identifying potential study locations started by identifying sites that regularly experience
spillback into freeways, and have instrumentation and data available that can be used by the research
team. Another key requirement for suitable study locations was that the off-ramp is the primary and only
freeway bottleneck to allow the observation of queue spillback effects in isolation. Any locations
experiencing overlapping bottlenecks at the diverge region were discarded from the process.
The data required for studying spillback into freeways is shown in Figure 4, and each of the components
is briefly discussed next.
- 14 -

Figure 4 – Data collection framework for queue spillback into freeway facilities
1. Video Cameras: video observations are the most critical data for the study of queue spillback, as
they provide information that cannot be accurately captured by loop detectors. Video recordings
can provide views of the off-ramp area so that the queues forming longitudinally and laterally due
to spillback along the freeway can be observed and measured. It also provides important insight
on driver behavior, lane changing activity, and forced merging.
2. Upstream Detectors: detectors are a critical source for speed and flow data. It is essential that
detectors are able to provide data on individual lanes and in raw format (minimal aggregation).
The available sources used for this project provide raw data aggregated in intervals between 20s
to 60s. Locations with multiple detectors upstream of the off-ramp were also preferred, as they
provide more comprehensive data to evaluate the changes in performance measures along the
freeway longitudinally.
3. Downstream Detectors: downstream detectors are not strictly required for the analysis, but are
useful to ensure that conditions downstream are undersaturated. Any sites where downstream
detectors showed oversaturated conditions were discarded.
4. Ramp Detectors: ramp detectors along the off-ramp can provide data to estimate the off-ramp
demand and capacity.
5. Geometry: geometric features such as number of lanes in the freeway and ramp, deceleration lane
length, lane width and others can be obtained using satellite tools such as Google Maps.
Agencies Contacted
The strict requirements for data collection to observe off-ramp queue spillback, as previously mentioned,
created a significant challenge. The research team contacted state Department of Transportation (DOT)
staff in each of the 50 states, obtaining a positive response from 21 states (Figure 5). From this sample, we
were able to identify study sites from five states that met all the required criteria: California, Georgia,
Virginia, Florida and Minnesota. The remaining 16 states that responded were able to identify locations
with queue spillback, but they did not meet the full data requirements previously stated, and therefore these
locations could not be used.
- 15 -

Figure 5 – Survey for off-ramp queue spillback study sites – outcome by state
Dataset Description
Several potential locations were selected for data collection, and only those that met all the criteria
previously described were kept in the final dataset. For the selected locations, detector data were extracted
from online repositories for each State DOT. Video recordings were extracted from online repositories or
recordings provided by DOT staff. Table 1 summarizes the data sources by state.
Table 1 – Data sources by State DOT – off-ramp queue spillback
State Detector Data Source Video Recordings Source

(1)
California Caltrans PeMS Caltrans CCTV Map (2)
Florida RITIS (3) Recording provided by agency staff
Virginia VDOT PeMS (4) RITIS
Georgia GDOT ATMS (5) GDOT ATMS
Minnesota MN Data Tools (6) Recording provided by agency staff
(1)http://pems.dot.ca.gov (4)https://vdot.iteris-pems.com
(2) cwwp2.dot.ca.gov (5) navigator-atms.dot.ga.gov
(3)http://ritis.org (6) http://data.dot.state.mn.us/datatools
Table 2 summarizes the final list of ten study locations, with a description of their key characteristics and
number of video observations. A video observation consists of one peak period recording, where the
development and discharge of queues can be observed, which typically lasts between 2-4 hours.
- 16 -

Table 2 – Summary of study locations – data collection – off-ramp queue spillback
Segment Type
Observations
Downstream
Peak Period
Directional
Off-Ramp
Terminal
Spillback
Regime
Ramp
Lanes
Video
lanes
LOCATION
Signalized
Miami/FL - I-95 SW 25th Rd. 3 Diverge 2 13 PM 4
Intersection
Freeway
Tampa/FL - I-275 NB to W Kennedy Blvd 4 Diverge 2 6 PM 4
Merge
Signalized
Norfolk/VA - I-64 WB to Northampton Blvd 4 Diverge 2 10 PM 3
Intersection
Centreville/VA - I-66 WB to SR-28 (Sully Signalized
4 Diverge 1 11 AM 3
Rd) Intersection
Signalized
Centreville/VA - I-66 EB to SR-28 (Sully Rd) 4 Diverge 1 11 AM 3
Intersection
Signalized
Minneapolis/MN - I-35W SB to 35th St. 4 Weaving 1 5 PM 3
Intersection
Freeway
Atlanta/GA - I-285 NB to I-20 5 Diverge 1 7 PM 3
Merge
Freeway
Miami/FL - I-75 SB to SR 826 5 Diverge 2 13 AM 4
Merge
Freeway
Atlanta/GA - I-285 NB to GA-141 5 Diverge 1 12 PM 3
Merge
Freeway
Sacramento/CA - SR-99 NB to SR-50 5 Weaving 2 5 AM 4
Merge
TOTAL 93
Schematics and sample screenshots of the study locations are presented in Figure 6 through Figure 15.
Source: Photo provided by the Florida Department of Source: Photo provided by the Florida Department of
Transportation Transportation
Figure 6 – Miami, FL – I-95 SB to SW 25th Rd. Figure 7 – Tampa, FL – I-275 NB to SR-60
- 17 -

Source: Photo provided by CATT Lab (Ritis.org) Source: Photo provided by CATT Lab (Ritis.org)
Figure 8 – Norfolk, VA – I-64 WB to Northampton Figure 9 – Centreville, VA – I-66 WB to SR-28
Blvd (Sully Rd)
Source: Photo provided by CATT Lab (Ritis.org) Source: Photo provided by the Minnesota Department of
Figure 10 – Centreville, VA – I-66 EB to SR-28 Transportation
(Sully Rd) Figure 11 – Minneapolis, MN – I-35W SB to 35th
St.
- 18 -

Source: Photo provided by the Georgia Department of Source: Photo provided by the Florida Department of
Figure 12 – Atlanta, GA – I-285 NB to I-20 Figure 13 – Miami, FL – I-75 SB to SR 826
Source: Photo provided by the Georgia Department of Source: Photo provided by the California Department of
Figure 14 – Atlanta, GA – I-285 NB to GA-141 Figure 15 – Sacramento, CA – SR-99 NB to SR-50
- 19 -

Data Reduction
Video observations were the most challenging part of the data reduction, as the process of obtaining the
recordings was very time-consuming. After the recordings were obtained from the respective agencies, the
research team performed a first screening at the videos for an initial validation, which included the
following conditions:
• Camera is able to show the queues in the diverge area as required for project purposes;
• No occurrence of incidents, disabled vehicles, lane closures or other factors that may affect the
daily dynamics of vehicular traffic;
• No overlapping bottlenecks – the off-ramp is the only source of congestion.
After this first screening, the next step was downloading detector raw data (speed and flow) from online
repositories for the periods captured in the video files. Then, any observations with the following issues
were also excluded from the dataset:
• Poor detector data health, as evaluated by the data repositories;

• Missing or null readings for long periods, making the data analysis unfeasible.
The valid observations remaining after the initial screenings make up the study dataset, previously
presented in Table 2. The next step in the data reduction was to measure the queue lengths from video
observations. Queue lengths were measured visually from video starting from the exit point by lane, as
illustrated in Figure 16. Vehicles queued on the adjacent lane were counted as part of the deceleration lane
queue, even though they are in a mainline lane. We chose this approach because the downstream end of
this queue is not always at the same location. Also, this approach makes the L2 queue measurements
consistent with the L1 queue, which starts from the end of the deceleration. Measurements were taken in
time intervals consistent with the detector aggregation times so queue lengths and flow/speed data can be
matched for further analyses. For example, if raw detector data from a given location are aggregated in 20-
second intervals, then queue lengths were measured every 20 seconds.
Figure 16 – Back-of-queue length measurement – off-ramp queue spillback
After the data reduction, queue lengths were matched with detector data to provide insights on the effects
of queue spillback in the freeway performance. Figure 17 provides a sample of data illustrating queue
spillback, where (a) shows the development of queues over time, while (b) shows the speed drops consistent
with the development of mainline queues. At this site, queues along lane 2 were longer than those in lane 1
due to demands at the downstream intersection. Speeds on lane 1 (S1) are lower than lane 4 (S4), consistent
with the occurrence of queue spillback on the right side of the freeway.
- 20 -

Figure 17 – Sample of data illustrating queue spillback: (a) queue length and (b) speeds by lane
Qualitative Observations
The videos obtained were used to observe operations during off-ramp queue spillback, in order to inform
the development of analytical models. These observations are discussed in the following paragraphs.
Unbalanced lane usage at off-ramp
For off-ramps with two lanes, it was observed that queues may not distribute evenly along the two lanes.
Drivers typically choose a position at the off-ramp based on their next movement at the downstream ramp
terminal. Therefore, if the downstream ramp terminal has one particular movement with excessive demand-
to-capacity ratio, queues are likely to develop along the lane connected to that specific movement, while
the other off-ramp lane remains underutilized. Figure 18 shows examples of unbalanced demand at the off-
ramp on (a) the right lane and (b) the left lane of a two-lane off-ramp.
- 21 -

Source: Photos provided by (a)CATT Lab (Ritis.org) and (b)Florida Department of Transportation
Figure 18 – Unbalanced lane usage at the off-ramp: (a) right lane and (b) left lane
Increasing operational impacts across lanes when queues are longer
When multiple detector stations are present upstream of the off-ramp, it is possible to compare the effects
of queue spillback along multiple locations during the exact same time. Field data show that in the area
close to the ramp exit, the effects of queue spillback are restricted to the blocked lanes, while the through
vehicles in the leftmost lanes are not affected. However, for locations further upstream, speed drops are
more homogenous and evenly spread across all lanes of the freeway. Figure 19 illustrates the impacts of
queue spillback at three locations upstream of an off-ramp bottleneck: (a) at the ramp influence area, (b)
1,800 ft. upstream of the exit and (c) 5,500 ft. upstream of the exit.
Source: Photos provided by the Florida Department of Transportation

Figure 19 – Effects of queue spillback across freeway lanes at three locations upstream of the exit
experiencing spillback (I-275 EB – Tampa, FL)
Number of blocked lanes is inherent to each location experiencing spillback
When there is queue spillback from an off-ramp, queues may block one or two lanes in the freeway
mainline (Figure 20). Video observations of queues show that at each site experiencing recurrent queue
spillback that extends beyond the deceleration lane, the number of blocked lanes does not change. In other
words, queue length does not affect whether the site experiences the conditions of Figure 20(a) or (b). The
condition shown in Figure 20(b) occurs more frequently in locations with more aggressive driver behavior.
- 22 -

When the segment is a lane-drop (rather than a diverge) the exiting traffic can access the off-ramp with
a single lane change. Therefore, drivers are more likely to wait until they are closer to the exit to change
lanes, blocking the adjacent through lane.
Figure 20 – Blockage of one (a) or two (b) mainline lanes due to off-ramp queue spillback
Simulated Sites
Given the complexity of obtaining field data to evaluate queue spillback, simulation was used to
complement the data collection. The selection of locations for simulation took into consideration the use of
pre-calibrated locations that were available to the research team. The simulated sites were used with
increasing input demands so that queue spillback into freeways would occur. Table 3 presents the list of
simulated locations for this study.
Table 3 – Summary of simulated locations – off-ramp queue spillback
Number of Number of
Downstream
Location freeway Segment type off-ramp
ramp terminal
lanes lanes
I-105 SB to Bellflower Blvd. 3 Diverge Signalized int. 1
I-105 NB to Bellflower Blvd. 4 Diverge Signalized int. 1
I-710 SB to Martin Luther King Blvd. 4 Diverge Signalized int. 2
I-105 WB to Garfield Ave. 4 Major Diverge Signalized int. 2
I-710 SB to I-105 5 Diverge Freeway merge 2
I-710 SB to Martin Luther King Blvd. 5 Weaving Signalized int. 2
Simulation models developed and calibrated with field data in AIMSUN were used to obtain simulated
data. The following assumptions were made for the simulated data:
Queue measurement: Queued vehicles in a freeway off-ramp are not completely stationary. During
queue spillback, exiting vehicles are typically moving at slow speeds. Additionally, vehicles are closely
spaced but not as close as vehicles stopped in an intersection. Queue lengths were measured visually from
video observations. However, quantitative criteria must be set to define freeway queue lengths in
microsimulation. Vehicles were considered in a queue if they meet the following criteria:
• Vehicle speeds are not greater than 5 mi/h
• Distance between vehicles is shorter than 40 ft.
Detectors: The greatest benefit of microsimulation is the ability to obtain a variety of performance
measures at any desired location of the simulated network. For field data, speed and flow readings were
- 23 -

available according to the position of detectors and were different for each study location. For the simulated
sites, detector stations were placed at three locations upstream of the exit: 1,500 ft, 4,000 ft and 8,000 ft.
Speeds and flows on a lane-by-lane basis were extracted in 20-second intervals, similarly to the lowest
resolution obtained from field data.
Forced merging: As queues extend further upstream of the ramp exit, drivers wishing to exit are more
likely to change lanes aggressively to join the back of the queue. Some vehicles may fail to join the back
of the queue and then attempt to find a gap to merge into the queue (forced merging). A microsimulation
model where drivers can perfectly anticipate a lane blockage ahead and always join the back of queue would
fail to replicate the field conditions of an off-ramp queue spillback. Therefore, for the simulation models, a
vehicle with an O-D that includes the off-ramp as a destination adjusts its position stochastically, which
allows a possibility that it may miss the back of the queue. If that happens, it attempts to find gaps in the
queue to perform a lane change, as illustrated in Figure 21.
Figure 21 – Example of a forced merging maneuver for a vehicle attempting to join the off-ramp
queue
Figure 22 provides an example of a simulated location where queue spillback occurs (I-105@Bellflower
Interchange). As shown, at the vicinity of the off-ramp the blockage occurs in the rightmost lane, with
negligible effects on the adjacent lanes. At sections further upstream, additional turbulence starts affecting
the performance of the other lanes in the freeway mainline. As shown, the simulation replicates the field
observations as expected.
Figure 22 – Micro-simulated off-ramp queue spillback (I-105@Bellflower Interchange – Los Angeles,

CA)
- 24 -

Queue Spillback Check
The first step to evaluate queue spillback into freeways is to assess whether it is expected to occur. The
detailed methodology for off-ramp spillback check is provided in Appendix B - Off-ramp Queue Spillback
Check.
The methodology evaluates two potential capacity bottlenecks in the off-ramp (Figure 23):
• Ramp proper: If the off-ramp demand is greater than the capacity of the ramp proper, spillback is
expected to occur.
• Downstream ramp terminal (intersection or a merge segment, in the case of a freeway-to-freeway
connector): if there is insufficient capacity at the ramp terminal, queues will develop along the off-
ramp. The procedure then compares the expected queue length and the available queue storage. If
the expected queue length is greater than the queue storage, spillback is expected to occur.
Figure 23 – Procedure for identifying spillback occurrence at an off-ramp/weaving segment
If queue spillback is not expected to occur, no adjustments are required for the current HCM methods. If
queue spillback is expected to occur, the procedure for evaluating queue spillback must be applied.
- 25 -

Evaluation of Queue Spillback Impacts

If queue spillback is expected to occur, the analyst must refer to the procedure for evaluation of impacts
of queue spillback, described under Appendix C - Off-Ramp Queue Spillback Analysis. The procedure takes
an approach similar to the Oversaturated Segment Evaluation (HCM Chapter 25), where the freeway facility
is analyzed in 15-second time steps instead of 15-minute time periods. The facility structure also changes
from segments to link-nodes for the analysis, and the proposed methodology expands the structure to
include the off-ramp (Figure 24).
Figure 24 – Expanded link-node structure to evaluate the off-ramp segment
- 26 -

6. Queue Spillback into Urban Streets
Queue spillback into an urban street occurs due to insufficient merging capacity in a freeway on-ramp,
and may have the following causes:
• Insufficient capacity at the freeway merge segment, per guidance provided on HCM Chapter 14
– Merge and Diverge Segments;
• Insufficient capacity of the on-ramp (HCM Exhibit 14-12);
• Active ramp metering at the on-ramp.
If insufficient capacity at the on-ramp occurs and its queue storage is also insufficient, queue spillback is
expected to occur at the upstream intersection. The project has developed procedures for evaluating
spillback into signalized intersections as well as unsignalized intersections (TWSC, AWSC and
roundabouts). This section presents the data collection process for queue spillback into urban streets. It
discusses field data and simulation, qualitative analysis, and the developed methodology to evaluate the
occurrence and impacts of queue spillback from an on-ramp.
Data Collection
The data collection process for queue spillback into urban streets is very similar to the method used for
off-ramp queue spillback. This section describes the details of data collection for spillback into urban
streets.
Data Requirements
The data collection needs for studying spillback into urban streets are shown in Figure 25. The figure
refers specifically to a signalized intersection as this type of facility has the most complex data collection
requirements. Unsignalized intersections have a similar set of data collection requirements, excluding the
signal controller configuration.
Figure 25 – Data collection framework for queue spillback into urban streets (signalized
intersection)
The data collection specifics for this portion of the project are as follows:
- 27 -

1. Mainline detectors: Data were obtained from loop detectors located upstream and downstream of
the merge area, providing lane-by-lane speed/volume/occupancy measurements, with resolution
of 1 minute or less.
2. Queue/ramp detectors: Data from detectors along the ramp were obtained to provide the queue
length and available queue storage along the ramp. If the ramp is metered, the metering rates were
also provided.
3. Signal controller configuration: For signalized intersections, the following signal timing
parameters were collected: pre-timed/actuated, phasing, cycle length, green/yellow/all red
intervals, and actuation parameters (min green, max green, passage time, etc.)
4. Video cameras: It was essential to have video at the interchange in order to view spillback
occurrence and the available queue storage along the ramp together with the approaching
movements’ discharge rates.
5. Automated traffic volume counts: If available, traffic volume counts were obtained to save time
and effort in data reduction.
Agencies Contacted
The same agencies that were contacted for off-ramp queue spillback data (Figure 5) were also contacted
for potential locations to observe on-ramp queue spillback. The data collection for urban street queue
spillback was significantly more challenging when compared to off-ramp queue spillback, for the following
reasons:
• A very limited number of DOTs have access to cameras located in urban streets. In most cases,
these cameras are operated by municipalities or counties, which frequently lacked the resources to
capture and record videos for our research purposes;
• Identifying locations with queue spillback into unsignalized intersections was extremely difficult.
The research team was able to identify a few locations where roundabout ramp terminals experience
on-ramp queue spillback, but in all cases these locations did not have cameras able to capture video.
For this reason, unsignalized intersections were analyzed using microsimulation.
Dataset Description
Table 4 summarizes the list of the four study locations where field data were collected, with a description
of their key characteristics and number of video observations. Each video observation typically lasts
between 1-3 hours, and it corresponds to one peak period recording, where the development and discharge
of queues can be observed.
- 28 -

Table 4 – Summary of study locations – field data collection – on-ramp queue spillback
Number of
Interchange Intersection # video
Location on-ramp
type type observations
lanes
Atlanta/GA - I-285W NB @
Diamond Signalized 2 9
South Cobb Dr NB
Atlanta/GA - I-285W SB to
Cobb Pkwy Dr.
Atlanta/GA - I-285W NB to
Cobb Pkwy Dr.
San Diego/CA - Friars Rd. @ I-
Parclo Signalized 2 10
15 NB
Schematics and sample screenshots of the study locations are presented next.
Atlanta, GA - I-285W NB@ South Cobb Dr.
This diamond interchange connects the I-285W NB freeway with the South Cobb Dr. arterial corridor.
During the AM peak period, the freeway facility experiences heavy congestion, while ramp metering at the
on-ramp limits the number of vehicles merging into the freeway. This causes queues to develop along the
on-ramp, which has insufficient storage capacity and causes spillback into the upstream signalized
intersection.
Two movements at the intersections are affected by the queue spillback. First, the SB-L movement Figure
26a) discharges directly into the on-ramp, which reaches its capacity before the end of green. When this
occurs, SB-L vehicles are held behind the stop bar as they are unable to proceed to the on-ramp. The second
affected movement is the NB-Th/R (Figure 26b), which receives green immediately after the SB-L. The
on-ramp is completely occupied by the queue from the previous movement, restricting the capacity of the
NB-R movement. The NB-Th movement is indirectly affected, as the last vehicles discharging from the
SB-L movement get trapped inside the box and partially block the movement of NB-Th vehicles at the
beginning of their green.
- 29 -

Source: Photo provided by the Georgia Department of Transportation and Google Maps
Figure 26 – I-285 NB @ South Cobb Dr. and affected movements by on-ramp queue spillback: (a)
NB-Th/R and (b) SB-L
Atlanta, GA - I-285W SB @ Cobb Pkwy Dr.
This diamond interchange connects the I-285W SB freeway with the Cobb Parkway Dr. arterial corridor.
During the PM peak period, the freeway facility experiences heavy congestion, and the number of vehicles
merging into the freeway is constrained by the capacity of the merge. The spillback pattern observed at this
intersection is similar to the previously described location (I-285W NB@ South Cobb Dr). The heavy
demand of the left-turn movement from the major street causes queue spillback at the on-ramp.
Consequently, the opposing through movement is also impacted by the residual left-turn vehicles which
block the intersection.
- 30 -

Source: Photos provided by the Georgia Department of Transportation and Google Maps
Figure 27 – I-285W SB @ Cobb Pwky Dr. and affected movements by on-ramp queue spillback: (a)
NB-L and (b) SB-Th/R
Atlanta, GA - I-285W NB @Cobb Pkwy Dr.
This intersection is also part of the diamond interchange connecting the I-285W freeway with the Cobb
Parkway Dr. arterial corridor, previously described. The northbound direction of the freeway also
experiences heavy congestion, causing queue spillback into the signalized intersection. The intersection
does not have a high demand for the SB-L movement, therefore it does not cause queue spillback. However,
the NB-R movement’s demand is often higher than the on-ramp capacity and causes spillback (Figure 28).
Source: Photos provided by the Georgia Department of Transportation and Google Maps
Figure 28 – I-285W NB @Cobb Pkwy Dr. with NB-R movement affected by on-ramp queue spillback
- 31 -

San Diego, CA - Friars Rd. @ I-15 NB
This partial cloverleaf interchange connects the I-15 NB freeway facility to the Friars Rd. arterial
corridor. The freeway experiences heavy congestion during the AM peak period. Active ramp metering
also limits the on-ramp throughput into the freeway. As a consequence, queue spillback occurs frequently
into this intersection.
The only movement affected at this intersection is the WB-R (Figure 29). This is a protected-only right-
turn movement with a high demand. At the onset of green, the on-ramp has considerable storage space, but
it is occupied quickly as the WBR discharges into the on-ramp. After several cycles of high demand,
vehicles are unable to discharge into the on-ramp during the green interval, causing queues to grow further
upstream.
Source: Photos provided by the City of San Diego and Google Maps
Figure 29 – Friars Rd. @ I-15 NB with WB-R movement affected by on-ramp queue spillback
Data Reduction
Similar to the data collection for off-ramps, the process of obtaining video observations was very
challenging. After the recordings were obtained from the respective agencies, the research team performed
a first screening of the videos for an initial evaluation, which considered the following:
• Camera shows the approaches at the intersection and at least part of the on-ramp;
- 32 -

• No occurrence of incidents, disabled vehicles, lane closures or other factors that may affect the
natural dynamics of vehicular traffic;
During the data reduction, the following were measured:
• Displayed green for each movement during each cycle;

• For movements discharging into the on-ramp: the observer noted whether the subject movement
experienced blockage during the given cycle. (Blockage was defined as the occurrence of queue
spillback during the green, negatively impacting its discharge rate.)
• For movements impacted by blockage of the intersection: the observer noted whether the through
movement was impacted by trapped vehicles blocking the intersection (similar to Figure 27b), for
any given cycle.
• For every movement, the headways of vehicles crossing the stop bar were recorded by lane. This
measurement procedure followed the guidelines provided by HCM Chapter 31 (Signalized
Intersections Supplemental) for Field Measurement of Saturation Flor Rate (Section 6).
Qualitative Observations
The videos obtained were used to observe operations during queue spillback, in order to inform the
development of analytical models. These observations are discussed in the following paragraphs.
Partial or total blockage of lanes for through movement
When queue spillback from an on-ramp reaches the upstream intersection, the movements that discharge
into the on-ramp are directly affected. However, field observations show that other movements that do not
discharge into the on-ramp can be affected by vehicles trapped inside the intersection box. The most
common case occurs at intersections with leading left turn operation, as illustrated in the example of Figure
30. The SB-L movement discharges into the on-ramp that has insufficient storage to accommodate the
demand. At the end of the SB-L movement, some vehicles are trapped inside the intersection box.
Therefore, at the onset of green for the NB-Th movement, only the leftmost lane (L1) is clear to discharge
at the saturation flow rate. The other lanes (L2, L3 and L4) cannot discharge immediately at the start of
green and have to wait until the on-ramp queue clears, resulting in additional lost time for these lanes.
Figure 30 – Partial blockage of northbound through movement by vehicles trapped inside the
intersection box
- 33 -

Simulated Sites
The use of microsimulation is especially important for on-ramp queue spillback, due to the difficulties
collecting data for unsignalized intersections. The same interchanges used for simulation of off-ramp queue
spillback were used to simulate on-ramp queue spillback. These models were calibrated with a signalized
intersection operation, and these were replaced with stop-controlled and roundabout intersections, as
illustrated in Table 5. The intersection volumes were also changed to ensure on-ramp queue spillback
occurs.
Table 5 – Summary of simulated locations – on-ramp queue spillback
Location Intersection type

Signalized
I-105 NB to Bellflower Blvd. Stop-controlled
Roundabout
I-105 SB to Bellflower Blvd. Signalized
Signalized
I-605 SB to Firestone Blvd Stop-controlled
Roundabout
I-605 NB to Firestone Blvd Signalized
Queue Spillback Check Procedure

The first step of the methodology evaluates whether queue spillback is expected to occur. The detailed
methodology for on-ramp spillback check is described in Appendix D - On-ramp Queue Spillback Check.
The proposed approach evaluates two potential capacity bottlenecks at the on-ramp (Figure 31):
• Merge capacity at the freeway;

• Active ramp metering, if present.
- 34 -

Figure 31 – Procedure for identifying spillback occurrence at an on-ramp
If spillback is detected, the queue length along the on-ramp is estimated and compared to the available
storage. If the queue length is greater than the available storage length, then spillback is expected to occur.
The analyst must then refer to the methodology described in Appendix E – On-Ramp Queue Spillback
Analysis to evaluate the impacts of spillback on the performance of the arterial intersection.
7. Lane-by-Lane Speed and Flow Estimation Methods for Freeways
Spillback into freeways results in uneven operations of mainline lanes, with some lanes blocked, while
some operating in undersaturated conditions. Also, the development of trip-based travel time measures
requires the evaluation of performance measures on individual lanes, as each O-D within a freeway system
uses a specific lane or set of lanes. Therefore, estimating travel time measures in a freeway facility requires
two key components: identifying the set of lanes selected for the trip, and estimating the operating speeds
on each of these lanes.
- 35 -

This section summarizes the framework developed for lane-by-lane analysis of freeway facilities. The
full methodology for evaluation of lane-by-lane performance measures in freeway facilities is described in
detail in Appendix F: Freeway Facilities – Lane-by-Lane Analysis.
Lane Selection Framework

Predicting lane selection by the traveler requires understanding of the dynamics of flow distribution
among freeway lanes under varying operational conditions. For a given freeway segment, the percent of
the total flow assigned to each lane is defined as the Lane Flow Ratio (LFR).
Preliminary Field Observations

This section briefly discusses and presents examples on the behavior of flow distribution along different
freeway segments as a function of the demand-to-capacity ratio (v/c).
For 2-lane freeway segments, Figure 32 demonstrates that flow distribution follows a “scissors” pattern,
with the flow highly concentrated in Lane 1 during free-flow conditions. As the demand for the segment
increases, flow gradually migrates to Lane 2. During near-capacity conditions, flow is higher in Lane 2.
Figure 32(a) illustrates lane flows along a freeway segment of I-694 (Minneapolis/MN). At near-capacity
conditions, lanes 1 and 2 carry 45% and 55% of total flow, respectively. Figure 32(b) provides lane flows
for a segment of SR-67 (Salt Lake City/UT), where lanes 1 and 2 carry 40% and 60% of total flow when
demand approaches capacity. As shown, the lane flow distribution varies between sites, and thus there are
additional parameters that need to be considered in estimating lane-by-lane flows.
- 36 -

Figure 32 – Comparison of lane flow distribution on two different 2-lane segments: (a) Minneapolis,
MN and (b) Salt Lake City, UT
Next, two different 3-lane freeway segments are compared (Figure 33). The lane distributions for these
are different than those for 2-lane segments. At low demand most of the flow of 3-lane segments is
concentrated in the center lane (lane 2), followed by lanes 1 and lane 3. As demand increases, lane flow
distribution increases in lane 3 and decreases in lanes 1 and 2.
- 37 -

Figure 33 – Comparison of lane flow distribution on two different 3-lane segments: (a) Tampa, FL
and (b) St. Paul, MN
As for 2-lane freeways, the values for boundary conditions at 3-lane freeways differ from one location
to another. For example, Figure 33(a) shows that during near-capacity conditions lane 3 carries the majority
of flow but it is similar to that of lane 2. However, in the location represented by Figure 33(b), the proportion
of flow allocated to lane 3 is higher when compared to the other lanes.
Finally, two 4-lane segments were examined. As shown in Figure 34, lane 4 is typically underused during
free-flow conditions, but when demand approaches capacity it carries the majority of flow. However, in
Figure 34(a), flow is highly concentrated on lanes 1 and 2 during free-flow, while Figure 34(b) shows that
flow is more concentrated in lanes 2 and 3 for similar demand levels.
- 38 -

Figure 34 – Comparison of lane flow distribution on two different 4-lane segments: (a) Salt Lake
City, UT and (b) Tampa, FL
Modeling of Lane Flow Ratio (LFR)

Analytical models were developed to predict LFR for each lane as a function of the logarithm of the
segment volume-capacity ratio (v/c):
𝐿𝐹𝑅 𝑎 𝑙𝑛 𝑏 (Equation 1)
𝐿𝐹𝑅 1−∑ 𝐿𝐹𝑅 (Equation 2)
Where:
LFRi = share of the total flow on lane i, where i ranges from 1 to n-1 (n = total number of segment
lanes)
LFRn = share of the total flow on the leftmost lane (lane n);
a= multiplicative calibration parameter
v/c = volume/capacity ratio
b = additive calibration parameter
- 39 -

The adjustment factors fa and fc are calculated as a function of a series of parameters, as follows:
𝑎 =𝑎 +𝐺×𝑎 +𝑡×𝑎 +𝑛×𝑎 (Equation 3)
𝑏 =𝑏 +𝐺×𝑏 +𝑡×𝑏 +𝑛×𝑏 (Equation 4)
where:
G = grade (%)
a0 = empirical constant
aG = empirical coefficient due to impact of grade
cG = empirical coefficient due to impact of grade
t = truck percentage (%)
at = empirical coefficient due to impact of trucks
bt = empirical coefficient due to impact of trucks
n = access point density – number of ramps half a mile upstream and half mile downstream
an = empirical coefficient due to impact of access point density
b = empirical constant
bn = empirical coefficient due to impact of access point density
vR = ramp flow (vph)
avR = empirical coefficient due to impact of ramp flow
bvR = empirical coefficient due to impact of ramp flow Evaluation of speeds on individual lanes
After the flows for individual lanes are obtained, the next step in the methodology calculates the speeds
on individual lanes. HCM Chapter 12 (Basic segments) proposes the following equation to describe the
speed-flow relationship of a basic segment:
𝑆 = 𝐹𝐹𝑆 − (Equation 5)
Where
𝑆 = segment speed (mi/h)
𝐵𝑃 = breakpoint value (pc/h/ln)
𝑐 = segment capacity (pc/h/ln)
𝐹𝐹𝑆 = segment free-flow speed
𝑣 = demand flow rate for the segment (pc/h/ln)
The same speed-flow relationship is used to predict speeds on individual lanes, as long as the free-flow
speed (FFS) and capacity (c) inputs can be provided on an individual lane basis. Appendix F provides a
procedure to estimate these values based on the segment-wise average values of FFS and capacity. Figure
35 illustrates the field data and the resulting speed-flow relationship of each lane for a 2-lane basic freeway
segment.
- 40 -

Figure 35 – Field data and predicted speed-flow curve for (a) lane 1 and (b) lane 2 (CA-1 NB – Santa
Cruz, CA)
8. System Analysis
This section describes briefly the methodology developed for estimating travel time performance
measures for specific O-D trips considering both urban streets and freeways. The details of the methodology
are provided in Appendix A: Chapter 38 – Systems Analysis. The methodology provides the detailed steps
to evaluate networks with freeway and urban street movements, as illustrated in the example of Figure 36.
- 41 -

Figure 36 – Origins and destinations for a sample network (Gainesville, FL)
The methodology in Chapter 38 generates the following performance measures:
Freeway Facilities:
• Flow, free-flow speed, operating speed, and capacity for individual lanes
• Expected travel speed along each segment and each lane
Urban Streets Facilities:
• Travel time along each segment
• Expected travel speed along each segment
System Analysis:
• Total and free-flow travel times
• Travel Time Index
• Average travel speed
- 42 -

9. Software Implementation
A computational engine with the proposed methodology has been developed and is available to HCQSC
and Panel Members on request for beta-testing. The computational engine has been evaluated using a series
of examples and use cases to ensure it replicates the methods accurately. The computational engine is not
a commercial product expected to address all use cases that may arise; however, the chapter provides
guidance for addressing a wide variety of use cases that may be encountered. Appendix A: Chapter 38 –
Systems Analysis and the other report appendices contain a series of examples illustrating the application
of the developed procedures.
10. Conclusions and Recommendations
This project conducted research on the analysis of highway systems and produced a new chapter (Chapter
38-System Analysis) for the HCM 6th Edition. These new methods can be used to evaluate operations along
networks that include both freeways and urban streets. The methods can also evaluate the impact of
spillback into freeways and into urban streets from downstream facilities. In summary, the following were
accomplished:
Selection of appropriate performance measures: Travel time was selected as the performance measure
to evaluate highway systems. Travel time measures are already used in the HCM to evaluate urban streets
facilities. For freeway facilities, we developed additional models and methods to evaluate freeway
performance by lane, as spillback affects each lane of the freeway differently. In addition, a trip-based
performance measurement framework was developed to provide travel time estimates for given O-Ds
within a highway network. O-D measures reflect traveler experience and are well aligned with recently
available data collection methods which track individual trips. These new measures are intended to
complement segment-based measures provided in other HCM chapters.
Evaluation of queue spillback into freeways: Queue spillback into the freeway occurs due to insufficient
capacity in at least one element of the off-ramp: either the ramp proper, or the downstream ramp terminal.
The blockage of one or more freeway lanes adversely affects performance, and the extent of the blockage
effects depend on various factors including the design of the facility, the cause of the blockage, and the
length of the queue. Video and detector data from several locations were obtained, and used along with
microsimulation to develop the methodological framework. The methodology developed is based on the
calculation of demand and capacity at the downstream ramp terminal using the respective Interrupted Flow
methods. It expands the Oversaturated Segment Evaluation for freeway facilities (HCM Chapter 25) and
accounts for spillback and its effects by lane along the freeway mainline.
Evaluation of queue spillback into urban streets: Queue spillback into urban streets occurs due to
insufficient discharge capacity into the freeway merge. It may occur due to oversaturated conditions at the
merge segment or the presence of ramp metering. Video and detector data from several locations were
collected to understand how intersections are affected by on-ramp queue spillback. Microsimulation was
used to complement the evaluation of signalized ramp terminals and to analyze systems with unsignalized
intersections. The proposed methodology integrates the Interrupted Flow methodologies with the Freeway
Facilities procedure to account for constraints of the on-ramp capacity. Several adjustments were developed
to estimate the impacts of queue spillback from an on-ramp into upstream signalized and unsignalized
intersections, including roundabouts.
Lane by lane performance measures for freeways: Freeway speeds can vary widely depending on the
lane used, and each O-D is likely to use a specific lane or set of lanes along each segment. Spillback affects
- 43 -

each freeway lane differently, and its effects depend on the site design and the length of the queue. This
project developed models that estimate speeds and flows by lane. Detector data were collected from a
variety of locations around the US, and analytical models were developed to predict the lane flow
distribution and lane speed. These models considered a variety of factors including v/c ratio, presence of
nearby ramps, heavy vehicle percent, and grade. Regression models built from the field data demonstrated
that FFS and capacity values for each lane can be obtained as a percentage of the segment average with
satisfactory results.
Development of an O-D analysis framework: A new methodology was developed to estimate travel
times by O-D within a highway system. This methodology combines the tools of several HCM chapters
within the Uninterrupted Flow and Interrupted Flow volumes. It also builds on the research previously
described to evaluate queue spillback and system effects
The limitations of the methods include the following:
Queue spillback into freeways:

• Overlapping bottlenecks cannot be addressed as they require iterative processes;
• Managed lanes are not addressed by the methodology.
Queue spillback into urban streets:

• Roundabouts with two lanes cannot be addressed;
• The HCM methodology for roundabouts does not provide a multi-period analysis procedure.
Therefore, the delay results for the proposed methodology may not be accurate when there is a
queue at the start of the analysis period.
• The procedures do not specifically address alternative intersection designs, such as SPUI, DDI;
however, the analyst may estimate capacities and queue lengths associated with a variety of
facilities and implement the methods described here for a variety of configurations;
• Indirect impacts of queue spillback, such as turn bay overflow are not addressed by this
methodology;
• The procedure relies on accurate estimates of the capacity of the merge obtained using the
Oversaturated Segment Evaluation (HCM Chapter 25); however the estimation of this capacity
is listed as a limitation of Chapter 25.
Freeway lane by lane analysis:

• Flow distribution models were not developed for segments with 5+ lanes. For these cases, using
equal distributions of flows and speeds are recommended.
System analysis:
• HCM Travel time reliability methodologies for Freeways (Chapter 11) and Urban Streets
(Chapter 17) have significant differences in their procedures. Therefore this project made no
attempt to incorporate reliability analysis in the new procedures.
In the future, it would be useful to develop a LOS framework for the travel time performance measures
yielded by this methodology to evaluate highway systems. Similar to other performance measures used in
the HCM, communicating the values of performance measures to a lay audience may be challenging, while
LOS may be a more useful construct.
- 44 -

References
[1] M. Armstrong, Methodology For Evaluating Spillback From Freeway Diverge

Segments In The HCM (Master's Thesis), Gainesville: University of Florida, 2015.
[2] A. Arun, S. Velmurugana and M. Errampalli, "Methodological Framework towards
Roadway Capacity Estimation for Indian Multi-Lane Highways," Procedia - Social
and Behavioral Sciences, vol. Volume 104, pp. 477-486, 2013.
[3] M. Cassidy, S. B. Anani and J. M. Haigwood. , "Study of freeway traffic near an off-
ramp," Transportation Research Part A: Policy and Practice, vol. 36, p. 6, 2002.
[4] J. Dong, C. Lu, C. Liu and N. Hawkins, "Assessing Segment- And Corridor-Based
Travel-Time Reliability On Urban Freeways," U.S. Department of Transportation,
Washington D.C., 2016.
[5] R. Dowling, "FHWA Report HOP-08-054," in Highway Capacity Manual 6th Edition:
A Guide for Multimodal Mobility Analysis, 2016 ed., Vols. IV: Definition,
Interpretation, and Calculation Of Traffic Analysis Tools Measures of
Effectiveness, Washingon, D.C., Federal Highway Administration, 2007.
[6] L. Elefteriadou, M. Armstrong, Y. Zheng and G. Riente, Highway Capacity Manual
(HCM) Systems Analysis Methodology, Washingon D.C.: Federal Highway
Administration, 2016.
[7] M. Friedrich, Evaluating the Service Quality in Multi-modal Transport Networks,
Berlin: International Symposium on Enhancing Highway Performance (ISEHP),
2016.
[8] G. Genevieve, Application of a regional Multi-Modal Transportation System
Performance Monitoring Framework, Vols. METRANS Project 15-08, Washington
D.C.: U.S. Department of Transportation, 2016.
[9] C. Lu and L. Elefteriadou, "An investigation of freeway capacity before and during
incidents," Transportation Letters, pp. 5(3), 144-153, 2013.
[10] J. Munoz and C. Daganzo, Experimental characterization of multi-lane freeway
traffic upstream of an off-ramp bottleneck, California Partners for Advanced Transit
and Highways (PATH), 2000.
[11] J. Munoz and C. Daganzo, "The bottleneck mechanism of a freeway diverge,"
Transportation Research Part A: Policy and Practice, p. 36.6, 2002.
[12] Z. Tian, "Modeling and Implementation of an Integrated Ramp Metering-Diamond
Interchange Control System," Journal of Transportation Systems Engineering and
Information Technology, Vols. Volume 7, Issue 1, pp. 61-69, 2007.
[13] Cambridge Systematics, Inc., Dowling Associates, Inc., System Metrics Group,
Inc., and Texas Transportation Institute. NCHRP Report 618: Cost-Effective
Performance Measures for Travel Time Delay, Variation, and Reliability,
Washington D.C.: National Academies, National Research Council, 2008.
[14] R. Kimber and E. M. Hollis, "Traffic Queues and Delays at Road Junctions,"
Transport and Road Research Laboratory, Berkshire, United Kingdom, 1979.
- 45 -

[15] E. Aakre and A. Aakre, "Modeling cooperation in unsignalized intersections," in

The 6th International Workshop on Agent-based Mobility, Traffic and
Transportation Models, Methodologies and Applications (ABMTRANS), 2017.
[16] B. W. Robinson, L. Rodegerdts, W. Scarbrough, W. Kittelson, W. Brilon, L.
Bondzio, K. Corage, M. Kyte, J. Mason, A. Flannery and J. Bunker, "Roundabouts:
An informational Guide," FHWA-RD-00-06, Washington DC.
[17] L. Rodegerdts and G. Blackwelder, "Analytical Analysis of Pedestrian Effects on
Roundabout Exit Capacity," in National Roundabout Conference, 2005.
- 46 -

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis
CHAPTER 38
SYSTEM ANALYSES (DRAFT)
CONTENTS
1. INTRODUCTION..................................................................................................... 56
Overview ................................................................................................................. 56
Chapter Organization ............................................................................................ 56
Related HCM Content............................................................................................ 56
2. CONCEPTS ................................................................................................................ 58
Overview ................................................................................................................. 58
Spillback Impact on Freeways .............................................................................. 58
Spillback Impact on Urban streets........................................................................ 62
Lane-by-Lane Analysis .......................................................................................... 63
Performance Measurement for Systems and O-D.............................................. 63
3. METHODOLOGY .................................................................................................... 64
Scope of the Methodology ..................................................................................... 64
Required Data and Sources ................................................................................... 66
Computational Steps .............................................................................................. 67
4. EXAMPLE PROBLEMS............................................................................................ 84
Example Problem 1: O-D Based Travel Time Estimation for I-75 NB Freeway
in Gainesville, Florida ..................................................................................... 84
Example Problem 2: I-10 On-Ramp Spillback analysis in Baton Rouge,
Louisiana .......................................................................................................... 95
Example Problem 2, Part 1: Signalized Intersection Ramp Terminal .............. 97
Example Problem 2, Part 2: TWSC Ramp Terminal......................................... 118
Example Problem 2, Part 3: AWSC Intersection Ramp Terminal .................. 123
Example Problem 3: Off-Ramp Queue Spillback Analysis for a Freeway-to-
Freeway Ramp in Miami, Florida. .............................................................. 127
Example Problem 4: On-Ramp Queue Spillback Analysis into a Single-Lane
Roundabout in Los Angeles, California ..................................................... 137
5. REFERENCES .......................................................................................................... 143
APPENDIX A: OFF-RAMP QUEUE SPILLBACK ANALYSIS .......................... 144

Capacity Checks.................................................................................................... 144
Queue Length Estimation .................................................................................... 146
Chapter 38 System Analyses (Draft) INTRODUCTION

Version 1.0 Page 47

Evaluation of Off-Ramp Queue Spillback Impacts .......................................... 152
APPENDIX B: ON-RAMP QUEUE SPILLBACK ANALYSIS ............................ 188

Demand Estimation .............................................................................................. 189
Capacity Estimation ............................................................................................. 195
Evaluation of On-Ramp Queue Spillback Impacts .......................................... 196
All-Way Stop-Controlled (AWSC) Intersections .............................................. 208
Roundabout ramp terminals ............................................................................... 208
APPENDIX C: LANE-BY-LANE ANALYSIS FOR FREEWAY

FACILITIES ................................................................................................................. 214
Lane-by-Lane Flow Models by Segment Type ................................................. 214
Speed Flow Curves by Lane and by Segment Type......................................... 220
Application Examples .......................................................................................... 224
INTRODUCTION Chapter 38 System Analyses (Draft)

Page 48 Version 1.0

LIST OF EXHIBITS
Exhibit 38-1 Off-Ramp Components ........................................................................... 59

Exhibit 38-2 Definition of Spillback Regimes ............................................................. 60
Exhibit 38-3 Capacity Adjustment Factors (CAFBL) for Through Lanes
Adjacent to Blocked Lanes during Queue Spillback.......................................... 60
Exhibit 38-4 Queue Influence Area with Increased Turbulence.............................. 61
Exhibit 38-5 Length of Queue Influence Area as a Function of the
Segment Free-Flow Speed (FFS) ........................................................................... 61
Exhibit 38-6 Queue Spillback from an On-Ramp into Urban Street
Intersections ............................................................................................................ 62
Exhibit 38-7 Required Input Data, Potential Data Sources, and Default
Values for the Systems Analysis Methodology .................................................. 66
Exhibit 38- 8 Default spillback regimes as a function of ramp geometry
and driver aggressiveness ..................................................................................... 67
Exhibit 38-9 Systems Analysis Methodology Flowchart .......................................... 68
Exhibit 38-10 Sample Study Network, with Multiple Origins and
Destinations ............................................................................................................. 69
Exhibit 38-11 Potential Bottlenecks Constraining the Ramp Terminal
Demand.................................................................................................................... 70
Exhibit 38-12 Potential Bottlenecks Constraining the On-Ramp Demand ............ 71
Exhibit 38-13 Spillback Check Procedure for Off-Ramps ......................................... 72
Exhibit 38-14 Spillback Check Procedure for On-Ramps ......................................... 74
Exhibit 38-15 Probability of Lane Choice for Entry/Exit Segments on
Freeway Facilities ................................................................................................... 76
Exhibit 38-16 Illustration of Lane Choice Probabilities Along a Freeway
Facility ...................................................................................................................... 76
Exhibit 38-17 Speed-flow Curves for Freeway Ramps ............................................. 78
Exhibit 38-18 Sample Calculation of Total Travel Time Using Multi-
Period Analysis ....................................................................................................... 80
Exhibit 38-19 Reference Input Values for O-D Analysis at Free-Flow
Conditions ............................................................................................................... 81
Exhibit 38-20 List of Example Problems ..................................................................... 84
Exhibit 38-21 Example Problem 1 Network Interchanges, with indication
of origins and destinations: ................................................................................... 85
(a) Williston Rd.(b) Archer Rd.(c) Newberry Rd.(d) NW 39th Ave. ........................ 85
Exhibit 38-22 Freeway Origins and Destinations for Example Problem 1 ............. 85
Exhibit 38-23 O-D Matrix for Example Problem 1..................................................... 86
Exhibit 38-24 Urban Street Facilities Evaluated for Example Problem 1 ............... 86
Exhibit 38-25 List of Segments Included Within D-H............................................... 86

Version 1.0 Page 49

Exhibit 38-26 Input Data for Freeway Facility Analysis ........................................... 87

Exhibit 38-27 Input Data for Intersection Analysis – Archer Rd. WB..................... 88
Exhibit 38-28 Input Data for Segment Analysis – Archer Rd. WB .......................... 88
Exhibit 38-29 Input Data for Intersection Analysis – NW 39th Ave. EB .................. 88
Exhibit 38-30 Input Data for Segment Analysis – NW 39th Ave. EB ....................... 88
Exhibit 38-31 Demands at the On-Ramps Along the Freeway Facility for
Example Problem 1 ................................................................................................. 89
Exhibit 38-32 LOS for the Freeway Segments of Example Problem 1 .................... 89
Exhibit 38-33 Demands at the Off-Ramps Along the Freeway Facility for
Example Problem 1 ................................................................................................. 90
Exhibit 38-34 Queue Length Estimation and Queue Storage Checks for
Off-Ramps ................................................................................................................ 91
Exhibit 38-35 Flow Distribution and Speeds for Freeway Segments ...................... 92
Exhibit 38-36 Estimated Speeds by Segment Based on Lane Choice
Probability and Speeds .......................................................................................... 92
Exhibit 38-37 Speeds for Urban Streets Segments ..................................................... 92
Exhibit 38-38 Travel Times for Urban Streets Segments........................................... 93
Exhibit 38-39 Travel Times for Freeway Segments ................................................... 93
Exhibit 38-40 Estimated Travel Times for Ramps Entering or Exiting the
Freeway Facility ...................................................................................................... 93
Exhibit 38-41 Estimated Travel Times for Ramps Entering or Exiting the
Freeway Facility ...................................................................................................... 94
Exhibit 38-42 Example Problem 2 Network Intersections: ....................................... 96
(a) Perkins Rd.; (b) Acadian Center; (c) I-10 EB;(d) I-10 WB .................................... 96
Exhibit 38-43 Origins and Destinations for the freeway facility (I-10 EB)
in Baton Rouge, LA................................................................................................. 97
Exhibit 38-44 Acadian Thruway Urban Street Facility ............................................. 97
Exhibit 38-45 Signalized Intersection Geometry – Acadian Thruway @ I-
10 EB ......................................................................................................................... 98
Exhibit 38-46 Phasing Sequence – I-10 EB Intersection............................................. 98
Exhibit 38-47 Demand Flow Rates (veh/h) – I-10 EB Intersection ........................... 98
Exhibit 38-48 Input Data – I-10 EB Intersection ......................................................... 99
Exhibit 38-49 Freeway Facility Segmentation– I-10 EB ............................................. 99
Exhibit 38-50 Freeway facility (I-10 EB) - Geometric Features............................... 100
Exhibit 38-51 Calculation of NBR Capacity for a Single Cycle – Time
Period 2 .................................................................................................................. 102
Exhibit 38-52 NBR Capacity, Computed for Each Time Period ............................ 102
Exhibit 38-53 Calculation of the On-Ramp Demand (vR) Based on the
Intersection Operation. ........................................................................................ 103

Page 50 Version 1.0

Exhibit 38-54 Freeway Facility (I-10 EB) – Demand Inputs ................................... 103
Exhibit 38-55 Performance Measures for the Freeway Facility (I-10 EB) ............. 104
Exhibit 38-56 Spillback Check – I-10 EB on-Ramp .................................................. 104
Exhibit 38-57 Freeway Facility, Segment 5 (merge) Performance: a)
Merge Capacities and b) Queue Lengths .......................................................... 106
Exhibit 38-58 Freeway Performance During Time Period 4 – with and
without the Queue Storage Constraint .............................................................. 106
Exhibit 38-59 Estimated Queue Lengths And Merge Capacities – Time
Period 2 .................................................................................................................. 107
Exhibit 38-60 Discharge Flow Rates into the On-Ramp for each Phase
Throughout the Cycle – Time Period 2 .............................................................. 110
Exhibit 38-61 Estimated Queue Lengths and Merge Capacities – Time
Period 3 .................................................................................................................. 111
Exhibit 38-62 Discharge Flow Rates Into the On-Ramp for Each Phase
Throughout the Cycle – Time Period 3 .............................................................. 113
Exhibit 38-63 Calculation of Spillback Capacity Reduction Factor for the
SBL Movement for Time Period 3 ...................................................................... 114
Exhibit 38-64 Estimated Queue Lengths and Merge Capacities – Time
Period 4 .................................................................................................................. 115
Exhibit 38-65 Calculation of Spillback Capacity Reduction Factor for the
SBL Movement During Time Period 4............................................................... 116
Exhibit 38-66 Comparison of Performance Measures – with and without
Consideration of Spillback Effects...................................................................... 117
Exhibit 38-67 TWSC Intersection Geometry – Acadian Thruway @ I-10
EB. ........................................................................................................................... 118
TWSC Intersection Operation. ............................................................................ 119
Exhibit 38-69 Queue Accumulation Plot Calculations for On-Ramp –
TWSC Intersection ................................................................................................ 120
Exhibit 38-70 Queue Accumulation Polygon for the On-Ramp – TWSC
Intersection ............................................................................................................ 121
Exhibit 38-71 Comparison of Performance Measures in a TWSC
Intersection – Time Period 3 - with and without Spillback Effects ................ 122
Exhibit 38-72 AWSC Intersection Geometry – Acadian Thruway @ I-10
EB ............................................................................................................................ 123
AWSC Intersection Operation ............................................................................ 124
Exhibit 38-74 Check for Spillback Occurrence – AWSC Intersection ................... 124
Exhibit 38-75 Queue Accumulation Plot Calculations for On-Ramp –
AWSC Intersection ............................................................................................... 125

Version 1.0 Page 51

Exhibit 38-76 Queue Accumulation Polygon for the On-Ramp – AWSC

Intersection ............................................................................................................ 125
Exhibit 38-77 Equivalent Capacities and Headways for on-ramp – Time
Period 3 – AWSC Intersection ............................................................................. 126
Exhibit 38-78 Comparison of Performance Measures – Time Period 3 -
with and without Spillback Effects .................................................................... 126
Exhibit 38-79 Study Site for Freeway-to-Freeway Queue Spillback Check,
Miami, FL ............................................................................................................... 127
Exhibit 38-80 Individual Freeway Facilities: (a) I-75 SB and (b) SR-826 SB ......... 128
Exhibit 38-81 Traffic Demands for the Subject Freeway Facilities ........................ 128
Exhibit 38-82 Performance Measures for I-75 (Freeway Facility 1) ....................... 129
Exhibit 38-83 Performance Measures for SR-826 (Freeway Facility 2) ................. 129
Exhibit 38-84 Estimation of Queue Length and Storage Ratio at the SR-
826 On-Ramp ......................................................................................................... 130
Exhibit 38-85 Link-node Structure for Spillback Analysis – I-75 SB ..................... 131
Exhibit 38-86 Queued Vehicles and Total Number of Vehicles in the
Ramp – Time Period 2 .......................................................................................... 132
Exhibit 38-87 Ramp Capacity and Ramp Inputs – Time Period 2 ........................ 133
Exhibit 38-88 Ramp Capacities and Ramp Inputs – Time Period 3 ..................... 134
Exhibit 38-89 Spillback Queue Length – Segment 3 (Diverge) – I-75 SB .............. 134
Exhibit 38-90 Available Queue Storage – Segment 3 (Diverge) – I-75 SB............. 135
Exhibit 38-91 ................................................................................................................. 135
Back of Queue Length, Including QIA, at the End of Time Period 3.................... 135
Exhibit 38-92 Schematic of the Study Interchange for Example Problem 4 ......... 137
Exhibit 38-93 Flows and Queues at the Roundabout of Example Problem
4 ............................................................................................................................... 139
Exhibit 38-94 Priority Order for the Roundabout of Example Problem 4 ............ 139
Exhibit 38-A1 Off-Ramp Queue Spillback Check Flowchart ................................. 144
Exhibit 38-A2 Capacity of Ramp Roadways (veh/h)............................................... 145
Exhibit 38-A3 Examples of Unbalanced Ramp Lane Usage: (a)
Norfolk/VA and (b) Tampa/FL ........................................................................... 147
Exhibit 38-A4 Spillback Occurrence by Lane at an Off-Ramp / Weaving
Segment .................................................................................................................. 148
Exhibit 38-A5 Expanded Link-Node Structure to Evaluate the Off-Ramp
Segment .................................................................................................................. 153
Exhibit 38-A6 Sample Geometry of an off-Ramp Considering the Arterial
Intersection with Heavy Demanded Left-Turn ................................................ 153
Exhibit 38-A7 Off-Ramp Queue Spillback Regimes ................................................ 155
Exhibit 38-A8 Freeway Facilities Oversaturated Segment Evaluation
Procedure, Adapted for Off-Ramp Queue Spillback Evaluation ................... 159

Page 52 Version 1.0


Procedure, Adapted for Off-Ramp Queue Spillback Evaluation -
Continued .............................................................................................................. 160
Continued .............................................................................................................. 161
Continued .............................................................................................................. 162
Exhibit 38-A12 Capacity Adjustment Factors for Lane Blockage (CAFBL)
as a Function of the Number of Directional Lanes and the Number of
Blocked Lanes ....................................................................................................... 163
Exhibit 38-A13 Equivalent Segment Capacity for Unblocked Lanes When
Lane Blockage Occurs .......................................................................................... 163
Exhibit 38-A14 Maximum Off-Ramp Queue Storage Length at Diverge
Segments with Occurrence of (a) Regime 3 Queue Spillback And (b)
Regime 4 Queue Spillback, when no Shoulder is Available ........................... 165
Exhibit 38-A15 Maximum Off-Ramp Queue Storage Length at Diverge
Segments with Occurrence of (A) Regime 3a Queue Spillback and (B)
Regime 4a Queue Spillback, when Shoulder is Available .............................. 165
Exhibit 38-A16 Node Structure for Example 1......................................................... 166
Exhibit 38-A19 Default Spillback Regimes as a Function of Ramp
Geometry and Driver Aggressiveness ............................................................... 168
Exhibit 38-A20 Queue Influence Area with Increased Turbulence....................... 168
Exhibit 38-A21 Queue Influence Area as Function of the Segment FFS............... 169
Exhibit 38-A22 Capacity of Ramp Proper for Off-Ramps ...................................... 169
Exhibit 38-A23 Speed-flow Curves for Freeway Ramps ........................................ 170
Exhibit 38-A24 Ramp Density at Capacity as a Function of Ramp FFS ............... 170
Exhibit 38-A25 Reference HCM Equations for Back-of-Queue Length
Estimation .............................................................................................................. 171
Exhibit 38-A26 Selection of a Cycle Reference Point to Determine the
Initial Number of Vehicles Within the Approach ............................................ 172
Exhibit 38-A27 Sample Signalized Intersection Approach from an Off-
Ramp ...................................................................................................................... 173
Exhibit 38-A28 Conversion of Green Times to Time Steps .................................... 174
Exhibit 38-A29 Illustration of Mainline Flow Rate Split into Blocked and
Unblocked Lanes .................................................................................................. 175

Version 1.0 Page 53

Exhibit 38-A30 Procedure for Evaluating the Impact of Queue Spillback

on Upstream Nodes and Determination of the Queue Length within
Upstream Segments .............................................................................................. 179
Exhibit 38-A31 Illustration of Different Impacts of an off-Ramp Queue at
Node i: (a) Lane Blockage, (b) Increased Turbulence and (c) No Effect ........ 180
Exhibit 38-A32 Distribution of pi as Function of Distance from the Off-
Ramp Exit, for a 3-Lane Segment ....................................................................... 182
Exhibit 38-A33 Illustration of Lane Change Maneuvers Within the Queue
Influence Area in a 4-Lane Segment With Regime 3 ....................................... 182
Exhibit 38-A34 Illustration of Lane Change Maneuvers Within the Queue
Influence Area in a 4-Lane Segment With Regime 4 ....................................... 182
Exhibit 38-A35 Impact of a queue spillback on the discharge capacity of
an upstream on-ramp ........................................................................................... 184
Exhibit 38-A36 Illustration of Different Density Values Within One
Diverge Segment ................................................................................................... 184
Exhibit 38-B1 Procedure for Detecting Spillback Occurrence at an On-
Ramp ...................................................................................................................... 188
Exhibit 38-B2 Schematic of Movements Turning to an On-Ramp from a
TWSC Intersection ................................................................................................ 191
Exhibit 38-B3 Schematic of Movements Turning to an On-Ramp from an
AWSC Intersection ............................................................................................... 192
Exhibit 38-B4 Schematic of Movements Turning to an On-Ramp from a
Roundabout ........................................................................................................... 193
Exhibit 38-B5 Signalized Intersections Methodology With Adjustments to
Address On-Ramp Queue Spillback .................................................................. 197
Exhibit 38-B6 Typical Signalized Intersection Ramp Terminal in a
Diamond Interchange .......................................................................................... 198
Exhibit 38-B7 Step 7B - Estimation of Merging Capacity in a Freeway
Ramp ...................................................................................................................... 200
Exhibit 38-B8 Sample Intersection for Calculation of a QAP for the On-
Ramp ...................................................................................................................... 201
Exhibit 38-B9 On-Ramp Queue Accumulation Polygon During Queue
Spillback ................................................................................................................. 202
Exhibit 38-B10 Illustration of Cooperative Behavior in Unsignalized
Intersections With Queue Spillback ................................................................... 203
Exhibit 38-B11 TWSC intersections Core Methodology With Adjustments
to Address On-Ramp Queue Spillback .............................................................. 204
Exhibit 38-B12 On-ramp Queue Accumulation Polygon – TWSC
Intersection ............................................................................................................ 205
Exhibit 38-B13 AWSC Intersections Core Methodology With
Adjustments to Address On-Ramp Queue Spillback ...................................... 208

Page 54 Version 1.0

Exhibit 38-B14 Roundabouts Methodology With Adjustments to Address

On-Ramp Queue Spillback .................................................................................. 209
Exhibit 38-B15 Required Data and Potential Data Sources – Roundabout
Spillback Evaluation............................................................................................. 210
Exhibit 38-B16 Priority Order for a Roundabout Upstream of an On-
Ramp ...................................................................................................................... 210
Exhibit 38-C1 Adjustment Factors for Lane Flow Distribution on Basic,
Merge and Diverge Segments ............................................................................. 216
Exhibit 38-C2 Adjustment Factors for Lane Flow Distribution on
Weaving Segments ............................................................................................... 217
Exhibit 38-C3 LFR Distribution for a Sample 2-Lane Segment
(Minneapolis/MN) ................................................................................................ 218
Exhibit 38-C4 LFR Distribution for a Sample 3-Lane Segment (Tampa/FL)........ 218
Exhibit 38-C5 LFR Distribution for a Sample 4-Lane Segment (Tampa/FL)........ 218
Exhibit 38-C6 Check for Negative Lane Flows ........................................................ 219
Exhibit 38-C7 Check for Lane Capacity .................................................................... 220
Exhibit 38-C8 Multipliers to Estimate Lane FFS from Segment FFS ..................... 221
Exhibit 38-C9 Capacity of Individual Lanes as a Percentage of Segment
Capacity, by Segment Type and Number of Lanes ......................................... 222
Exhibit 38-C10 Comparison of Speed-Flow Curves for Each Lane and for
the Segment ........................................................................................................... 226
Exhibit 38-C11 Example of LFR Calculation for a Weaving Segment .................. 226
Exhibit 38-C12 Field × Predicted Speed-Flow Curve for (a) Lane 1 and (b)
Lane 2 (CA-1 NB – Santa Cruz/CA) ................................................................... 231

Version 1.0 Page 55

1. INTRODUCTION
VOLUME 4: APPLICATIONS OVERVIEW

GUIDE
25. Freeway Facilities: This chapter provides methodologies for evaluating the interactions between
Supplemental
26. Freeway and Highway freeways and urban streets and the effects of spillback from one facility to
Segments: Supplemental another. The methodology of this chapter can be applied to a system of
27. Freeway Weaving:
Supplemental
interconnected freeways and to freeway-to-arterial connections. It can also be
28. Freeway Merges and applied when the freeway-arterial interchange consists of signalized
Diverges: Supplemental
29. Urban Street Facilities:
intersections, stop-controlled intersections, and roundabouts. The analysis tools
Supplemental of this chapter provide travel times and speeds for networks and for origin-
30. Urban Street Segments:
Supplemental
destination pairs (O-D) within these facilities.
31. Signalized Intersections:
Supplemental
The methodology builds on the analysis methods of individual points and
32. STOP-Controlled segments and points and extends them in several ways in order to consider
Intersections:
Supplemental
spillback effects from the downstream facility. First, because spillback affects
33. Roundabouts: each lane differently, the analysis is conducted on a lane-by-lane basis. Second,
Supplemental
supplemental performance measures are provided at the network level and at
34. Interchange Ramp
Terminals: Supplemental the O-D level for undersaturated and oversaturated conditions. Travel time
35. Pedestrians and Bicycles:
measures are also provided for segments and facilities, and their values are
Supplemental
36. Concepts: Supplemental consistent with the analysis methods described in other parts of the manual.
37. ATDM: Supplemental
38. System Analyses
CHAPTER ORGANIZATION
Section 2 provides the performance measures used at the systems level and
includes example calculations of O-D travel time and An origin - destination pair (O-
D) represents the route
network travel time. between two specific points in
the analysis network. The
Section 3 describes the procedures to evaluate the definition of “point” is provided
spillback impact on the freeway due to congestion on in the HCM Chapter 2 -
Applications
the ramp or urban street.
Section 4 describes the procedures to evaluate the
spillback impact on the urban street due to congestion on the freeway or on-
ramp.
Section 5 provides case studies to illustrate the application of the methods
described in this chapter.
A series of appendices provide detailed information on specific models and
analysis steps.
RELATED HCM CONTENT

Other HCM content related to this chapter includes:
• Chapters 10 and 25, which present the freeway systems analysis
methodology,
• Chapters 12, 13, and 14, which present the freeway segment
methodologies for basic freeway segments, freeway weaving segments,
and freeway merge and diverge segments, respectively,
• Chapter 26, which provides additional details for basic freeway segments
capacity measurement and driver population factors,

Page 56 Version 1.0

• Chapters 16 and 18, which provide methodologies for evaluating urban

street facilities and urban street segments, respectively,
• Chapters 19, 20, 21, and 22, which provide analysis tools for signalized
intersections, two-way stop-controlled intersections, all-way stop-
controlled intersections, and roundabouts, respectively, and
• Chapter 23, which provides methods for evaluating ramp terminals and
alternative intersections.

Version 1.0 Page 57

2. CONCEPTS
OVERVIEW
This section discusses concepts related to spillback on the freeway, spillback
on the urban street, lane-by-lane analysis, and performance measurement for
systems and O-Ds. Concepts related to freeway analysis and urban street
analysis are described in the respective chapters of this manual.
SPILLBACK IMPACT ON FREEWAYS

Spillback on the freeway may occur either due to inadequate capacity of the
ramp roadway, or due to inadequate capacity at the ramp terminal (typically the
intersection at the downstream interchange). The capacity of the ramp roadway
is defined as the off-ramp’s maximum allowable hourly flow rate based on its
geometric characteristics (mainly number of lanes and free-flow speed). The
capacity of the ramp terminal is defined as the capacity of the signalized or
unsignalized approach to the surface street.
The methodology compares demand and capacity at the off-ramp and at the
ramp terminal to determine whether oversaturation conditions will occur. If
demand exceeds capacity at either of those two locations, then the queue length
is estimated and compared to the available storage on the ramp and along the
deceleration lane. When the queue extends beyond the ramp roadway, blockage
may occur on one or more mainline freeway lanes. In that case, the methodology
estimates the impact of this queue spillback along the freeway by reducing the
segment capacity dependent on the number of blocked lanes and the effects of
that blockage on adjacent lanes.
Off-ramp elements
A freeway off-ramp typically consists of three components (Exhibit 38-1):
• Deceleration lane(s): its distance is measured from the beginning of the
taper of the auxiliary lane to the gore
• Ramp roadway: the road section connecting the deceleration lane and the
downstream ramp terminal; its distance is measured from the gore to the
taper of the ramp terminal;
• Ramp terminal: ramp terminals connecting to urban street facilities can be
uncontrolled, stop-controlled or signalized intersections; its distance is
measured from the point where additional lanes are added to the
intersection approaches to the stop bar of the approach. The length of this
section should be at least as long as the turn bay lengths of the approach.
When the ramp connects two freeway facilities, the downstream ramp
terminal is replaced by the merge section of the on-ramp, with no storage length.
Concepts Chapter 38 System Analyses (Draft)

Page 58 Version 1.0

Exhibit 38-1
Off-Ramp Components
Queue spillback regimes
The impact of queue spillback on the freeway mainline varies as a function of

the queue length and the lanes blocked. Four spillback regimes are defined:
a) Regime 1
Under this regime, the queue ends within the deceleration lane and does not
spill back into the mainline freeway (Exhibit 38-2 (a)) Deceleration lanes typically
serve as a transition zone between speeds on the mainline (typically 55 – 75 mi/h)
and advisory speeds posted along the off-ramp roadway (typically 20 – 50 mi/h).
When queues begin to form on the deceleration lane, the available deceleration
distance is reduced, and speeds begin to be affected in the rightmost lane.
b) Regime 2
Under this regime, the queue of vehicles extends upstream beyond the
deceleration lane, but sufficient lateral clearance on the right-hand shoulder
allows for additional queue storage. In this case the deceleration lane does not
serve as a transition zone and drivers decelerate and join the back of the queue
more abruptly, resulting in turbulence and reduced speeds in the rightmost lane
(Exhibit 38-2 (b)). If no lateral clearance exists immediately upstream of the
deceleration lane, Regime 2 conditions are not possible. In some cases, this
regime does not occur even if storage is available; this depends on local driver
behavior and is site-specific.
c) Regime 3
Under this regime, the queue extends to the rightmost lane of the freeway
mainline (Exhibit 38-2 (c)). This may occur either when there is no shoulder
available for additional queue storage, or when drivers choose to queue in the
rightmost lane once the deceleration lane is entirely occupied. Non-exiting
vehicles on the rightmost lane are delayed or change lanes, which causes
increased turbulence and reduced speeds in the two rightmost lanes.
d) Regime 4
Chapter 38 System Analyses (Draft) Concepts

Version 1.0 Page 59

Under this regime, the queue blocks the rightmost lane, and drivers
occasionally or often use the adjacent freeway mainline lane next to the
rightmost freeway mainline lane to force their way into the queue, blocking thus
an additional lane (Exhibit 38-2 (d)). During this regime, mainline speed and
capacity are significantly reduced.
The effects of spillback vary from site to site and from time period to time
period due to driver behavior and site geometry. Data collection has shown that
at some sites, drivers block the adjacent lane, while at other sites they do not,
regardless of the queue spillback length at the site.
Exhibit 38-2
Definition of Spillback
Regimes
(a) Regime 1 – Queue within the (b) Regime 2 – Queue along the
deceleration lane shoulder
(c) Regime 3 – Queue in the (d) Regime 4 - Queue blockage of

rightmost lane the adjacent lane
For unblocked lanes adjacent to those completely or temporarily blocked, the

methodology uses a “friction factor” in the form of a Capacity Adjustment Factor
(CAFBL). This adjustment factor is applied only to segments where Regime 3 or
Regime 4 occur.
The values for this factor are equal to the Incident Capacity Adjustment
Factors of Chapter 11, Freeway Reliability Analysis (Exhibit 11-23), as there are
currently no data available to accurately assess the impacts on capacity for this
case. However, these values may be conservative, as capacities during incidents
may be further reduced due to rubbernecking and the presence of police
vehicles. Exhibit 38-3 presents the adjustment factors to be applied in order to
obtain the capacity of through lanes adjacent to blocked lanes during queue
spillback. This adjustment factor is not applicable for 2-lane segments with
Regime 4, as there are no unblocked lanes.
Directional Lanes 1 Queued Lane 2 Queued Lanes
Exhibit 38-3
Capacity Adjustment Factors
(CAFBL) for Through Lanes
Adjacent to Blocked Lanes
during Queue Spillback

Page 60 Version 1.0

2 0.70 N/A
3 0.74 0.51
4 0.77 0.50
5 0.81 0.67
6 0.85 0.75
7 0.88 0.8
8 0.89 0.84
A Capacity Adjustment Factor (𝐶𝐴𝐹 ) is also applied to the Queue

Influence Area (QIA) upstream of the back of the queue (Exhibit 38-4). Along this
area, there is additional turbulence due to increased lane changing, which results
in a reduction of capacity.
Exhibit 38-4
Queue Influence Area with
Increased Turbulence
The length of the QIA is estimated as function of the

Additional discussion on the
determination of the Queue segment free-flow speed (FFS), as shown in Exhibit 38-5.
Influence Area (QIA) is During undersaturated operations, drivers have
presented in Appendix A
adequate warnings regarding the presence of a ramp
through signage and navigation aids and can position
themselves according to their destination. However, when queue spillback
occurs drivers can only detect a downstream queue visually and therefore have
shorter times to react, resulting in more aggressive lane changes and additional
turbulence.
Segment Free-Flow Speed (mi/h) Queue Influence Area (ft) Exhibit 38-5
50 810 Length of Queue Influence
55 900 Area as a Function of the
60 980 Segment Free-Flow Speed
65 1060 (FFS)
70 1140
75 1220

Version 1.0 Page 61

SPILLBACK IMPACT ON URBAN STREETS

Similar to spillback on freeways, spillback on urban streets may occur due to
oversaturated conditions on freeways. Exhibit 38-6(a) illustrates spillback at a
signalized intersection, while Exhibit 38-6(b) illustrates spillback at a
roundabout. Using the Chapter 13, Freeway Merge and Diverge Segments or
Chapter 12, Freeway Weaving Segments procedures, the analyst can determine
whether oversaturated conditions will prevail for a single freeway segment and
analysis period. The methodology of this chapter provides an estimate of the
discharge rate from the intersection to the on-ramp during congested conditions,
while also considering any effects from ramp-metering. Estimating this discharge
rate is necessary in order to estimate the resulting queue length along the on-
ramp. If the ramp is metered, the metering rate should be used instead.
Exhibit 38-6
Queue Spillback from an On-
Ramp into Urban Street
Intersections
(a) Signalized Intersection Spillback (b) Roundabout Spillback
The queue length along the on-ramp also depends on the upstream
demands. In the example shown in Exhibit 38-6(a), there are three possible
movements contributing to this demand: NB right, SB left, and EB through. If the
NB right movement is very heavy and/or has the right-of-way for a significant
amount of time, the SB left movement may not have as much of an opportunity
to contribute to the demand and may spill back upstream, affecting the adjacent
SB through movement, as well as the upstream intersection. Thus, in the case of
signalized intersections, the relative contribution of demands to the queue length
will depend on the relative demands of these movements and the respective
signal timings and right-of-way allocation. The discharge rate of these upstream
intersection movements will depend on the storage availability on the on-ramp
during the respective phase. The analysis estimates the additional lost time due
to the presence of the downstream queue and adjusts the effective green of these
movements.
In the roundabout example shown in Exhibit 38-6(b), the same three
movements contribute to the on-ramp demand. However, in this case the
movements have priority in the following order: (1) SB left, (2) EB through and
(3) NB right. A high-priority movement with a heavy demand may constrain the
entry capacity of lower priority movements, resulting in total throughput that is
lower than the sum of the three contributing movement demands.

Page 62 Version 1.0

LANE-BY-LANE ANALYSIS
Spillback affects each lane of a facility differently. For example, when
spillback occurs at a freeway off-ramp, the right-most lanes of the freeway may
be blocked, while the left-most lanes operate in free-flow conditions. Therefore,
the methodology estimates operating conditions by lane as well as by segment.
The lane-by-lane performance metrics are also used to obtain O-D based travel
times.
The demand flow rates by lane The lane-by-lane analysis provides lane flow ratios
are estimated as a percentage
of the segment demand. (LFR) which represent the percentage of the entering
demand by lane. LFR is a function of the segment-wide
v/c ratio and values are provided for each segment type (basic, merge, diverge
and weaving). In addition, FFS, speeds, and capacities are estimated by lane.
When the facility reaches oversaturated conditions, the speeds are estimated
based on the Chapter 10, Freeway Systems method, which is based on
interactions between successive segments.
PERFORMANCE MEASUREMENT FOR SYSTEMS AND O-D

In order to evaluate network and O-D performance, it is necessary to have a
common performance measure across different types of facilities. Therefore, the
methodology estimates travel time by segment and lane, and aggregates these
for O-Ds and for the network.
For urban streets, Chapter 16 provides tools for obtaining speeds for all
segments, and these are used in the systems analysis methodology. For freeway
systems, operational performance is determined based on the density and speed
at each segment along the network. The average travel time for each segment can
be derived based on the respective average speeds. The average travel time for
the entire facility can be obtained as a sum of the segments’ average travel times.
However, the travel time of some O-D’s cannot be accurately obtained, as they
may predominantly or exclusively use specific lanes. The speeds in these lanes
could differ substantially from the average segment speed. Generally, speed
varies widely between lanes, especially during congested conditions around off-
ramp bottlenecks, which may lead to significantly different travel times. For
example, travelers exiting at a congested off-ramp will experience a much
different travel time than those using the left most lanes of the same segment.
Therefore, the O-D based analysis along a freeway network is based on:
• Prevailing speeds by individual lanes: A set of models have been developed
for estimating the speeds and capacities of each lane for each type of
freeway segment.
• Selected travel lanes for each O-D: The set of lanes used by an O-D in every
segment of the freeway facility is also necessary to calculate the
corresponding travel times at each segment. For every feasible O-D, the
set of lanes that may be selected are obtained and considered in the
estimation.

Version 1.0 Page 63

3. METHODOLOGY
The methodology of this chapter provides tools for evaluating the

performance of networks consisting of freeway and urban street facilities. It also
provides methods to evaluate the interactions between freeway and urban street
facilities and assess the impact of queue spillback if it occurs. The methodology is
based on lane-by-lane analysis for freeway facilities. For signalized and
unsignalized intersections the methodology relies on lane group analysis, while
for urban street segments there is no differentiation between travel lanes. The
methodology provides travel times and speeds for the network, each segment,
and by O-D.
HCM Chapters that address segments
SCOPE OF THE METHODOLOGY and facilities are:
10. Freeway Facilities Core Methodology
The methodology of this chapter builds on the
12. Basic Freeway and Multilane Highway
freeway systems and urban streets analysis methods, Segments
and therefore incorporates the scope and all aspects of 13. Freeway Weaving Segments
these chapters’ methodologies. The method of this 14. Freeway Merge and Diverge
chapter can evaluate interconnected freeway facilities, Segments
and interconnected freeway and urban street facilities. It 16. Urban Street Facilities
can consider signalized intersections, stop-controlled 18. Urban Street Segments
intersections, all-way stop-controlled intersections, and 19. Signalized Intersections
roundabouts, as well as a wide range of interchange 20. TWSC Intersections
ramp terminal configurations. 21. All-Way Stop-Controlled Intersections

22. Roundabouts
Spatial and Temporal Limits 23. Ramp Terminals and Alternative
Intersections
The spatial scope of the analysis is a function of the
network to be studied, the extent of congestion, and the
specific O-D pairs of interest. The external links to the network should remain
uncongested throughout the study period.
The definition of analysis boundaries, in practical terms, follow the guidance
provided by the Freeway Facilities Core Methodology. The temporal and spatial
extent of the analysis should be sufficiently long to fully contain the formation
and dissipation of all queues within the corridor. Similar to the spatial scope, the
temporal scope of the analysis must be compatible with the selected O-D pairs,
the study period, and the duration of congestion. The first and last analysis
periods should be free of congestion. The methodology can perform multi-period
analysis when the travel time is longer than 15 minutes. Performance Measures
The methodology of this chapter generates the following performance
measures:
Freeway Facilities:
• Flow, free-flow speed, operating speed, and capacity for individual lanes
Urban Streets Facilities:
• Travel time along each segment
METHODOLOGY Chapter 38 System Analyses (Draft)

Page 64 Version 1.0


System Analysis:
• Total and free-flow travel times
• Travel time index
• Average speed
Strengths of the Methodology

The strengths of the methodology include:
1. The methodology evaluates the effects of spillback from one facility to
another and considers the interactions between urban streets and
freeways.
2. The methodology evaluates oversaturated and undersaturated conditions
by lane, by segment, and for the entire network.
3. The methodology produces travel times and other performance measures
by O-D within the network.
4. The methodology tracks the formation and dissipation of queues across
lanes, segments, and facilities.
5. The methodology can be used to evaluate the impacts of modifications in
one facility to an adjacent one.
Limitations
The methodology has the following limitations:
1. Multiple overlapping breakdowns or bottlenecks cannot be fully
evaluated by this methodology. Consult Chapter 6, HCM and Alternative
Analysis Tools for a discussion of simulation and other models.
2. Demand is an input into the process, and the methodology does not
address any changes in demand that are due to traffic operational
conditions.
3. Managed lanes can be analyzed as part of the freeway system. However,
the interaction of managed lanes operations with spillback conditions are
not addressed.
4. The methodology does not explicitly consider alternative intersection and
interchange designs, such as DDI and SPUI. However, it can be extended
to consider these, assuming turning movements, demands, and queues
can be accurately estimated for the movements of interest.
5. The methodology does not consider two-lane roundabouts and their
interaction with freeway on-ramps.
6. The reliability method cannot be applied for systems analysis because the
process for developing reliability scenarios is different for freeways and
arterials.
Chapter 38 System Analyses (Draft) METHODOLOGY

Version 1.0 Page 65

REQUIRED DATA AND SOURCES

The system analysis requires details concerning each freeway and urban
street segment’s geometric characteristics, as well as each segment’s demand
characteristics during each analysis time period. Exhibit 38-7 shows the data
inputs that are required for an operational analysis of a system, potential sources
of these data, and suggested default values.
Required Input Potential Data Source Suggested Default
Value
Exhibit 38-7
Trajectory Parameters by O-D
Required Input Data, Potential Origin and destination points Set by analyst Must be provided
Data Sources, and Default Route between origin and Set by analyst Must be provided
Values for the Systems destination points
Analysis Methodology
Freeway Facilities
Input data for current methods As recommended by HCM As recommended by HCM
(Chapters 10, 12, 13 and (Chapters 10, 12, 13 and
14) 14)
Ramp access density (number of Road geometry Must be provided
ramps within 1 mile)
Grade (%) Road geometry Must be provided
Urban Street Facilities

Input data for current methods As recommended by HCM As recommended by HCM
(Chapters 16 and 18–23) (Chapters 16 and 18–23)
Urban street segments - Set by analyst, according to Must be provided
corresponding movement at the selected route
downstream intersection
Off-Ramp Queue Spillback
Off-ramp queue spillback – Road geometry, field Function of the diverge
expected number of queued lanes observations geometry and driver
aggressiveness
Length of available shoulder (ft) Road geometry Must be provided
Off-ramp detailed geometry Road geometry Must be provided
On-ramp Queue Spillback

On-ramp metering rate (veh/h) (if Field data Must be provided
applicable)
On-ramp detailed geometry Road geometry Must be provided
Roundabouts - exit capacity (pc/h) Field data, past counts 1,300 pc/h
Off-ramp queue spillback – expected number of queued lanes

If queue spillback from the off-ramp is expected to be extended beyond the
length of the deceleration lane, the expected prevailing spillback regime (3 or 4)
must be provided by the analyst.
Field observations [1] have shown that locations that experience recurring
queue spillback always have the same type of spillback regime when the queue
extends beyond the deceleration lane (Regime 3 or 4). Regime 4 occurs often at

Page 66 Version 1.0

ramp junctions with a lane drop. At these locations, the exiting traffic can
access the off-ramp with a single lane change. Therefore, drivers are more likely
to wait until they are closer to the exit to change lanes, blocking the adjacent
through lane. However, not all lane drop exits experience a Regime 4 queue
spillback. Generally, Regime 4 occurs more frequently in locations with more
aggressive driver behavior. Local information and driver behavior should be
taken into consideration in determining the prevailing regime at a given site.
For operational analyses of existing locations, it is recommended that the
analyst provides the expected spillback regime based on observed field
conditions. For planning level purposes where no field data is available, Exhibit
38- 8 provides the expected queue spillback regime as a function of the number
of exiting lanes and driver aggressiveness.
Driver Aggressiveness
Ramp Geometry Exhibit 38- 8
Low Medium High
Diverge with Default spillback regimes as a
Regime 3 Regime 3 Regime 3 function of ramp geometry
deceleration lane
and driver aggressiveness
Diverge with lane drop Regime 3 Regime 4 Regime 4
COMPUTATIONAL STEPS
This section describes the methodology’s computational steps. Exhibit 38-9
illustrates the process used to evaluate systems operations.

Version 1.0 Page 67

Exhibit 38-9
Systems Analysis Methodology
Flowchart
Step 1: Define Spatial and Temporal Analysis Scope

The first step in the analysis requires identification of the spatial and
temporal extent of the network to be evaluated. For accurate evaluation of traffic
operations, it is essential that the spatial and temporal extent of congestion is
contained within the network. If initial analysis determines that queues extend
beyond the limits of the network, the analysis area should be modified
accordingly in order to contain all congestion effects.
The analyst should also select any O-D pairs to be evaluated, along with the
respective set of links to be traveled for each selected O-D. Exhibit 38-10
illustrates a sample network with 6 possible origin/destination nodes.

Page 68 Version 1.0

Exhibit 38-10
Sample Study Network, with
Multiple Origins and
Destinations
Step 2: Provide Input Parameters for Freeway and Urban Street

Analysis
The urban street and freeway facilities are first modeled separately using the
methodologies from the respective chapters. If multiple facilities of the same type
are to be analyzed (for example, two distinct urban street facilities), each facility
must first be modeled separately. The performance measures for each of these
facilities must also be computed at this step, as they are used next to analyze the
freeway-arterial interactions.
Step 3: Balance Demands at Freeway-Urban Street Interface

When urban street and freeway facilities are modeled independently, the
analyst is required to provide demand flow rate values for both facilities. In the
case of an interface between a freeway and an urban street, the demand flows
traveling through a freeway ramp and the demands at the ramp terminal should
be the same in order to conduct systems analysis.
The presence of any bottlenecks upstream of the freeway exit may reduce the
demand to the ramp junction. If the total off-ramp demand is greater than the
ramp roadway capacity, the intersection demand will be reduced accordingly.
Similarly, any movements operating above capacity at the ramp/surface street
junction would constrain the demand to the downstream freeway on-ramp.
This process must be performed for every time period in the analysis and
starting from the upstream end of the facility. When demand exceeds capacity at
any given location, the downstream demands must be recalculated considering
the throughput from the bottleneck.
Off-Ramp Demand vs. Downstream Ramp Terminal Demand

The demand for the turning movements at the ramp terminal downstream of
an off-ramp can be metered by insufficient capacity of the ramp roadway, as
shown in Exhibit 38-11. If this bottleneck is not active, the sum of intersection
demands vLT and vRT are equal to the off-ramp demand vR.

Version 1.0 Page 69

Exhibit 38-11
Potential Bottlenecks
Constraining the Ramp
Terminal Demand
However, if the demand at the off-ramp exceeds its capacity, the flow that
will reach the ramp terminal will be lower than the off-ramp demand vR. In this
case, the following adjustments are performed:
a) Insufficient Capacity at a Bottleneck Freeway Segment

In order to balance demands, the OFRF is first aggregated for a 15-minute
time period as follows:
𝑇
Equation 38- 1 𝑣 , 𝑂𝐹𝑅𝐹 𝑖, 𝑡, 𝑝
𝑆
where
𝑣 , = adjusted demand at the subject off-ramp (pc/h);
The parameter OFRF(i, t, p) 𝑂𝐹𝑅𝐹 𝑖, 𝑡, 𝑝 = actual flow that can exit at off-ramp 𝑖 during time step 𝑡 in time
is defined as the “actual
flow that can exit at off- interval 𝑝;
ramp i during time step t in
time interval p” (Chapter
𝑇 = number of time steps in 1 h; and
25). It can account for the 𝑆 = number of computational time steps in an analysis period (typically
effects of bottlenecks
upstream of the off-ramp S=240 for time steps of 15s)
that can meter the traffic
that arrives to the ramp. If the freeway facility operates at undersaturated conditions, the value of
𝑣 , is equal to the off-ramp demand 𝑣 .
If the subject freeway facility operates at oversaturated conditions, the total
demand of the off-ramp may be metered at an upstream bottleneck segment. The
Oversaturated Segment Evaluation methodology (HCM Chapter 25) provides
equations to estimate the off-ramp flow parameter OFRF (Equations 25-23
through 25-25) at every 15-second time step.
b) Insufficient Capacity at the Ramp Roadway

If the total demand at a freeway exit is greater than the capacity of the ramp
roadway (cR ), the flow that will reach the downstream ramp terminal will be
constrained by the ramp roadway capacity. For each movement 𝑖 at the
intersection, the adjusted demand is calculated as follows:
𝑣 𝑐
Equation 38-2 𝑣, 𝑣 𝑚𝑖𝑛 ,1
∑ 𝑣 𝑣 ,
where
𝑣, = adjusted demand for movement 𝑖 at the downstream intersection
(pc/h);
𝑣 = demand for movement 𝑖 at the downstream intersection (pc/h);
𝑣 = off-ramp demand (pc/h);

Page 70 Version 1.0

𝑣 , = adjusted off-ramp demand (Equation 38- 1) and

𝑐 = capacity of ramp roadway (Exhibit 14-12).
On-Ramp Demand vs. Upstream Ramp Terminal Demand

At a freeway merge segment the on-ramp demand flow rate vR can be
constrained by the following bottlenecks:
1. Insufficient capacity of one or more movements in the ramp terminal
2. Insufficient capacity at the ramp roadway
These potential bottlenecks are illustrated in Exhibit 38-12. If capacity is not

exceeded at any of those locations, the on-ramp demand vR is equal to the sum of
intersection demands that contribute to the on-ramp (vNBR, vEBT and vSBL).
Exhibit 38-12
Potential Bottlenecks
Constraining the On-Ramp
Demand
However, if capacity is exceeded at any of those locations, the flow that will
reach the freeway merge will be lower than the on-ramp demand vR and
adjustments should be made to the respective volumes.
If any of the ramp terminal movements that discharge into the on-ramp
operates over capacity, the total throughput to the on-ramp will be:
Equation 38-3
𝑣 , 𝑚𝑖𝑛 𝑣 , 𝑐
where
𝑣 , = adjusted on-ramp demand (veh/h);
𝑣 = demand for movement 𝑖 at the intersection (veh/h);
𝑐 = demand for movement 𝑖 at the intersection (veh/h);
𝑁 = number of intersection movements that discharge into the on-ramp
If the total on-ramp demand vR is greater than the ramp roadway capacity cR,
the adjusted on-ramp demand is:
Equation 38-4 𝑣 , 𝑚𝑖𝑛 𝑣 , 𝑐
where
𝑣 , = adjusted on-ramp demand (veh/h);

Version 1.0 Page 71

𝑣 = on-ramp demand (veh/h)

𝑐 = ramp roadway capacity (veh/h), as provided in Exhibit 14-12.
Step 4A: Check for Queue Spillback (Off-Ramp)

During this step, the methodology evaluates the network to determine
whether there is queue spillback from a freeway off-ramp. The analysis is first
conducted using 15-minute time periods (single period or multi-period) to
determine whether queue spillback is expected to occur. If spillback is expected,
Step 5 will perform an analysis based on 15-second time steps. If spillback is not
expected, Step 5 will evaluate the performance of the freeway segments in 15-
minute intervals.
Exhibit 38-13 summarizes the process for conducting a spillback check at off-
ramps.
Exhibit 38-13
Spillback Check Procedure for
Off-Ramps
The process evaluates whether the spillback originates from the demand to the
ramp roadway, or from the demand to the ramp junction at the surface street, or
from the downstream freeway on-ramp. Based on this determination, the
procedure uses the demand and the capacity for the analysis interval, as well as
the previous queue length, to calculate the anticipated queue length for this

Page 72 Version 1.0

interval. The detailed calculations for off-ramp spillback check are presented in
Appendix A.
Step 4B: Check for Queue Spillback (On-Ramp)

Queue spillback into a surface street intersection (or upstream freeway facility)
can occur when the freeway merge segment has insufficient capacity to process
the ramp demand. During this step, the methodology evaluates the network to
determine whether there is queue spillback from a freeway on-ramp onto
upstream facilities. Exhibit 38-14 illustrates the process for conducting a queue
spillback analysis at on-ramps.
When the freeway facility operates at oversaturated conditions (at least one
segment with LOS F), on-ramp queues are computed using the Freeway Facility
Oversaturated Segment evaluation procedure (HCM Chapter 25), through the
parameter ONRQ (Equation 25-21). The parameter ONRQ(i, t, p) is defined as the
“unmet demand that is stored as a queue on the on-ramp roadway at node i
during time step t in time interval p (veh)”

Version 1.0 Page 73

Exhibit 38-14
Spillback Check Procedure for
On-Ramps
Appendix B details the calculations used to estimate the on-ramp demand

based on the intersection operation as well as the procedures for conducting the
on-ramp spillback check.

Page 74 Version 1.0

Step 5A: Compute Operating Speeds for Individual Lanes Along the
Freeway Facility
Along freeway facilities, operational performance is determined based on the
density and speed at each segment along the network. The average travel time
for each segment can be derived based on the respective average speeds.
For a system analysis, the speed along a segment is function of:
• Estimated speeds for individual lanes;
• Probability that a lane will be selected by the subject O-D.
To estimate the speeds and capacities for individual lanes, a set of models
have been developed for each type of freeway segment considering the total
number of mainline freeway lanes. These models are valid only for
undersaturated conditions, and they predict the Lane Flow Ratio (LFR) for each
lane. They are of the form:
𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 𝑣/𝑐 + 𝑏
Equation 38-5
𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 Equation 38-6
where
𝑎 = multiplicative calibration parameter (Equation 38-C3, Equation 38-C5, The full methodology to predict lane by
and Equation 38-C7); lane speeds on freeway facilities is
discussed in Appendix C.
𝑏 = additive calibration parameter (Equation 38-C4, Equation 38-C6, and
Equation 38-C8);
𝐿𝐹𝑅 = share of the total flow on lane 𝑖, where 𝑖 ranges from 1 to n-1 (n = total
number of segment lanes);
𝐿𝐹𝑅 = share of the total flow on the leftmost lane (lane n); and
𝑣/𝑐 = volume/capacity ratio 0 < 𝑣/𝑐 ≤ 1 .
Using these LFR values, the methodology next estimates the lane-by-lane
free-flow speeds and capacities. These are used to obtain the speeds of each lane
using the speed-flow models defined in HCM Equation 12-1.
The LFR models and their coefficients, along with the procedures for
estimating lane-by-lane free-flow speeds, capacities, and speeds are provided in
Appendix C. These models can be used to analyze basic, merge, diverge and
weaving segments and mainline freeways with two to four lanes.
Freeway segments with 5 or more lanes were not modeled due to insufficient
data. Limited field observations for these facilities indicate that flow distributions
become more homogenous at wider segments. Therefore, the flow distribution
for these segments can be estimated as:
𝑣
𝐿𝐹𝑅 = Equation 38-7
𝑛
where
𝑣 = segment entering demand (pc/h) and
𝐿𝐹𝑅 = share of the total flow on lane 𝑖, where 𝑖 ranges from 1 to n (n = total
number of segment lanes).

Version 1.0 Page 75

For all segment types the share of flow is estimated on the mainline
upstream of the segment. The oversaturated portion of the speed-flow curve
(when density is greater than density at capacity) cannot be addressed by the
speed flow models, as this is a limitation of the existing methods. The lane-by-
lane flows for oversaturated conditions are estimated using the procedures of
Chapter 25, adjusted to determine the incoming and outgoing flow on a lane-by-
lane basis. If off-ramp queue spillback occurs in the freeway facility, then the
methodology in Appendix A provides a procedure to determine the lane-by-lane
flow distribution.
The probability that a given lane is selected depends on the type of O-D. For
segments where a driver enters (merge segment) or leaves a freeway facility
(diverge segment), the probability of lane selection is shown in Exhibit 38-15
(assuming right-side ramps).
Lane choice probability for lane i Number of lanes in the segment
Exhibit 38-15
2 3 4+
Probability of Lane Choice for
p1 0.90 0.90 0.90
Entry/Exit Segments on
p2 0.10 0.05 0.05
Freeway Facilities
p3 - 0.05 0.05
p4+ - - 0
For other segments within a freeway facility the probability of choice for a
given lane i is equal to the Lane Flow Ratio of lane i (LFRi), defined as the
percentage of the total flow assigned to lane i:
Equation 38-8 𝑝 = 𝐿𝐹𝑅

This concept is illustrated in Exhibit 38-16 for a 3-lane freeway facility with 9
segments. The exhibit shows the lane choice probabilities for the O-D where the
traveler enters the freeway facility on segment 2 (merge) and leaves the freeway
on segment 8 (diverge). For segments 2 and 8, the choice probabilities for lanes 1,
2 and 3 are 0.90, 0.05 and 0,05 respectively (Exhibit 38-15). For segments 3
through 8, the probabilities of lane choice are equal to LFR (Equation 38-3),
calculated for each lane of each segment.
Exhibit 38-16
Illustration of Lane Choice
Probabilities Along a Freeway
Facility
The speed for each segment is then computed as the sum of products of
speeds for each lane and the corresponding probability of lane choice:
Equation 38-9 𝑆 = 𝑝 ×𝑠

Page 76 Version 1.0

where
𝑆 = expected speed for the segment (mi/h)
𝑝 = probability that lane i is selected
𝑁 = number of lanes in the segment
𝑆 = speed at lane i (mi/h) (Equation 38-C14)
Step 5B: Compute Speeds for Urban Street Segments

For urban street facilities, the speeds along each segment are calculated using
the Chapter 18, Urban Streets Segments procedures. However, for the
intersection at the ramp junction, the control delay value for the corresponding
movement (typically right- or left-turn movement into the on-ramp) must be
used in the analysis. If there is queue spillback from the on-ramp into the urban
street intersection, the increased control delay of the movement towards the on-
ramp is obtained using the methodology used in Appendix B.
Step 6: Compute Travel Times for Each Segment

This step calculates the travel times for each segment using the speeds
obtained in Steps 5A and 5B by dividing each segment’s length by its respective
speed:
𝐿 Equation 38-10
𝑇𝑇 =
1.47 × 𝑆
where
𝑇𝑇 = travel time for segment i (s)
𝐿 = length of segment i (mi)
𝑆 = speed for segment I, depending on the facility:
If a freeway facility: S = Se (expected speed), from Equation 38-9
If a urban street facility: S = St,seg (travel speed), from Equation 18-15
Step 7: Compute Travel Time for Freeway Ramps

Ramp speeds can be obtained through the following equation:
𝑣 Equation 38-11
𝑆 = 1 − 0.109 × ×𝑆
1000
where
𝑆 = ramp speed (mi/h)
𝑣 = ramp demand flow rate (pc/h)
𝑆 = ramp free-flow speed (mi/h)
The speed-flow relationship for ramps is linear and speed decreases with
higher ramp flows, as shown in Exhibit 38-17. The maximum allowed values of
vR are bounded by ramp capacity, consistent with guidance provided by Chapter
14 – Merge and Diverge segments (Exhibit 14-12).

Version 1.0 Page 77

Exhibit 38-17
Speed-flow Curves for
Freeway Ramps
For ramps with lower values of free-flow

speed, the threshold value of 45 pc/h/ln
for density at capacity is not feasible as it
would result in ramp capacity values
The travel time along freeway ramps is calculated by dividing the ramp
inconsistent with Exhibit 14-12. The length by its respective speed. When an O-D includes an off-ramp, the control
values of density at capacity increases as delay for the corresponding movement at the at-grade intersection must also be
free-flow speed goes down. These values
are used to estimate ramp queue lengths added to the off-ramp travel time. This calculation is consistent with the Urban
in case of off-ramp queue spillback, as Streets Facilities methods, where each segment’s travel time includes the control
discussed in Appendix A.
delay of the corresponding movement at the downstream intersection.
For off-ramps:
Equation 38-12 𝐿
𝑇𝑇 = +𝑑 +𝑎
1.47 × 𝑆
For on-ramps:
Equation 38-13 𝐿
𝑇𝑇 = +𝑎
1.47 × 𝑆
where
𝑇𝑇 = ramp travel time (s)
𝑆 = ramp speed (mi/h)
𝐿 = ramp length (ft)
𝑑 = control delay of the corresponding movement in the downstream
ramp terminal (s); applicable for off-ramps only
𝑎 = delay due to acceleration or deceleration, assumed to be 5s
In the case of queue spillback, Appendix A describes the procedure for
estimating the speed at the ramp, which uses a procedure similar to the
Oversaturated Segment Evaluation method described in HCM Chapter 25.
Off-ramp Queue Spillback

If the ramp roadway is the bottleneck, the off-ramp flow will be constant
(equal to the ramp roadway capacity), with the prevailing density equal to the
ramp density at capacity. The ramp speed is then computed as equal to the ramp
free-flow speed;
If the downstream intersection is the bottleneck, queues will build at the
intersection and limit the number of vehicles that can exit the ramp roadway and
enter the intersection. As a result, the number of vehicles (NV) stored inside the

Page 78 Version 1.0

ramp roadway will increase until the limit value of jam density. The NV
parameter for the ramp roadway is computed every time step (15 seconds) and
then aggregated to the 15-minute period to compute the average density at the
ramp roadway. Similarly, the flow through the ramp roadway is aggregated to
15-minutes and then the speed at the off-ramp is obtained through Equation 12-1,
which is repeated here for convenience: below:
𝑆 = 𝐹𝐹𝑆 , 𝑖𝑓 𝑣 ≤ 𝐵𝑃
𝑆 = 𝐹𝐹𝑆 − 𝑖𝑓 𝐵𝑃 < 𝑣 < 𝑐
where
𝑆 = mean speed of a basic segment (mi/h)
𝐹𝐹𝑆 = adjusted free-flow speed (mi/h)
𝑐 = adjusted segment capacity (pc/h/ln)
𝐵𝑃 = breakpoint (pc/h/ln)
𝐷 = density at capacity, typically 45 pc/mi/ln
𝑣 = adjusted 15-min demand flow rate (pc/h/ln)
On-ramp Queue Spillback

If the on-ramp demand is greater than the merge capacity or any active ramp
metering, the number of vehicles (NV) stored in the on-ramp will be increased at
every time step by the difference between vehicles that are discharged from the
upstream intersection and the number of vehicles that are discharged into the
freeway. Similar to off-ramp bottlenecks that form due constraints at a
downstream intersection, flows and density values at the on-ramp are computed
at every time step (15 seconds) and then aggregated to a 15-minute time period.
Next, the speed is computed through Equation 12-1.
Step 8: Compute Travel Times for the Network and Each O-D
This step computes the total travel time TTO-D for the network as the sum of
travel times over all segments along the route. For multi-period analysis, it is
important that the travel time for the correct time period at each segment is
selected, as a long O-D may encompass several time periods. Exhibit 38-18
presents a sample calculation for a facility with two time periods (15 minutes
each). The first segment in the O-D is traversed during Time Period 1, and the
Cumulative Travel Time column is updated with the respective value.
Subsequent segments follow the same procedure until the cumulative travel time
exceeds the length of the first time period (900 seconds). For the next segment in
the network, travel times from Time Period 2 are added to the Cumulative Travel
Time. This procedure is then repeated until the final segment is reached. The
total travel time is obtained as the last value of the Cumulative Travel Time
column

Version 1.0 Page 79

Segment Travel Time

Selected Active Cumulative
Segment (s)
Travel Time Travel
ID Time Time
Time (s) Period Time (s)
Period 1 Period 2
Exhibit 38-18 1 34 28 34 TP 1 34
Sample Calculation of Total 2 26 29 26 TP1 60
Travel Time Using Multi- 3 73 86 73 TP1 133
Period Analysis 4 345 390 345 TP1 478
5 185 195 185 TP1 663
6 310 359 310 TP1 973
7 240 240 240 TP2 1213
8 120 122 122 TP2 1335
9 20 18 18 TP2 1353
10 45 53 53 TP2 1406
Total travel time (s): 1406
* Cells shaded in gray highlight the selected Time Period applicable to each segment within
the O-D
Step 9: Compute Performance Measures for Segments

The last step in the methodology computes performance measures for each
of the segments in the network, using the methods of the respective chapters.
Also, the mean travel time index (TTImean,O-D) for a specific O-D can be calculated
for each segment and for the network by dividing the O-D total time TTO-D by the
respective free-flow total time (Equation 38-14). The free-flow travel time TTFF
can be obtained by repeating Steps 1 through 8 for free-flow conditions.
Equation 38-14 𝑇𝑇
𝑇𝑇𝐼 , =
𝑇𝑇 ,
where
𝑇𝑇 = total travel time for a specific O-D (s)
𝑇𝑇 , = free-flow travel time for a specific O-D during (s)
The free-flow travel time 𝑇𝑇 , can be obtained by applying the

methodology steps for the subject O-D assuming free-flow conditions. Exhibit 38-
19 provides guidance on key input parameters to be considered for such analysis.

Page 80 Version 1.0

Performance measure Reference parameter Input value
Freeway Facilities
Lane flow ratio (LFR) v/c 0.1
Speed by lane Free-flow speed by lane (FFSi) Equation 38-C9
Urban Street Segments
Travel speed Running time Equation 18-7
Urban Street Intersections Exhibit 38-19
Reference Input Values
Control delay - Signalized Intersections Demand-to-capacity ratio (X) 0
for O-D Analysis at
Control delay - TWSC Intersections Movement demand (vx) 0 Free-Flow Conditions
Control delay - AWSC Intersections Demand-to-capacity ratio (x) 0
Control delay - Roundabouts Demand-to-capacity ratio (x) 0
Freeway ramps
Ramp speed Ramp free-flow speed Analyst input
The computation of free-flow performance measurements for different

facility types is discussed next.
Freeway Facilities
At free-flow, the speed at freeway segments is computed as equal to their
free-flow speed. When a lane-by-lane analysis is applied, the methodology
computes the free-flow speed for each lane (Equation 38-C9).
Next, the probabilities of lane choice on each segment are calculated for each
segment. If the subject segment is a entry/exit segment (segments where the
driver enters or leaves the freeway facility, as illustrated in Exhibit 38-16), the
lane choice probabilities are obtained from Exhibit 38-15. For other segments, the
lane choice probability is equal to its LFR (Equation 38-5). For the calculations of
LFR under free-flow conditions, a value of v/c = 0.1 is recommended to provide
results consistent with field data for free-flow conditions. Due to the log form of
the LFR equation (Equation 38-5), using v/c = 0 is mathematically unfeasible, and
very low values of v/c would yield unrealistic results
Urban Street Segments

The travel speed along urban street segments (Equation 18-15) is calculated
as a function of the segment running time (18-7), as shown:
3,600𝐿
𝑆 , =
5,280 𝑡 + 𝑑
6.0 − 𝑙 3,600𝐿
𝑡 = 𝑓 + 𝑓 + 𝑑 , +𝑑
0.0025𝐿 5,280 𝑆
where
𝑆 , = travel speed of through vehicles for the segment (mi/h) (s)
𝑡 = segment running time (s)
𝑙 = start-up lost time (2s if signalized, 2.5s if stop or yield-controlled)
𝐿 = segment length (ft)

Version 1.0 Page 81

𝑑 = control delay at the downstream intersection (s)

𝑆 = segment free-flow speed (mi/h)
𝑓 = control-type adjustment factor
𝑓 = segment length (ft)
𝑑 , = delay due to left and right turns into intersection i (s/veh)
𝑑 = delay due to other sources along the segment (e.g., curb parking or
pedestrians) (s/veh)
As shown by Equation 18-7, the running time along an urban street segment
is not directly affected by variations in demand. Therefore, free-flow running
time is calculated according to Equation 18-7. The only parameter in the segment
travel speed that accounts for congestion is the control delay at specific O-D
related movement at the downstream intersection, which is discussed next.
Urban Street Intersections

When intersections are analyzed as part of an urban street facility, the
computed control delay is taken into account when estimating the travel speed of
the upstream segment. Even at free-flow, intersections still experience a small
amount of delay intrinsic to their operation.
The control delay for a given lane at a signalized intersection is provided by
Equation 19-18:
𝑑 =𝑑 +𝑑 +𝑑
where
𝑑 = control delay (s/veh)
𝑑 = uniform delay (s/veh)
𝑑 = incremental delay (s/veh)
𝑑 = initial queue delay (s/veh)
At free-flow conditions, the values of 𝑑 and 𝑑 are equal to zero. Therefore,
the free-flow control delay is equal to the value of uniform delay (𝑑 ) computed
for a demand-to-capacity ratio 𝑋 = 0.
TWSC Intersections
The control delay d for TWSC intersections (Rank 2 through Rank 4
movements) is computed through Equation 20-64:
⎡ 3,600 𝑣 ⎤
3,600 ⎢𝑣 𝑣 𝑐 , 𝑐 , ⎥
𝑑= + 900𝑇 ⎢ −1+ −1 + ⎥+5
𝑐 , 𝑐 , 𝑐 , 450𝑇
⎢ ⎥
⎣ ⎦
where
𝑐 , = capacity of movement x (veh/h)
𝑣 = flow rate for movement x (veh/h)
𝑇 = analysis time period (0.25 h for a 15-min period) (h)

Page 82 Version 1.0

At free-flow conditions, the demand 𝑣 is set at zero, which allows Equation

20-64 to be reduced to the following form:
3,600 Equation 38-15
𝑑= +5
𝑐 ,
AWSC Intersections
The control delay d for AWSC intersections is computed through Equation
21-30:
ℎ 𝑥
𝑑 = 𝑡 + 900𝑇 𝑥 − 1 + 𝑥−1 + +5
450𝑇
where
𝑡 = service time (s)
𝑥 = volume-to-capacity ratio of the subject lane
ℎ = departure headway (s)
At free-flow conditions, the demand-to-capacity ratio 𝑥 is set at zero, which
allows Equation 21-30 to be reduced to the following form:
Equation 38-16
𝑑 =𝑡 +5
The estimation of service time 𝑡 requires an iterative and computationally
intensive procedure described in the AWSC Intersections methodology (Chapter
21). It must be performed setting x = 0.
Roundabouts
The control delay d for roundabouts is computed through Equation 22-17:
3,600
3,600 𝑥
𝑑= + 900𝑇 𝑥 − 1 + 𝑥−1 + 𝑐 + 5 × 𝑚𝑖𝑛 𝑥, 1
𝑐 450𝑇
where
𝑥 = volume-to-capacity ratio of the subject lane
𝑐 = capacity of the subject lane (veh/h)
Similar to TWSC intersections, setting the demand-to-capacity ratio x=0

reduces Equation 22-17 to a simpler form:
3,600
𝑑= +5 Equation 38-17
𝑐 ,
Freeway Ramps
Freeway ramp speeds at free-flow are equal to the ramp free-flow speed 𝑆 ,
as provided by the analyst, and do not require additional adjustments.

Version 1.0 Page 83

4. EXAMPLE PROBLEMS
This section presents four example problems illustrating the evaluation of

networks and addressing several cases of spillback into freeways and into urban
street facilities.
Example
Problem Description Application
Exhibit 38-20 1 O-D Based Travel Time Estimation For I-75 NB Operational Analysis
List of Example Freeway in Gainesville, FL
Problems 2 I-10 On-Ramp Spillback Check in Baton Rouge, LA on Operational Analysis
different ramp terminal intersections
2a Signalized intersection ramp terminal Operational Analysis
2b TWSC ramp terminal Operational Analysis
2c AWSC ramp terminal Operational Analysis
3 Queue Spillback Analysis for a Freeway-to-Freeway Operational Analysis
Ramp in Miami, FL.
4 On-Ramp Queue Spillback Analysis into a Single-Lane Operational Analysis
Roundabout in Los Angeles, CA
EXAMPLE PROBLEM 1: O-D BASED TRAVEL TIME ESTIMATION FOR I-75

NB FREEWAY IN GAINESVILLE, FLORIDA
A freeway section of I-75 NB, with length of 8.72 miles in Gainesville, Florida
is evaluated to obtain selected O-D travel times. Four consecutive interchanges
are evaluated: (a) Williston Rd., (b) Archer Rd., (c) Newberry Rd., and (d) NW
39th Ave., shown in Exhibit 38-21.
Example Problems Chapter 38 System Analyses (Draft)

Page 84 Version 1.0

Exhibit 38-21
Example Problem 1
Network Interchanges,
with indication of origins
and destinations:
(a) Williston Rd.(b)
Archer Rd.(c) Newberry
Rd.(d) NW 39th Ave.
When a freeway facility is analyzed in isolation, each on-ramp is a unique

origin and each off-ramp is a unique destination. However, for a systems
analysis approach, these must be expanded to include turning movements at the
urban street intersections. Each turning movement is a different origin /
destination with a distinct travel time.
The subject network has three freeway lanes throughout its entire length.
Four on-ramps and four off-ramps are connected to surface streets. Exhibit 38-22
provides the schematic representation of the freeway network, with five possible
origins (A, C, E, G and I) and five possible destinations (B, D, F, H and J).
Exhibit 38-22
Freeway Origins and
Destinations for Example
Problem 1
The analysis steps for evaluating this network are discussed below.
Step 1: Define Spatial and Temporal Analysis Scope

The first step in the methodology is the selection of origin and destination
nodes in the network. For each selected O-D pair, the methodology lists the
segments traversed and their travel times are estimated.
Chapter 38 System Analyses (Draft) Example Problems

Version 1.0 Page 85

As shown in Exhibit 38-21, the system has 9 nodes and 72 O-Ds, shown in
Exhibit 38-23. This case study estimates the travel time for the O-D from Archer
Rd. East (D) to NW 39th Ave (H), as depicted in red in Exhibit 38-21.
Exhibit 38-23 Destinations

O-D Matrix for Example Origins A B C D E F G H J
Problem 1
A - A-B A-C A-D A-E A-F A-G A-H A-J
B B-A - B-C B-D B-E B-F B-G B-H B-J
C C-A C-B - C-D C-E C-F C-G C-H C-J
D D-A D-B D-C - D-E D-F D-G D-H D-J
E E-A E-B E-C E-D - E-F E-G E-H E-J
F F-A F-B F-C F-D F-E - F-G F-H F-J
G G-A G-B G-C G-D G-E G-F - G-H G-J
H H-A H-B H-C H-D H-E H-F H-G -
J J-A J-B J-C J-D J-E J-F J-G J-H -
The total average travel time for each O-D can be obtained by adding the
travel times on each segment plus any delay experienced at all intersections
traversed. Travel time for each ramp traversed is also computed.
The O-D from node D to node H will traverse two urban street facilities, as
shown in Exhibit 38-24:
• Archer Rd. Westbound, comprised of two urban street segments and two
signalized intersections (SW 40th Blvd. and I-75 NB on-ramp);
• NW 39th Ave. Eastbound, comprised of one urban street segment and
two signalized intersections (I-75 NB off-ramp and NW 95th Blvd).
Exhibit 38-24
Urban Street Facilities
Evaluated for Example
Problem 1
The movements that must be

accounted for their control
delay in the traversed
(a) Urban Street Facility 1: Archer Rd. WB (b) Urban Street Facility 2: NW 39th Ave. EB
intersections are specified in
parentheses in Exhibit 38-24
The O-D also includes the freeway facility (I-75 NB), starting at segment 8
and ending at segment 16 (Exhibit 38-22). The on-ramp and off-ramp at the
boundary ends of the facility are also included in the travel time evaluation.
Exhibit 38-25 summarizes the list of segments, ramps and intersections
traversed for this O-D.
Facility 1 - Archer Rd WB Facility 2 - I-75 NB Facility 3 - NW 39th Ave.

Ramp
Exhibit 38-25 Intersections Segments Junctions Segments Intersections Segments
List of Segments Included 8, 9, 10, 11, I-75 NB -
Within D-H SW 40th Blvd. SW 37th Blvd - Archer Rd. On- I-75 NB (NB-
12, 13, 14, NW 95th
(WB-Through) SW 40th Blvd Ramp Right)
15, 16 Blvd.
I-75 NB (WB- SW 40th Blvd. - NW 39th Ave NW 95th Blvd.
- -
Right) I-75 WB Off-Ramp (EB-Through )
The temporal scope of the analysis must also be defined. Given the short
length of the subject network, a single-period analysis will be performed. When

Page 86 Version 1.0

the final travel time is obtained, its value will be checked and if it exceeds the 15-
minute study period the temporal scope of the study will be reevaluated.
Step 2: Provide Input Parameters for Freeway and Urban Street

Analysis
For this step, the facilities within the subject O-D must be modeled
individually using the respective HCM methods.
Freeway Facility – I-75 NB

The freeway facility was divided into 19 segments for capacity analysis and
modeled according to the methodology described in Chapter 10, Freeway
Facilities Core Methodology. The detailed input data for each segment are
presented in Exhibit 38-26.
Ramp Accel/ Ramp Exhibit 38-26

Segment Length Mainline Flow Grade Flow Rate Decel Lane Length Input Data for Freeway
ID Type (ft) Rate (veh/h) (%) (veh/h) Length (ft) (ft) Facility Analysis
1 Basic 2220 4800 0 - - -
2 Diverge 1500 4800 -2 480 800 900
3 Basic 990 4320 0 - - -
4 Merge 1500 4240 0.5 580 1124 1000
5 Basic 1600 4900 3 - - -
6 Diverge 1500 4900 0 364 541 1650
7 Basic 1800 4536 0 -
8 Merge 1500 4536 1.7 868 438 2250
9 Basic 6300 5404 0 - - -
10 Basic 5385 5404 0 - - -
11 Diverge 1500 5404 -1 936 490 660
12 Basic 2014 4468 0 -
13 Merge 1500 4468 1.8 380 1443 1850
14 Basic 6494 4848 0 - - -
15 Basic 2480 4848 0 - - -
16 Diverge 1500 4848 1 960 377 2380
17 Basic 1000 3888 0 - - -
18 Merge 1500 3888 -2.2 148 747 2200
19 Basic 3760 4036 0 - - -
Additional input parameters for the urban street facility are as follows:
• Urban area, 3 lanes in each direction;
• Base FFS: 75.4 mi/h;
• Ramp FFS: 35 mi/h;
• Ramp side: Right;
• Lane width: 12 ft;
• Right side clearance: 10 ft;
• Traffic composition: 2% trucks on both freeway and ramps; and
• Familiar facility users.
Urban Street Facility 1 – Archer Rd Westbound

This facility contains two signalized intersections and two segments (Exhibit
38-24(a)). The corresponding input data are presented in Exhibit 38-27 and
Exhibit 38-28.

Version 1.0 Page 87

Exhibit 38-27 Eastbound Westbound Northbound Southbound

Input Data for Intersection Intersection Parameter L T R L T R L T R L T R
Analysis – Archer Rd. WB
Archer Rd. @ Demand (veh/h) 320 2064 - - 524 548 104 - 260 - - -
I-75 NB Phase Split (s) 20 80 - 70 20 30 - - - - - -
Archer Rd. @ Demand (veh/h) 120 2348 88 36 864 548 60 208 96 36 480 304
SW 40th Blvd. Phase Split (s) 20 50 - 20 50 - 20 30 - 20 30 -
Exhibit 38-28 Input Parameter SW 40th Blvd - I-75 WB SW 37th Blvd - SW 40th Blvd
Input Data for Segment Segment length (ft) 530 1288
Analysis – Archer Rd. WB Speed limit 45 45
Through lanes 3 3
Restrictive median length (ft) 0 0
Upstream Intersection width (ft) 50 50
Curb proportion (%) 70 70
Base FFS (mi/h) 46.42 46.42
Running Speed (mi/h) 32.24 41.37
Running time (s) 11.21 21.23
Percent of base FFS 50.84 52.04
Urban Street Facility 2 – NW 39th Ave. Eastbound

This facility contains two signalized intersections and one segment (Exhibit
38-24(b)). The corresponding input data are presented in Exhibit 38-29 and
Exhibit 38-30.
Exhibit 38-29 Eastbound Westbound Northbound Southbound

Input Data for Intersection Intersection Parameter L T R L T R L T R L T R
Analysis – NW 39th Ave. EB NW 39th @ I- Demand (veh/h) 72 1416 - - 872 76 336 - 624 - - -
75 NB Phase Split (s) 20 80 - - 70 - 20 30 - - - -
NW 39th @ Demand (veh/h) 180 1772 68 96 640 128 84 160 76 60 228 120
NW 95th Blvd. Phase Split (s) 20 50 - 20 50 - 20 30 - 20 30 -
Input Parameter I-75 NB - NW 95th Blvd

Segment length (ft) 510
Speed limit 45
Exhibit 38-30 Through lanes 2
Input Data for Segment Restrictive median length (ft) 0
Analysis – NW 39th Ave. EB Upstream Intersection width (ft) 50
Curb proportion (%) 70
Base FFS (mi/h) 46.42
Running Speed (mi/h) 31.53
Running time (s) 11.03
Percent of base FFS 58.38
Additional input parameters for this facility are as follows:

• Base saturation flow rate: 1,900 veh/h/ln;
• Traffic composition: 0% heavy vehicles;
• Cycle length: 120s;
• Grade: 0%;
• Arrival type: 3;
• Speed limit: 45 mi/h;

Page 88 Version 1.0

• Yellow change interval: 4s;

• Red clearance interval: 0s; and
• No pedestrians.
Step 3: Balance Demands at Freeway-Urban Street Interface

After each facility along the O-D is modeled individually, this step checks
the consistency of traffic flows in the interfaces between urban streets and
freeway facilities.
For each of the four on-ramps along the freeway facility, there are two
movements at the corresponding urban street intersection that contribute to the
on-ramp demand: eastbound left-turn (EBL) and westbound right-turn (WBR).
Exhibit 38-31 compares the demand volumes at the intersection (𝑣) with their
respective movement capacities (c), and the minimum of each is added to the
total on-ramp demand 𝑣 . As observed, no movement operates with 𝑣/𝑐 > 1.0,
therefore no adjustments are required, and the on-ramp demands 𝑣 are equal to
the sum of the turning movement demands at the intersection.
Parameter
Intersection Movement Demand c Merge Exhibit 38-31
v/c min(v, c)
(v), veh/h (veh/h) demand vR Demands at the On-Ramps
Along the Freeway Facility for
Williston Rd. EBL 160 0.15 1055 160
580 Example Problem 1
@ I-75 NB WBR 420 0.43 985 420
Archer Rd. @ EBL 320 0.34 935 320
868
I-75 NB WBR 548 0.53 1037 548
Newberry Rd. EBL 216 0.25 862 216
380
@ I-75 NB WBR 164 0.14 1163 164
NW 39th Ave. EBL 72 0.14 501 72
148
@ I-75 NB WBR 76 0.075 1012 76
Next, the off-ramp volumes are checked against the intersection turning
movement demands. The first check determines whether there are bottlenecks
along the freeway facility that may meter off-ramp demands. Exhibit 38-32
shows the estimated LOS for all 19 segments in the freeway facility. Since no
segment is oversaturated, the off-ramp demand is not metered, and no
adjustments are necessary.
Segment Number Exhibit 38-32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 LOS for the Freeway
Type B D B M B D B M B B D B M B B D B M B Segments of Example Problem
LOS D D D D D D D E E E D D C D D D C C C 1
Segment types: Basic (B), Merge (M), Diverge (D)
The second check compares the off-ramp demands to the respective ramp
roadway capacity, as shown in Exhibit 38-33. The demand does not exceed
capacity for any of the ramps, therefore no adjustments to the intersection
volumes are performed.

Version 1.0 Page 89

Exhibit 38-33 Off-Ramp Demand Ramp Ramp Roadway Ramp

Demands at the Off-Ramps Segment (pc/h) Lanes Capacity (pc/h) v/c
Along the Freeway Facility for 2 480 1 2000 0.24
Example Problem 1 6 364 1 2000 0.18
11 936 1 2000 0.47
16 960 2 4000 0.24
Step 4: Check for Queue Spillback

The next step determines whether there are bottlenecks at the on-ramps and
off-ramps.
Off-ramp spillback check

The procedure presented in Exhibit 38-10 is applied to each of the four off-
ramps in the freeway facility:
• Capacity of ramp roadway: The off-ramp demand was previously compared
to ramp roadway capacity (Exhibit 38-33), and no capacity constraint was
detected.
• Queue length estimation: The back-of-queue length (95th percentile) in the
downstream terminals (signalized intersections) are obtained through the
HCM methodology (Chapter 31) and are presented in Exhibit 38-34. The
resulting 95th percentile queues are expected to be within the available
turn bay lengths at the intersection, except for the left-turn movement at
Williston Rd. (freeway segment 2). The queue length will spillback into
the ramp roadway, and the next check will evaluate if it its storage is
adequate.
• Queue storage ratio: Any queues exceeding the available turn bay length at
the intersection must be checked against the available storage along the
ramp roadway. For single-lane off-ramps, any queues upstream of the
intersection will share the same storage and must then be aggregated. If a
ramp has two or more lanes, the analyst must determine how ramp lanes
are channelized relative to intersection approaches, based on the off-ramp
geometry. As shown in Exhibit 38-33, only the off-ramp at segment 16
(NW 39th) has two lanes - the ramp leftmost lane L2 is connected to left-
turn movement, while the ramp rightmost lane L1 is connected to the
right turn movement. For this step, the only movement that must be
evaluated is the left turn at Williston Rd. The queue length upstream of
the intersection is compared to the available ramp length, with a resulting
queue storage ratio RQ = 436/900 = 0.48 < 1.0. Therefore, spillback is not
expected to occur along the off-ramps.

Page 90 Version 1.0

2 6 11 16
(Williston (Archer (Newberry (NW 39th
Rd.) Rd.) Rd.) Ave.)
Parameter LT RT LT RT LT RT LT RT
Ramp length (ft) 900 1650 660 2380
Number of Ramp Lanes 1 1 1 2 Exhibit 38-34
Upstream Ramp Lane L1 L1 L1 L2 L2 L1 Queue Length Estimation and
Turn Bay Length (ft) 250 210 480 480 800 800 1260 1200 Queue Storage Checks for
Back of Queue Length Q95 (ft/ln) 689 21 120 363 223 363 193 482 Off-Ramps
Exceeding Turn Bay Queue Length (ft) 439 - - - - - -
Queue Storage Ratio (RQ) 0.49 - - - - - - -
On-ramp Spillback Check

On-ramp queue spillback is expected to occur when a freeway merge
segment operates above capacity or when there is active ramp metering with a
rate lower than demand. As shown in Exhibit 38-32, no merge segments operate
at LOS F and no ramp metering is present, therefore spillback is not expected to
occur.
Step 5A: Obtain Speeds for Individual Lanes in the Freeway Facility
First, the flow distribution among freeway lanes must be determined for the
segments in the freeway facility. Using the estimated flow rates, lane speeds are
computed as shown in Exhibit 38-35. The highlighted rows (8 through 16)
represent the segments included in the O-D and used to compute the overall
travel time. The rightmost lane is labeled Lane 1.
The expected speed for each segment is then computed as the sum of
products of speeds for each lane and the corresponding probability of lane The step by step calculations
choice, as provided in Equation 38-9. (Exhibit 38-36). to determine lane-by-lane
flows and speeds on segment
16 (diverge) are presented in
Even though the travel times of the remaining segments are not directly used an example problem under
in calculating the O-D travel time, the entire facility must be analyzed, as any Appendix C
existing bottleneck would affect the performance of other segments in the

facility. For this example, no segment operates under LOS F, and no queues are
developed at the ramps connecting nearby urban street streets.

Version 1.0 Page 91

Segment Segment Lane Flow Ratio (LFR) Lane Speed (mi/h)

Exhibit 38-35 ID LOS Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3
Flow Distribution and Speeds 1 C 0.286 0.351 0.362 66.5 71.3 77.7
for Freeway Segments 2 C 0.338 0.319 0.343 56.7 73.1 77.5
3 C 0.279 0.356 0.365 68.3 71.6 77.2
4 C 0.259 0.388 0.353 72.0 72.4 77.3
5 C 0.281 0.348 0.371 66.4 69.9 75.6
6 C 0.336 0.326 0.337 55.3 72.2 77.4
7 C 0.286 0.354 0.36 67.7 70.6 76.5
8 C 0.253 0.387 0.359 71.7 71.5 76.8
9 C 0.294 0.346 0.36 56.3 67.3 74.0
10 C 0.288 0.344 0.368 58.2 67.7 73.9
11 D 0.358 0.290 0.352 41.6 71.7 75.2
12 C 0.286 0.355 0.359 67.8 70.8 76.6
13 B 0.253 0.382 0.365 71.9 72.1 76.8
14 C 0.281 0.349 0.37 66.8 70.0 75.7
15 C 0.281 0.349 0.37 66.8 70.0 75.7
16 C 0.350 0.296 0.354 50.6 74.1 76.8
17 B 0.278 0.362 0.361 68.3 72.6 78.1
18 B 0.252 0.383 0.365 72.0 74.2 77.7
19 B 0.272 0.358 0.37 68.7 72.7 78.1
Bold rows represent the segments included in the O-D that are used to compute the total travel time
Exhibit 38-36 Lane Choice Probability

Estimated Speeds by Segment Segment Lane Speeds (mi/h) Expected Speed
for the Subject O-D
Based on Lane Choice ID (mi/h)
L1 L2 L3 L1 L2 L3
Probability and Speeds
8* 90.0% 5.0% 5.0% 71.7 71.5 76.8 68.4
9 29.4% 34.6% 36.0% 55.2 68.7 75.8 67.3
10 28.8% 34.4% 36.8% 57.3 68.8 75.4 67.9
11 35.8% 29.0% 35.2% 41.6 71.7 75.2 62.2
12 28.6% 35.5% 35.9% 69.3 72.5 78.7 73.8
13 25.3% 38.2% 36.5% 71.9 72.1 76.8 73.8
14 28.1% 34.9% 37.0% 67.0 71.3 77.2 72.3
15 28.1% 34.9% 37.0% 67.0 71.3 77.2 72.3
16* 90.0% 5.0% 5.0% 50.6 74.1 76.8 53.1
(*): Entry/exit segments: require mandatory use of the rightmost lane
Step 5B: Compute Travel Speeds for Urban Street Segments

The travel speeds for urban streets segments are calculated using the core
methodology of HCM Chapter 16, Urban Streets Segments, adjusted to consider
the relevant turning movements. Exhibit 38-37 shows the three urban streets
segments analyzed, with their associated movements at the intersection.
Exhibit 38-37 Input parameters

Speeds for Urban Streets
Segments Facility Segment Segment Base Running Segment Downstream Control Travel
length FFS Speed Running Intersection delay d speed
(ft) (mi/h) (mi/h) time (s) movement (s) (mi/h)
SW 40th Blvd -
Facility 1 530 46.42 32.24 11.21 Right 7.6 19.21
I-75 WB
(Archer
SW 37th Blvd -
Rd. WB) 1288 46.42 41.37 21.23 Through 15.12 24.16
SW 40th Blvd
Facility 2 I-75 NB - NW
510 46.42 31.53 11.03 Through 26.2 9.34
(NW 39th 95th Blvd
St. EB)

Page 92 Version 1.0

Step 6 – Compute Travel Times for Each Segment

The travel times for each segment in the freeway and urban street facilities
are computed by dividing the segment length by the travel speed (Exhibit 38-39
and Exhibit 38-38).
Facility Segment Travel Length Travel

Exhibit 38-38
Speed (ft) Time (s)
Travel Times for Urban
(mi/h)
Streets Segments
SW 40th Blvd. @ I-75 BB 19.21 530 18.8
Archer Rd. WB
SW 37th Blvd. @ SW 40th Blvd. 24.16 1288 36.4
NW 39th Ave. EB I-75 NB @ NW 95th Blvd. 9.34 1040 75.9
Segment ID Expected Speed (mi/h) Segment Length (ft) Travel Time (s) Exhibit 38-39
8 68.4 1500 15.0 Travel Times for Freeway
9 66.5 6300 64.6 Segments
10 67.2 5385 54.6
11 64.4 1500 15.9
12 72.0 2014 19.1
13 73.8 1500 13.9
14 71.2 6494 62.2
15 71.2 2480 23.7
16 53.1 1500 19.3
Step 7: Obtain Travel Times for Freeway Ramps

As shown, the ramps at the freeway facility operate at undersaturated
conditions. Therefore, ramp roadway speeds can be estimated using Equation 38-
11, as shown in Exhibit 38-40. For the off-ramp at segment 16, the control delay at
the downstream ramp terminal is included on the computation of the ramp total
travel time.
Ramp Control Ramp Exhibit 38-40

Ramp Ramp Ramp
Segment Speed Roadway Delay - Total Estimated Travel Times for
Flow FFS Length
ID (mi/h) Travel Ramp Travel Ramps Entering or Exiting the
(pc/h) (mi/h) (ft)
time (s) Terminal (s) Time (s) Freeway Facility
8 886 35 31.6 2250 48.5 - 48.5
16 980 35 31.3 1200 26.2 96.6 122.8
Step 8: Compute Travel Times for the Network and Each O-D
All segments within the subject O-D (E1-H1) are sorted according to the
travel sequence and their respective travel times are listed, as shown in Exhibit
38-41. The cumulative travel time for the O-D must also be computed to evaluate
if the network analysis is correctly contained within the temporal scope defined
in Step 1. For this example, a single 15-min analysis period was considered, for a
total time of 900s. Since the cumulative travel time does not exceed this boundary
value, all travel times obtained from time period 1 are valid for the analysis.

Version 1.0 Page 93

Exhibit 38-41 Facility Cumulative

Travel Time
Estimated Travel Times for Segment ID travel time
Type Name time (s) Period
Ramps Entering or Exiting the (s)
Freeway Facility Urban Archer SW 37th Blvd @ SW 40th Blvd 18.8 40.5 1
Street 1 Rd. WB SW 40th Blvd @ I-75 WB 36.4 76.8 1
On-ramp to I-75 NB 48.5 125.3 1
8* 15.0 140.3 1
9 63.8 204.1 1
10 54.1 258.2 1
11 16.5 274.6 1
Freeway I-75 NB 12 18.6 293.2 1
13 13.9 307.1 1
14 61.3 368.4 1
15 23.4 391.8 1
16* 19.3 411.0 1
Off-ramp to NW 39th Ave. 122.8 533.8 1
Urban NW 39th
I-75 NB - NW 95th Blvd 75.9 609.7 1
Street 2 Ave. EB
Total travel time (s): 609.7
Step 9: Compute Performance Measures for Segments

Since no spillback occurred in the subject study period, the performance
measures obtained by the respective HCM methods for each type of segment are
valid.

Page 94 Version 1.0

EXAMPLE PROBLEM 2: I-10 ON-RAMP SPILLBACK ANALYSIS IN BATON

ROUGE, LOUISIANA
This case study illustrates the application of the on-ramp spillback
methodology by evaluating operations at an interchange when there is queue
spillback originating from the on-ramp. There are three parts to the case study
with each one analyzing a different intersection type at the ramp terminal:
signalized, TWSC and AWSC. The main objective in each analyzed scenario is to
determine the new control delay for the movements affected by queue spillback.
All other parameters in the network (freeway design and traffic demand, and
intersection demand) are kept the same.
An urban network in Baton Rouge, LA is comprised of the following
facilities:
• One freeway facility (I-10)
• One urban street facility (Acadian Thruway), with four signalized
intersections:
o Perkins Rd.
o Acadian Center Rd.
o I-10 WB
o I-10 EB
The subject network has three freeway lanes throughout its entire length.
One interchange connects the freeway to an urban street network (Acadian
Thruway), as illustrated in Exhibit 38-42. The selected origin and destination
points for analysis are H and F, respectively, with the traveled segments
highlighted in red.

Version 1.0 Page 95

Exhibit 38-42
Example Problem 2 Network
Intersections:
(a) Perkins Rd.; (b) Acadian
Center; (c) I-10 EB;(d) I-10
WB
The freeway facility (I-10 EB) is modeled according to the Freeway Facilities
methodology (Chapter 10), while the ramp terminal is modeled according to its
respective intersection methodology. First a check is performed to confirm the
occurrence of queue spillback. Next, the respective spillback analysis is applied
to evaluate the impacts of queue spillback in the capacity of each movement at
the intersection. With the estimated reduced capacities at the intersection, the
control delay values considering queue spillback are computed and compared to
the delay values without consideration of queue spillback.
Exhibit 38-43 illustrates the schematic representation of the freeway network
in the eastbound direction. Segments 3 (merge) and 5 (diverge) connect the
freeway to the urban street facility (Acadian Thruway).

Page 96 Version 1.0

Exhibit 38-43
Origins and Destinations for
the freeway facility (I-10 EB)
in Baton Rouge, LA
The analyzed urban street facility comprises four signalized intersections and
three segments, as shown in Exhibit 38-44. The on-ramp terminal subject to
analysis is the I-10 EB intersection.
Exhibit 38-44
Acadian Thruway Urban
Street Facility
EXAMPLE PROBLEM 2, PART 1: SIGNALIZED INTERSECTION RAMP

TERMINAL
Part 1 of the example problem evaluates the impacts of queue spillback
originating from the I-10 EB on-ramp when the upstream ramp terminal is
signalized.
Input data
Signalized Intersection
The geometry of the intersection connected to the I-10 EB on-ramp (I-10 EB)
is shown in Exhibit 38-45. There are three movements leading into the on-ramp:
• NBR: One channelized, unsignalized right-turn lane;
• SBL: One exclusive left turn lane with a protected phase; and
• EBT: One through lane.

Version 1.0 Page 97

Exhibit 38-45
Geometry – Acadian Thruway
@ I-10 EB
The phasing sequence of the subject intersection is presented in Exhibit 38-

46. The north-south direction corresponds to the major street, while the minor
streets correspond to the freeway off-ramp and on-ramp. The intersection has a
leading left turn phase with a protected left turn movement (SBL).
Exhibit 38-46
Phasing Sequence – I-10 EB
Intersection
The demand volumes for each time period are presented in Exhibit 38-47.
Additional input data are summarized in Exhibit 38-48.
Eastbound Northbound Southbound

Exhibit 38-47
Demand Flow Rates (veh/h) – L T R T R L T
I-10 EB Intersection
Time Period 1 8 48 87 362 315 652 804
Time Period 2 16 96 20 1812 521 586 1759
Time Period 3 16 96 20 271 630 1071 717
Time Period 4 8 24 28 845 80 463 201

Page 98 Version 1.0


L T R T R L T
Exhibit 38-48
General Information Input Data – I-10 EB
Base Sat. Flow Rate (s0), veh/h 1900 1900 1900 1900 1900 1900 1900 Intersection
Arrival Type (AT) 3 3 3 3 3 3 3

Lane Width (W), ft 11 11 11 11 11 11 11
Heavy Vehicles % 5 5 5 5 5 5 5
Grade (Pg), % 0 0 0
Speed Limit, mi/h 35 35 35 35 35 35 35
Phase Information
Maximum Green (Gmax), s 20 20 - 53 - 47 100
Yellow Change Interval (Y), s 4.7 4.7 - 4.7 - 4.7 4.7
Red Clearance Interval (Rc), s 1 1 - 1 - 1 1
Minimum Green (Gmin), s 5 5 - 15 - 5 15
Start-Up Lost Time (lt), s 2 2 - 2 - 2 2
Green Extension (e), s 2 2 - 2 - 2 2
Passage (PT), s 2 2 - 2 - 2 2
Recall Mode Off Off - Off - Off Off
Dual Entry No No - Yes - No Yes
Freeway Facility (I-10 EB)

The freeway facility (I-10 EB) is divided in seven segments (Exhibit 38-49),
where segment 3 (diverge) and segment 5 (merge) connect to the subject
signalized intersection (Acadian Thruway).
Exhibit 38-49
Freeway Facility
Segmentation– I-10 EB
The geometric features of the freeway facility are summarized in Exhibit 38-
50.

Version 1.0 Page 99

Acceleration /
Segment Length Grade Ramp
Type deceleration
Exhibit 38-50 ID (ft) (%) length (ft)
lane length (ft)
Freeway facility (I-10 EB) -
Geometric Features 1 Basic 5280 0 - -
2 Diverge 1500 0 800 1139
3 Diverge 720 0 0 965
4 Basic 732 0 - -
5 Merge 1000 0 1000 924
6 Basic 1200 0 - -
7 Basic 900 0 - -
Spillback check – on-ramp

The first step in the spillback check analysis is to determine the on-ramp
demand flow rates for each time period, based on the demands at the signalized
intersection. For each time period, the demand (v) and capacities (c) are
compared for each movement that flows into the on-ramp (EBT, NBR and SBL).
The minimum value between demand and capacity for each movement is
computed and the merge demand vR is then computed as the sum of the three
movements.
The capacities for protected movements (EBT and SBL) are computed for
each time period. Due to the actuated control operation, the green times for these
movements vary by time period; therefore the method uses the average green
time for each phase and for each time period. The NBR movement is
unsignalized and therefore no capacity estimation is provided by HCM methods.
The capacity for this movement is computed by calculating the maximum
throughput through one cycle and then aggregating to an hourly flow rate.
During the phases when there are no conflicting movements discharging into
the on-ramp, the NBR maximum throughput is computed as its respective
saturation flow rate, considering the applicable adjustment factors fRT (for right-
turn movements) and fHV (for the presence of heavy vehicles). During the
transition time between consecutive phases, the throughput of the unsignalized
turning movement is also assumed to be equal to its saturation flow rate.
Therefore:
𝑠 , =𝑠 , ×𝑓 ×𝑓
where
sNBR,FF = saturation flow rate of NBR movement during the phases with no
conflicting flows (veh/h/ln)
s0,NBR = base saturation flow rate (1,900 pc/h/ln)
fRT = adjustment factor for right-turn vehicle presence in a lane group
fHVg = adjustment factor for heavy vehicles and grade
The adjustment factor for right-turn vehicle presence is computed using

Equation 19-13:
1 1
𝑓 = =
𝐸 1.18
where

Page 100 Version 1.0

ET = equivalent number of through cars for a protected right-turning

vehicle (1.18)
The adjustment factor for heavy vehicles and grade is computed using
Equation 19-10:
100 − 0.78𝑃 − 0.31𝑃
𝑓 =
100
100 − 0.78 × 5 − 0.31 × 0
𝑓 = = 0.961
100
where
PHV = percentage heavy vehicles in the corresponding movement group (5%)
PHV = approach grade for the corresponding movement group (0%)
Therefore, the saturation flow rate is computed as:

1
𝑠 , = 1,900 ×
× 0.961 = 1,547 𝑣𝑒ℎ/ℎ
1.18
Since there are conflicting movements discharging into the on-ramp (for
example, a protected left-turn), the NBR capacity is constrained as drivers yield
to the higher priority movement. The estimated discharge flow rate for the NBR
movement with a conflicting protected flow vprot can be obtained by the
following equation, based on HCM equation 31-100:
𝑣 𝑒 ,
𝑠 =
1−𝑒 ,
where
sp = saturation flow rate of a permitted movement (veh/h/ln)
v0 = opposing demand flow rate (veh/h);
tcg = critical headway = 4.5 (s); and
tfh = follow-up headway = 2.5 (s);
The computation of the permitted saturation flow rates must take into
consideration that the conflicting phase may have two distinct flow rates on
signalized intersection operation, as discussed in Chapter 31 (Signalized
Intersections Supplemental):
• During the queue service time (gs) portion of the conflicting phase green,
the opposing movement flow rate is equal to its saturation flow rate;
• During the green extension time (ge), the opposing movement flow rate is
equal to its arrival flow rate during the effective green (qg);
Exhibit 38-51 illustrates the calculation of the NBR capacity for a single cycle
during time period 1. For each active phase, the procedure identifies the
respective conflicting flow to the on-ramp along with its duration and flow rate.
The NBR saturation flow rate is then computed using HCM Equation 31-100. The
last column computes the maximum number of vehicles that can be discharged

Version 1.0 Page 101

during each phase as the product of the NBR saturation flow rate and the phase
duration. Clearance times between consecutive phases are also taken into
consideration assuming that they have no conflicting flow rate to the on-ramp.
NBR
NBR
Exhibit 38-51 Conflicting saturation
Conflicting Duration discharge
Calculation of NBR Capacity Active phase flow rate flow rate
flow (s) volume
for a Single Cycle – Time (veh/h) sNBR
(veh)
Period 2 (veh/h)
φ1 (SBL) - gs,SBL sSBL 40.2 1739 282 3.1

φ1 (SBL) -ge,SBL qg,SBL 3.7 128 1282 1.3
Clearance time 1 - 5.7 - 1547 2.5
φ2 (NBT) - 50.7 - 1547 21.8
Clearance time 2 - 5.7 - 1547 2.5
φ7 (EBT) - gs,EBT sEBT 6.3 1811 263 0.5
φ7 (EBT) - ge,EBT qg,EBT 2 97.2 1319 0.8
Clearance time 7 - 5.7 - 1547 2.5
Total 120 34.8
gs: queue service time; ge: green extension time; qg: arrival flow rate during effective green; s: saturation flow rate
As shown, for a 120s cycle the capacity of the unsignalized NBR movement is
34.8 vehicles. Aggregated to an hourly flow rate:
3600
𝑐 = 34.8 × = 1045 𝑣𝑒ℎ/ℎ
120
Because of the actuated control operation, the discharging rates to the on-
ramp are different during each time cycle, and during each period. Therefore,
this procedure must be repeated for every time period to compute the capacity of
the NBR unsignalized movement cNBR (Exhibit 38-52).
Exhibit 38-52
NBR Capacity, Computed for Time Period NBR capacity (veh/h)
Each Time Period
1 1213
2 1045
3 978
4 1182
Exhibit 38-53 summarizes the calculations for this step. During time period 3,
the SBL movement operates at demand over capacity (v/c = 1.56), therefore its
throughput to the ramp is constrained by its capacity value (685 veh/h). For all
other movements and time periods the throughput to the on-ramp is equal to its
demand because v/c < 1.


Time Movements
Parameter Exhibit 38-53
Period EBT NBR SBL Calculation of the On-Ramp
Demand (veh/h) 8 315 652 Demand (vR) Based on the
v/c 0.064 - 0.96 Intersection Operation.
1 c (veh/h) 125 1213 677
min (v, c) 8 315 652
Merge demand vR (veh/h) 975
Demand (veh/h) 96 521 586
v/c 0.768 - 0.93
2 c (veh/h) 125 1045 630
min (v, c) 96 521 586
Demand (veh/h) 96 630 1071
v/c 0.77 - 1.56
3 c (veh/h) 125 978 685
min (v, c) 96 630 685
v/c 0.39 - 0.62
4 c (veh/h) 62 1182 746
min (v, c) 24 80 463
The calculated on-ramp demand is then provided as input into the freeway
facility analysis (Exhibit 38-54). As shown, the ramp flow rates for the merge
segment (segment 5) are obtained from Exhibit 38-53 and highlighted in bold.
Time Period 1 Time Period 2 Time Period 3 Time Period 4 Exhibit 38-54
ML Ramp ML Ramp Ramp Ramp Freeway Facility (I-10
Segment ML flow ML flow
flow flow flow flow flow flow EB) – Demand Inputs
ID rate rate
rate rate rate rate rate rate
(veh/h) (veh/h)
(veh/h) (veh/h) (veh/h) (veh/h) (veh/h) (veh/h)
1 5209 - 6300 - 5300 - 5000 -
2 5209 348 6300 450 5300 1200 5000 50
3 4861 135 5850 116 4100 1000 4950 96
4 4726 - 5734 - 3100 - 4854 -
5 4726 975 5734 1203 3100 1411 4854 567
6 5701 - 6937 - 4511 - 5421 -
7 5701 - 6937 - 4511 - 5421 -
The results of the freeway facility analysis are provided in Exhibit 38-55.
Oversaturated conditions occur during time periods 2 and 3, therefore queueing
may occur along the on-ramp.


Time Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7

Exhibit 38-55
period B D D B M B B
Performance Measures for the
Freeway Facility (I-10 EB) 1 D C D C D D D
2 E F F F F F E
3 D D F F F E E
4 D C C B C C C
Segment type: B: basic; D: diverge; M: merge
The next step will estimate the on-ramp queue length compared to the
available queue storage length to determine whether spillback is expected to
occur. Exhibit 38-56 shows the expected on-ramp queues from the freeway
facility analysis. For each time period, the ramp storage ratio (RQ) is computed by
dividing the ramp queue by the available storage length (924 ft). During time
period 2, a queue is expected on the ramp, but it is not long enough to cause
queue spillback (RQ < 1). During time period 3, however, the on-ramp is expected
to have RQ = 2.31, which indicates that spillback will occur at the intersection
during this time period.
Exhibit 38-56 Time vR Ramp queue Ramp queue Ramp storage Spillback
Spillback Check – I-10 EB on- period (veh/h) (veh) (ft) ratio (RQ) expected?
Ramp
1 975 0.0 0.0 0.00 No
2 1,203 15.0 388.6 0.42 No
3 1,411 82.1 2,133.6 2.31 Yes
4 567 0.0 0.0 0.00 No
Since spillback will occur for at least one time period, the impacts on the
operation of the signalized intersection must be evaluated. The next section
illustrates the application of the methodology to evaluate spillback effects at a
signalized intersection.
Evaluation of queue spillback impacts

The evaluation of queue spillback impacts on the signalized intersection
follows the procedure detailed in the methodology (Exhibit 38-B5). Since this is a
multiperiod analysis, the procedure must be applied for every time period. In
this example, time periods 2, 3 and 4 will be evaluated. Time period 1 is not
analyzed here since it does not have oversaturated conditions.
Time Period 2
The procedure to evaluate queue spillback into intersections is applied for
time period 2, even though spillback is not expected to occur during this time
period. The application of the methodology is presented for this time period to
facilitate the understanding of the calculations.
Step 7A – Determine intersection throughput to on-ramp

The throughput of movements into the on-ramp have been previously
determined as part of the queue spillback check, as shown in Exhibit 38-53.


Step 7B – Obtain merging capacity with Freeway Facilities method

When the freeway facility operates in oversaturated conditions, the capacity
of the subject merge section may be constrained by the presence of queues along
the mainline. The Oversaturated Segment Evaluation procedure (Chapter 25)
computes the on-ramp queue (ONRQ) and on-ramp capacity (ONRO) every 15
seconds. The merge capacity cmerge is then obtained by aggregating the ONRO
parameter into an hourly flow rate for each time period. Exhibit 38-57 shows the
values of ONRQ and ONRO over the analysis period (60 minutes), converted to
hourly flow rates.
Exhibit 38-57(a) compares the on-ramp capacity ONRO to the on-ramp
demand. During the first time period there are no oversaturated conditions along
the freeway, thus the on-ramp capacity ONRO equals 2,000 pc/h (corresponding
to the ramp roadway capacity as provided by HCM Exhibit 14-12), or 1,903
veh/h. During time periods 2 and 3, oversaturated conditions occur and the on-
ramp capacity drops to 5 pc per time step, corresponding to 1,142 veh/h. During
the last time period, the lower demand along the freeway allows the mainline
queue to clear within 4 time steps (60 seconds). Therefore, during the first 60
seconds the on-ramp capacity remains at 1,142 veh/h. From the fifth time step to
the end of the time period, there is no congestion at the merge and thus the on-
ramp capacity is again 1,903 veh/h.
Exhibit 38-57(b) provides the on-ramp queue as estimated by the
Oversaturated Segment Evaluation procedure. Since spillback is expected to
occur, an adjustment to the Freeway Facility Oversaturated Segment evaluation
procedure is necessary to account for the maximum ramp storage (35.5 vehicles).
This value is the upper boundary of the on-ramp queue length. At the end of
time period 3, the predicted on-ramp queue length would be 82 vehicles if there
were no storage constraints (black curve). The red curve represents the adjusted
queue profile for the on-ramp considering the maximum storage capacity. At the
start of time period 4, having an on-ramp queue of 35.5 vehicles instead of 82
results in a shorter queue clearance time, with a slight positive impact on the
freeway performance. In other words, the intersection has a metering effect,
which may improve operations along the freeway. Exhibit 38-58 compares the
performance results of the freeway segments downstream of the merge (see
Figure E-15) with and without consideration of the maximum storage constraint.


Exhibit 38-57
Freeway Facility, Segment 5
(merge) Performance: a)
Merge Capacities and b)
Queue Lengths
Exhibit 38-58 Seg 5 (Merge) Seg 6 (Basic) Seg 7 (Basic)

Freeway Performance During Without With Without With Without With
Time Period 4 – with and storage storage storage storage storage storage
without the Queue Storage constraint constraint constraint constraint constraint constraint
Constraint
Speed (mi/h) 67.2 67.4 67.7 67.8 72.2 72.5
Density
20.9 19.9 20.8 19.7 19.5 18.4
(pc/mi/ln)
Step 7C – Plot queue accumulation polygon for the on-ramp and unsignalized
movements
In this step, a queue accumulation polygon is plotted for the on-ramp as a
function of all protected and permitted movements entering the on-ramp, on a
cycle-by-cycle basis. Since an unsignalized movement (NBR) also discharges into
the on-ramp, a queue accumulation polygon must be developed for this
movement as well. This is required to: (a) determine the discharge pattern of the
unsignalized movement throughout the cycle and (b) allow the estimation of
control delay for this movement.
Exhibit 38-59 presents the queue accumulation profiles for (a) the on-ramp
and (b) for the NBR movement.


Exhibit 38-59
Estimated Queue Lengths And
Merge Capacities – Time
Period 2
The cycle starts with a permitted left-turn movement (Φ1: SBL) discharging
into the on-ramp with a green time g1 = 43.9s, divided in a queue service time gs1
= 40.2s and a queue extension time ge1 = 3.7s (as defined in Chapter 31 –
Signalized Intersections Supplemental). During the green interval for SBL, the
capacity of the NBR movement is constrained since drivers must yield to the
protected left-turn vehicles. The estimated saturation flow rate for the NBR
movement with a conflicting flow vSBL can be obtained by the following equation,
based on HCM equation 31-100:
𝜆 𝑒 ,
𝑠 , =
1−𝑒 ,
where
sNBR,perm = saturation flow rate of the NBR movement (veh/h/ln)
λSBL = throughput of the opposing SBL movement(veh/h)
tcg = critical headway = 4.5 (s)
tfh = follow-up headway = 2.5 (s)
The saturation flow rates of the NBR movement during Φ1 are determined
next. During the SBL queue service time is:
𝜆 = 𝑠 = 1,739 veh/h/ln → 𝑠 , = 282 veh/h/ln


where
sSBL = saturation flow rate of the SBL movement (veh/h/ln)
sNBR,perm1 = saturation flow rate of the NBR movement during the SBL queue
service time (veh/h/ln)
The throughput for the NBR movement is obtained as the minimum of the
demand and saturation flow rate. Since the demand flow rate is greater than the
saturation flow rate, a queue will develop for the NBR movement:
𝜆 , = 𝑚𝑖𝑛 𝑠 , ,𝑣 = 𝑚𝑖𝑛 282, 521
𝜆 , = 282 𝑣𝑒ℎ/ℎ
where
λNBR,1 = throughput for the NBR movement during the SBL queue service time
(veh/h/ln)
vNBR = demand flow rate of the NBR movement (veh/h)
During the SBL green extension time ge, the SBL throughput λSBL is equal to
the arrival flow rate during the effective green (qg,SBL, from Equation 19-32):
𝑣 𝐶
𝜆 =𝑞 , =𝑃 × ×
3600 𝑔
586 120
𝜆 = 0.08 × × = 0.0356 𝑣𝑒ℎ/𝑠/𝑙𝑛 = 128 𝑣𝑒ℎ/ℎ/𝑙𝑛
3600 43.9
where
P = proportion of vehicles arriving during the green indication (decimal);
VSBL = SBL demand flow rate (veh/h);
C = cycle time (s); and
gSBL = SBL effective green time (s)
For this conflicting flow, therefore, the NBR saturation flow rate sNBR,perm2 is
obtained using Equation 31-100:
𝜆 𝑒 ,
𝑠 , =
1−𝑒 ,
586 120
𝜆 = 0.08 × × = 0.0356 𝑣𝑒ℎ/𝑠/𝑙𝑛 = 128 𝑣𝑒ℎ/ℎ/𝑙𝑛
3600 43.9
with all variables previously defined.

Since a queue is present in the NBR movement, the throughput for the NBR
movement is equal to its saturation flow rate:
𝜆 , =𝑠 , = 1282 𝑣𝑒ℎ/ℎ
where
λNBR,2 = throughput for the NBR movement during the SBL green


extension(veh/h/ln)
sNBR,perm2 = saturation flow rate of the NBR movement during the SBL green
extension time (veh/h/ln)
With the discharge patterns for the NBR determined, the queue profile in the
on-ramp during Φ1 can be determined. During the SBL queue service time (cycle
time t = 0 to t = 40.2s), the throughput to the on-ramp is given by:
𝜆 = 𝜆 + 𝜆 , = 1,739 + 282 = 2,021𝑣𝑒ℎ/ℎ 𝑜𝑟 0.561𝑣𝑒ℎ/𝑠
Given the merge capacity cmerge = 1,142 veh/h for the current time period, the
on-ramp queue will grow at the following rate during the SBL queue service
time:
𝜆 −𝑐 = 2,021 − 1,142
𝜆 −𝑐 = 879𝑣𝑒ℎ/ℎ 𝑜𝑟 0.244 𝑣𝑒ℎ/𝑠
Therefore, at the end of the SBL queue service time (t = 40.2s), the queue at
the on-ramp will be 0.244 x 40.2 = 9.8 vehicles (Exhibit 38-59a).
This process is then repeated for all phases throughout the cycle. The results
for a single cycle (120 sec) are presented in Exhibit 38-60, where the maximum
on-ramp queue occurs at t = 50.48s, with 10.82 vehicles (t = 50.48s). The expected
on-ramp queue at the end of the cycle is 2.02 vehicles. The remaining cycles
within time period 2 show the same pattern, where the on-ramp queue at the end
of each cycle becomes the initial queue at the start of the next cycle.
Each row in Exhibit 38-60 describes a portion of the cycle, as follows:
• gs1: queue service time for SBL (Φ1), as previously discussed
• ge1: green extension time for SBL (Φ1). The NBR movement discharges at
the permitted saturation flow rate due to the queue that has developed
during gs1, and the on-ramp queue grows at a rate of 0.07 veh/s
• r1: effective red time for SBL (Φ1). There is no throughput from protected
movements and the NBR movement discharges freely at the saturation
flow rate. The on-ramp queue grows at a rate of 0.11 veh/s
• g2*: effective green for NBT (Φ2), with no throughput from protected
movements. The duration of 0.88s is calculated based on the queue
service time of the NBR approach. The on-ramp queue grows at a rate of
0.11 veh/s
• g2**: remaining effective green for NBT (Φ2). For this portion, no queue
remains on the NBR approach, therefore the NBR throughput is equal to
its demand flow rate (vNBR). The on-ramp queue discharges at a rate of
0.17 veh/s
• r2: effective red time for NBT (Φ2). There is no throughput from protected
movements and the NBR throughput is equal to its demand flow rate
(vNBR). The on-ramp queue discharges at a rate of 0.17 veh/s
• gs7: queue service time for EBT (Φ7). The EBT discharges into the on-ramp
at the saturation flow rate. The throughput of the NBR movement is


restricted to the permitted saturation flow rate, causing queues to develop

in the NBR approach. The on-ramp queue grows at a rate of 0.26 veh/s
• ge7*: green extension time for EBT (Φ7). The duration of 0.03s is calculated
based on the queue service time of the NBR approach. The NBR
movement discharges at the permitted saturation flow rate. The on-ramp
queue grows at a rate of 0.08 veh/s
• ge7**: remaining extension time for EBT (Φ7). The EBT movement
discharges at a rate equal to its arrival flow rate during the effective
green. For this portion, no queue remains on the NBR approach, therefore
the NBR throughput is equal to its demand flow rate (vNBR). The on-ramp
queue discharges at a rate of 0.15 veh/s
• r7: effective red time for EBT (Φ7). No throughput from protected
movements and the NBR throughput is equal to its demand flow rate
(vNBR). The on-ramp queue discharges at a rate of 0.17 veh/s.
Exhibit 38-60 Protected

Discharge Flow Rates into the Permitted movement On-ramp analysis
movement
On-Ramp for each Phase Active Duration On-
Throughout the Cycle – Time t (s) NBR λONR -
phase (s) vNBR λNBR λONR ramp
Period 2 λprot (veh/s) queue cmerge
(veh/s) (veh/s) (veh/s) queue
(veh) (veh/s)
(veh)
gs1 0 40.16 0.483 0.145 0.078 0 0.56 0.24 0
ge1 40.16 3.74 0.036 0.145 0.356 2.66 0.39 0.07 9.8
r1 43.9 5.7 0 0.145 0.43 1.87 0.43 0.11 10.08
g2* 49.6 0.88 0 0.145 0.43 0.25 0.43 0.11 10.72
g2** 50.48 49.82 0 0.145 0.145 0 0.14 -0.17 10.82
r2 100.3 5.7 0 0.145 0.145 0 0.14 -0.17 2.22
gs7 106 6.25 0.503 0.145 0.073 0 0.58 0.26 1.24
ge7* 112.25 2.02 0.027 0.145 0.366 0.45 0.39 0.08 2.85
ge7** 114.27 0.03 0.027 0.145 0.145 0 0.17 -0.15 3.01
r7 114.3 5.7 0 0.145 0.145 0 0.14 -0.17 3.01
Cycle
120 2.02
end
At the end of the time period, a residual queue of 23.32 vehicles is expected
along the on-ramp, and this value is carried to the start of the next time period.
The time period length of 900s does not correspond to an exact number of signal
cycles, and the last cycle is interrupted at t = 60s. Therefore, the next time period
will start the analysis from the same timestamp to maintain consistency.
Step 7D – Calculate equivalent capacities for the affected movements

Since spillback does not occur during time period 2, no adjustment to the
intersection capacity is necessary.


Time Period 3
The same steps performed for the analysis of time period 2 are applied again
for the analysis of time period 3.

The throughput for movements that discharge into the on-ramp have been
previously determined as part of the queue spillback check, and are shown in
Exhibit 38-53.

As in the analysis of the previous time period, the merging capacity cmerge is
obtained as an output from the Freeway Facilities method (Exhibit 38-57a). The
merging capacity for time period 3 is 1,142 veh/h.
movements
The procedure described earlier is applied but with an initial on-ramp queue
of 23.32 vehicles, which is the estimated queue at the end of time period 2. The
analysis begins at the middle of the cycle (t= 60s), which is the end of the
previous time period. Exhibit 38-61 illustrates the queue accumulation polygon
for both the on-ramp and the NBR movement.
Exhibit 38-61
Estimated Queue Lengths and
Period 3


Queue spillback occurs during the third cycle (SBL queue service time),
when the on-ramp queue reaches the maximum storage LONR = 35.5 vehicles. At
this time, the maximum flow rate that can enter the on-ramp is constrained by
the merge capacity cmerge. In other words, the maximum number of vehicles
allowed to enter the ramp is equal to the number of vehicles that are able to
merge to the freeway mainline. Also, the queues developed in the NBR are
longer during cycles 3 through 8, causing an increased delay on this movement
due to the queue spillback conditions at the on-ramp.
The on-ramp queue at the start of cycle 3 is 27.9 vehicles. The cycle starts
with the SBL movement, with an effective green time g1 = 47.3s. Since this
movement already operates with v/c > 1, the queue service time gs1 is equal to g1,
and no green extension time is available (ge1 = 0). The protected movement then
discharges at saturation flow rate sSBL = 0.483 veh/s, while the NBR movement
discharges at a permitted saturation flow rate sNBR = 0.078 veh/s. At the same
time, the on-ramp discharges to the freeway at a rate cmerge = 1,142 veh/h = 0.317
veh/s. Therefore, the on-ramp queue grows at the following rate:
𝜆 −𝑐 = 0.483 + 0.078 − 0.317 = 0.244 𝑣𝑒ℎ/𝑠
At this rate, the time remaining until spillback occurs is calculated by

dividing the remaining on-ramp queue storage by the growth rate:
35.5 − 27.9
𝑇𝑖𝑚𝑒 𝑡𝑜 𝑠𝑝𝑖𝑙𝑙𝑏𝑎𝑐𝑘 = = 31.2𝑠
0.244
Spillback is then expected to occur within 31.2 seconds of the onset of g1. The
total effective green g1 value of 47.3s is then divided in two portions:
• gs1* (31.2s): discharging at saturation flow rate
• gs1,sp (16.1s): the remainder of g1 will be affected by queue spillback,
limiting the maximum discharge to the on-ramp to the merge capacity
cmerge = 0.317 veh/s. Note that this constraint is shared by two movements
entering the on-ramp (SBL and NBR).
The effect of queue spillback on the intersection capacity during gs1,sp is then
measured by the capacity reduction factor β1,sp, defined as the ratio between the
maximum on-ramp capacity during queue spillback and the throughput from
the intersection movements (SBL and NBR):
𝑐 0.317
𝛽 , = = = 𝟎. 𝟓𝟔𝟓
𝜆 + 𝜆 0.483 + 0.078
A capacity reduction factor β1,sp= 0.565 means that only 56.5% of the expected
intersection throughput is able to enter the on-ramp when queue spillback occurs
during phase gs1,sp. This capacity adjustment factor is applied to each movement
to obtain their adjusted throughputs for this time period:
𝜆 , =𝜆 ×𝛽 , = 0.483 × 0.565 = 0.273 𝑣𝑒ℎ/𝑠
𝜆 , =𝜆 ×𝛽 , = 0.078 × 0.565 = 0.044 𝑣𝑒ℎ/𝑠


The procedure is then repeated for the remaining movements of the cycle, as
shown in Exhibit 38-62.
As shown, at time t = 31.2 s the maximum storage length of the on-ramp is
reached and spillback occurs. From this time through t = 83.3s, the throughput
from intersection movements to the on-ramp λONR is greater than the merge
capacity cmerge. Therefore, the maximum allowed throughput λONR,ajd is
constrained by the on-ramp discharge capacity cmerge = 0.137 veh/s. For these
cases, the spillback capacity reduction factor fsp is computed as the ratio of
λONR,ajd and λONR. Note that for this time range the on-ramp queue is kept constant
at the maximum storage of 35.54 vehicles.
From t = 83.3s, the on-ramp queue begins to discharge at a rate of 0.142 veh/s,
followed by a small increase during the green time of phase 7 (EBT), but it is not
sufficient to cause spillback. At the end of the cycle, the residual on-ramp queue
is 33.51 vehicles.
The subsequent cycles follow a recurring pattern, with the on-ramp reaching
maximum storage early in the cycle and slightly diminishing at the end of the
cycle.
Protected
Permitted movement On-ramp analysis
Exhibit 38-62
movement Discharge Flow Rates Into the
Active Duration QONR
t (s) λONR,adj - βsp On-Ramp for Each Phase
phase (s) (veh) λprot vNBR λNBR Q(NBR) λONR λONR,adj
cmerge
(veh/s) (veh/s) (veh/s) (veh) (veh/s) (veh/s) Throughout the Cycle – Time
(veh/s)
Period 3
gs1* 0.0 31.2 27.9 0.483 0.175 0.078 0 0.561 0.561 0.244 1
gs1,sp 31.2 16.1 35.5 0.483 0.175 0.078 3.01 0.561 0.317 0 0.565
r1 47.3 5.7 35.5 0 0.175 0.43 5.12 0.43 0.317 0 0.739
g2* 53.0 30.3 35.5 0 0.175 0.43 4.31 0.43 0.317 0 0.739
g2** 83.3 17 35.4 0 0.175 0.175 0 0.175 0.175 -0.142 1
r2 100.3 5.7 33.1 0 0.175 0.175 0 0.175 0.175 -0.142 1
gs7 106.0 6.3 32.3 0.503 0.175 0.073 0 0.576 0.576 0.259 1
ge7 112.3 2 33.9 0.027 0.175 0.366 0.64 0.393 0.393 0.076 1
r7* 114.3 1 34.1 0 0.175 0.43 0.25 0.43 0.43 0.113 1
r7** 115.3 4.7 34.2 0 0.175 0.175 0 0.175 0.175 -0.142 1

Cycle
120 0 33.5 - - - - - -
end
Step 7D – Calculate adjusted capacities for the affected movements

The adjusted capacities of the affected movements are estimated based on
the volume of vehicles that can actually be discharged during each time period.
Exhibit 38-63 provides the calculation of the adjusted capacity of the SBL
movement during time period 3. The table lists all occurrences of green times for
the SBL movement during the analysis time period and their respective
durations. For each row, the expected throughput from the intersection λONR and
the actual throughput λONR,adj are computed. Next, the capacity reduction factor
βsp is computed as the ratio of λONR and λONR,adj. A value of βsp < 1.0 indicates the
occurrence of queue spillback in the subject phase. The expected and actual
discharge volumes are obtained by multiplying the values of λONR and λONR,adj,


respectively, by their duration. At the end of the table, the expected and actual
volumes are aggregated and a capacity reduction factor βsp,SBL = 0.704 is obtained
as the ratio of these values.
The capacity of the SBL movement without consideration of queue spillback
is 685 veh/h (Exhibit 38-53). The adjusted capacity is calculated by applying the
spillback capacity reduction factor βsp, calculated in Exhibit 38-63
𝑐 , =𝑐 ×𝛽 , = 685 × 0.704 = 482.2 𝑣𝑒ℎ/ℎ
In this example, this step is not required for the EBT movement, since this
movement does not experience effects of queue spillback. As shown in Exhibit
38-61, the on-ramp queue during the EBT green does not reach the maximum
storage length of 35.5 veh.
Exhibit 38-63
On-ramp analysis Spillback adjustment
Calculation of Spillback
Capacity Reduction Factor for On-ramp On-ramp
Active Duration expected actual
the SBL Movement for Time Cycle λONR,adj
phase (s) λONR
βsp discharge discharge
Period 3
(veh/s) (veh/s)
volume volume
(veh) (veh)
2 gs1 47.3 0.561 0.561 1 26.56 26.56
3 gs1* 31.2 0.561 0.561 1 17.51 17.51
3 gs1,sp 16.1 0.561 0.317 0.565 9.04 5.11
4 gs1 8.3 0.561 0.561 1 4.67 4.67
4 gs1,sp 39 0.561 0.317 0.565 21.89 12.37
5 gs1 5.1 0.561 0.561 1 2.87 2.87
5 gs1,sp 42.2 0.561 0.317 0.565 23.68 13.39
6 gs1 4.7 0.561 0.561 1 2.62 2.62
6 gs1,sp 42.6 0.561 0.317 0.565 23.93 13.53
7 gs1 4.6 0.561 0.561 1 2.59 2.59
7 gs1,sp 42.7 0.561 0.317 0.565 23.97 13.55
8 gs1 4.6 0.561 0.561 1 2.58 2.58
8 gs1,sp 42.7 0.561 0.317 0.565 23.97 13.55
Total: 185.89 130.89

Capacity reduction factor (βsp,SBL): 0.704
Time Period 4
The same steps performed for time periods 2 and 3 are applied again in time
period 4.

The throughput for movements that enter the on-ramp has been previously
determined as part of the queue spillback check, and shown in Exhibit 38-53


The merge capacity for time period 4 has been previously determined, as
shown in Exhibit 38-57a. Since the congestion along the freeway mainline is
dissipating during this time period, the merge capacity is not constant: from time
steps 1 through 4, the merge capacity is 1,142 veh/h, consistent with
oversaturated conditions from previous time periods. After time step 5, the
merge capacity is set equal to the ramp roadway capacity (1,904 veh/h)
movements
The procedure described earlier is applied to plot the queue accumulation
polygons, shown in Exhibit 38-64. Queue spillback occurs during the first cycle,
due to the residual queue from the previous time period. However, due to low
volumes at the intersection and improvement of performance along the freeway
mainline, the on-ramp clears quickly. The queue has cleared by the end of the
second cycle.
Exhibit 38-64
Estimated Queue Lengths and
Period 4

The procedure described earlier is used to calculate the capacity reduction
factor for the SBL movement, as shown in Exhibit 38-65. The estimated capacity
reduction is minor, as spillback only occurs during the first cycle. The EBT
movement does not experience queue spillback, therefore no adjustment is
necessary.


On-ramp
Exhibit 38-65 Spillback adjustment
analysis
Calculation of Spillback Active Duration QONR On-ramp On-ramp
Capacity Reduction Factor for Cycle
phase (s) (veh) λONR λONR,adj expected actual
the SBL Movement During βsp
(veh/s) (veh/s) throughput throughput
Time Period 4 (veh) (veh)
1 gs1 6 34.4 0.505 0.505 1 3.02 3.02
1 gs1,sp 29.9 35.5 0.505 0.317 0.628 15.12 9.5
1 ge1 0 35.5 0.388 0.317 0.818 0 0
2 gs1 31.2 13.2 0.505 0.505 1 15.79 15.79
2 ge1 4.7 19.1 0.095 0.095 1 0.44 0.44
3 gs1 31.2 0.0 0.505 0.505 1 15.79 15.79
3 ge1 4.7 5.9 0.058 0.058 1 0.27 0.27
4 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55
4 ge1 3.7 9.8 0.392 0.392 1 1.46 1.46
5 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55
5 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46
6 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55
6 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46
7 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55
7 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46
8 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55
8 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46
Total: 170.49 164.86

Spillback capacity reduction factor: 0.967
The adjusted capacity of the SBL movement is calculated by applying the

spillback capacity reduction factor βsp:
𝑐 , =𝑐 ×𝛽 , = 746 × 0.967 = 721.4 𝑣𝑒ℎ/ℎ
With the adjusted capacity values obtained, the performance measures for
the intersection can be computed using the remaining steps from the Signalized
Intersections methodology (Chapter 19): compute the adjusted demand-to-
capacity ratio (Step 8) and compute control delay (Step 9). Exhibit 38-66
compares the performance measures for the affected movement (SBL) for the
cases with and without accounting for spillback effects. There is no change in the
performance measures in time period 2 even though the on-ramp demand is
greater than the merge capacity, as the queue can be stored in the on-ramp. Time
period 3 yields a significant increase in the SBL control delay due to the queue
spillback: 589.2 s/veh, while the intersection analysis without consideration of the
spillback effects would return a control delay of 293.5 s/veh. Time period 4 shows
a small increase in control delay, from 575.2 s/veh to 609.5 s/veh. Even though
spillback occurs for only a short time during this time period, the high value of
control delay obtained is due to the initial queue delay (d3), as a result of the
unmet demand at the end of time period 3.


Movement capacity (veh/h) Control delay (s/veh)

Time Period Without Without Exhibit 38-66
With spillback With spillback Comparison of Performance
spillback spillback
Measures – with and without
1 652 652 60.3 60.3 Consideration of Spillback
Effects
2 586 586 55.9 55.9
3 685 482 293.5 589.2


EXAMPLE PROBLEM 2, PART 2: TWSC RAMP TERMINAL

This scenario study will replace the signalized intersection from Part 1 with a
TWSC intersection, while keeping the freeway facility characteristics unchanged.
Similar to Part 1, the control delay for the intersection movements with the
occurrence of queue spillback will be evaluated and compared to the
Exhibit 38-67 shows the geometry of the study intersection.
Exhibit 38-67
TWSC Intersection Geometry
– Acadian Thruway @ I-10
EB.

demand flow rates for each time period, based on the demand inputs of the
TWSC intersection. For each time period, the demand (v) and capacities (c) are
compared for each movement that enters the on-ramp (EBT, NBR and SBL). The
minimum value between demand and capacity for each movement is computed
and the merge demand vR is then computed as the sum of the three movements.
The capacities for minor rank movements (EBT and SBL) are computed for
each time period, since they change as a function of the conflicting demand. The
NBR movement is unsignalized and therefore its capacity is computed by its
respective saturation flow rate, considering the applicable adjustment factors fRT
(for right-turn movements) and fHV (for the presence of heavy vehicles):
𝑠 =𝑠 , ×𝑓 ×𝑓
1
𝑠 = 1,900 × × 0.961 = 1,547 𝑣𝑒ℎ/ℎ
1.18


Different from the signalized intersection scenario, there are no conflicting

flows to the unsignalized right turn since it is a Rank 1 movement (highest
priority). Therefore, the capacity for the NBR movement is equal to its saturation
flow rate. Exhibit 38-68 summarizes the calculations for this step.
Time Movements
Parameter Exhibit 38-68
Period EBT NBR SBL Calculation of the On-Ramp
Demand (vR) Based on the
Demand (veh/h) 8 315 652 TWSC Intersection Operation.
v/c 0.064 - 0.96
1 c (veh/h) 125 1547 677
min (v, c) 8 315 652
v/c 0.768 - 0.93
2 c (veh/h) 125 1547 630
min (v, c) 96 521 586
Demand (veh/h) 96 630 1071
v/c 0.77 - 1.56
3 c (veh/h) 125 1547 685
min (v, c) 96 630 685
v/c 0.39 - 0.62
4 c (veh/h) 62 1547 746
min (v, c) 24 80 463
The on-ramp demand estimates are then used as inputs for the freeway
facility analysis. Since the input demands for the freeway are identical to the
example provided in Part 1, it is already known that spillback will occur during
time period 3 (Exhibit 38-56).

The evaluation of queue spillback impacts on the TWSC intersection follows
the procedure detailed in Exhibit 38-B11. Since this is a multiperiod analysis, the
procedure must be applied for each time period. In this example, time periods 2,
3 and 4 will be evaluated. Time period 1 will be excluded since no oversaturated
conditions occur in the freeway.
Step 9A - Determine intersection throughput to on-ramp

The throughput for movements that enter the on-ramp has been previously
determined as part of the queue spillback check, and these values are shown in
Exhibit 38-57.
Step 9B. Obtain merging capacity using the freeway facilities methodology
This step computes the merging capacity into the freeway cmerge. Since the
inputs of the freeway facility remain unchanged, the same values from the
previous case study are used:


• Time periods 2 and 3: 1,142 veh

• Time period 4: 1,142 veh/h during 4 time steps (60 seconds), then 1,903
veh/h. This time period considers a lower merge capacity while a
mainline queue is present at the first 60 seconds. For the remainder of the
time period, the merge capacity is constrained only by the on-ramp
capacity, similar to the scenario presented in the signalized intersection
example.
Step 9C. Determine proportion of time period with queue spillback

In order to determine the spillback time TSB, a queue accumulation polygon
is developed for the on-ramp. Exhibit 38-69 shows the calculations for plotting
the on-ramp queue. For each time period, the difference between the on-ramp
throughput λΟΝR and the merge capacity cmerge is calculated. Then, the time to
spillback is obtained considering the queue growth and the available queue
storage. Time period 4 is split into two rows (4a and 4b), since the merge capacity
changes within this time period. For the first minute of the time period (4a), the
merge capacity remains at 1,142 veh/h due to existing oversaturated conditions
along the freeway mainline. For the remaining of the time period (4b), the merge
capacity is equal to the ramp roadway capacity (1,903 veh/h).
The results show that queue spillback occurs only during time period 3. The
initial queue of time period 2 is 15.2 vehicles, and it takes 4.55 minutes for the on-
ramp to reach maximum storage capacity. Therefore, the spillback time TSB is
computed as 15 – 4.55 = 10.45 minutes.
On-
On-ramp Initial Spillback
Exhibit 38-69 ramp Time to Final ONR
Time Duration queue growth ONR time
Queue Accumulation Plot demand spillback queue
Period (min) rate (λONR - queue (TsB)
Calculations for On-Ramp – (vR) (min) (veh)
cmerge) (veh/s) (veh) (min)
TWSC Intersection (veh/h)
2 15 1203 0.017 0.0 - - 15.2

3 15 1411 0.075 15.2 4.55 10.45 35.5
4a 1 567 -0.160 35.5 - - 26.0
4b 14 567 -0.371 26.0 - - -
Exhibit 38-70 illustrates the queue accumulation polygon for the on-ramp,
based on the table results.


Exhibit 38-70
Queue Accumulation Polygon
for the On-Ramp – TWSC
Intersection
Step 10. Final capacity adjustments

When queue spillback occurs at a TWSC intersection, movements
discharging towards the on-ramp tend to follow a cooperative approach instead
of the priority-based regular operation. Therefore, the merge capacity cmerge is
shared among the three movements that enter the on-ramp:
𝑐 , + 𝑐 , +𝑐 , =𝑐 = 1,142 𝑣𝑒ℎ/ℎ
The capacities during spillback conditions are then obtained proportionally

to their demand flow rates (Equation 38-B22):
𝑐 ×𝑣 1,142 × 685
𝑐 , = = = 554.4 𝑣𝑒ℎ/ℎ
𝑣 +𝑣 +𝑣 685 + 708 + 18
𝑐 ×𝑣 1,142 × 708
𝑐 , = = = 573.0 𝑣𝑒ℎ/ℎ
𝑣 +𝑣 +𝑣 685 + 708 + 18
𝑐 ×𝑣 1,142 × 18
𝑐 , = = = 14.6 𝑣𝑒ℎ/ℎ
𝑣 +𝑣 +𝑣 685 + 708 + 18
The equivalent capacities cEQ,i for each movement i, aggregated for the 15-
min time period, are obtained proportionately to the spillback time TSB (Finally,
the adjusted capacity of each affected movement ci,EQ is obtained as a function of
the amount of time within the time period when spillback was present. The
adjusted capacity considers the):
, × × . × . × .
𝑐 , = = = 757 𝑣𝑒ℎ/ℎ
, × × × . × .
𝑐 , = = = 869 𝑣𝑒ℎ/ℎ
, × × × . . × .
𝑐 , = = = 24 𝑣𝑒ℎ/ℎ


the intersection can be computed using the next step from the TWSC
methodology (Chapter 20): compute movement control delay (Step 11).
Exhibit 38-71 compares the performance measures of the affected intersection
movements for the cases with and without spillback effects during time period 3.
All three movements discharging to the on-ramp experienced significant increase
in the control delay.
Exhibit 38-71
Comparison of Performance Capacity (veh/h) Control delay (s/veh)
Measures in a TWSC Demand
Movement Without With With
Intersection – Time Period 3 - (veh/h) Without spillback
with and without Spillback spillback spillback spillback
Effects EBT 18 28 18.7 166.5 479.8
NBR 708 1547 868.9 0 24.5
SBL 685 1222 757.2 9.4 37.2


EXAMPLE PROBLEM 2, PART 3: AWSC INTERSECTION RAMP TERMINAL

This scenario will replace the signalized intersection from Part 1 with an
AWSC intersection, while keeping the freeway facility characteristics unchanged.
A ramp meter is active at the freeway on-ramp, with a constant metering rate of
900 veh/h (4 s/veh). Additionally, the NBR movement is not channelized as
presented in the previous scenarios and now conflicts with the other movements
in the intersection. Exhibit 38-72 shows the geometry of the study intersection.
Exhibit 38-72
AWSC Intersection Geometry
– Acadian Thruway @ I-10 EB

demand flow rates for each time period, based on the demand inputs of the
AWSC intersection. For each time period, the demand (v) and capacities (c) are
compared for each movement that feeds the on-ramp (EBT, NBR and SBL). The
minimum value between demand and capacity for each movement is computed
and the merge demand vR is then computed as the sum of three movements.
Exhibit 38-73 summarizes the calculations for this step.


Exhibit 38-73 Time Movements

Parameter
Calculation of the On-Ramp Period EBT NBR SBL
Demand (vR) Based on the
AWSC Intersection Operation Demand (veh/h) 54 467 313
v/c 0.14 - 0.67
1 c (veh/h) 377 539 466
min (v, c) 54 467 313
v/c 0.11 - 0.98
2 c (veh/h) 350 521 439
min (v, c) 40 512 432
v/c 0.05 - 1.18
3 c (veh/h) 396 550 462
min (v, c) 19 539 462
v/c 0.06 - 0.62
4 c (veh/h) 455 619 511
min (v, c) 28 160 316
The estimated on-ramp demand values are provided as inputs for the
freeway facility analysis. The freeway facility is then analyzed and the expected
on-ramp queues are provided in Exhibit 38-74.
Ramp Ramp
Exhibit 38-74 Time vR Ramp Spillback
queue storage
Check for Spillback period (veh/h) queue (ft) expected?
(veh) ratio (RQ)
Occurrence – AWSC
Intersection 1 834 0 0 0 No
2 984 14.9 21.9 0.62 No
3 1020 82.1 53.4 1.5 Yes
4 504 0 0 0 No
Since spillback will occur, the impacts on the operation of the intersection
must be evaluated. The next section illustrates the application of the evaluation
methodology at the AWSC intersection.

The evaluation of queue spillback impacts on the AWSC intersection follows
the procedure detailed in Exhibit 38-B13. Since this is a multiperiod analysis, the
procedure must be applied for each time period. In this example, time periods 2,
3 and 4 will be evaluated. Time period 1 will be excluded since no oversaturated
conditions occur along the freeway.

The intersection throughput to the on-ramp was previously determined at
the spillback check (Exhibit 38-92).


Step 13B - Obtain merging capacity with Freeway Facilities method

For this example, the ramp metering rate (900 veh/h) is an additional input to
the freeway facility analysis and is considered as a potential constraint of the
merge capacity. Therefore, the merge capacity for this analysis is kept constant at
900 veh/h.
Step 13C - Determine fraction of time period with queue spillback

The procedure to evaluate the spillback time (TSB) is similar to the TWSC
procedure, and the calculations are provided in Exhibit 38-75.
On-ramp On-ramp queue Initial Spillback Final Exhibit 38-75

Time to Queue Accumulation Plot
Time Duration demand growth rate ONR time ONR
spillback Calculations for On-Ramp –
Period (min) (vR) (λONR - cmerge) queue (TsB) queue
(min) AWSC Intersection
(veh/h) (veh/s) (veh) (min) (veh)
2 15 984 0.023 0 - - 21
3 15 1020 0.033 15.2 7.25 7.75 35.5
4 15 504 -0.11 35.5 - - 0
Exhibit 38-94 illustrates the queue accumulation polygon for the on-ramp,
based on the table results.
Exhibit 38-76
Queue Accumulation Polygon
for the On-Ramp – AWSC
Intersection
Step 13D - Compute spillback departure headway

This step is similar to the calculation of adjusted capacities in the TWSC
procedure. The same calculations are performed, and adjusted capacity values
are converted into headways (hsp), as shown in Exhibit 38-77.


Capacity Spillback
Regular Equivalent
during departure
Movement Capacity Capacity (cEQ)
spillback (csp) headway (hsp)
(c) (veh/h) (veh/h)
Exhibit 38-77 (veh/h) (s)
Equivalent Capacities and
Headways for on-ramp – Time EBT 15 396 212.1 17
Period 3 – AWSC Intersection NBR 439 550 496.5 7.3
SBL 445 462 453.7 7.9
the intersection can be computed using the remaining steps from the AWSC
methodology (Chapter 21): compute the service times (Step 13) and compute
control delay (Step 14).
Exhibit 38-78 compares the performance measures of the intersection
movements for the cases with and without spillback effects during time period 3.
The three movements that discharge into the on-ramp (EBT, NBR and SBL)
experience increased delay, while the remaining movements have their
performance measures unchanged.
Departure headway
Exhibit 38-78 Capacity (veh/h) Control delay (s/veh)
Demand (s)
Comparison of Performance Movement
(veh/h) Without With Without With Without With
Measures – Time Period 3 -
spillback spillback spillback spillback spillback spillback
with and without Spillback
Effects EBL 75 359 359 15.6 15.6 10 10
EBT 19 396 212 12.6 21.7 9.1 17
NBT 229 497 497 16.3 16.3 7.2 7.2
NBR 539 550 497 58.9 92.3 6.5 7.3
SBL 546 462 454 128 136.5 7.8 7.9
SBT 220 494 494 16 16 7.3 7.3


EXAMPLE PROBLEM 3: OFF-RAMP QUEUE SPILLBACK ANALYSIS FOR A

FREEWAY-TO-FREEWAY RAMP IN MIAMI, FLORIDA.
This case study illustrates the application of the off-ramp spillback
methodology to evaluate a network comprised of two freeway facilities (I-75 SB
to SR-826 SB, Miami, Florida), as shown in Exhibit 38-79. Due to congested
conditions at the downstream merge segment (SR-826), spillback is expected to
affect the operations of the upstream freeway facility (I-75). Vehicles traveling
from node A to D are likely to have their travel time severely affected if spillback
occurs.
Exhibit 38-79
Study Site for Freeway-to-
Freeway Queue Spillback
Check, Miami, FL
This freeway-to-freeway connector is modeled as two separate freeway

facilities. The upstream freeway (Facility 1: I-75) is modeled as a diverge section
that is connected to the downstream freeway (Facility 2: SR-826). The system’s
detailed geometry is shown in Exhibit 38-80.


Exhibit 38-80
Individual Freeway Facilities:
(a) I-75 SB and (b) SR-826 SB
Input data
Traffic demands for the freeway facilities and ramps are provided in Exhibit
38-1 in 15-minute time periods.
Freeway Facility 1 (I-75 SB) Freeway Facility 2 (SR-826 SB)
Time Mainline Diverge Mainline Merge demand
Exhibit 38-81 Period demand flow demand flow demand flow flow rate
Traffic Demands for the
rate (veh/h) rate (veh/h) rate (veh/h) (veh/h)
Subject Freeway Facilities
1 5400 1400 4000 1400
2 6200 3000 5700 3000
3 6000 3400 5600 3400
4 4500 800 4500 800
Additional input parameters are as follows:

• Urban area with level terrain;
• Grade: 0%;
• Regime 4 is expected;
• Base FFS: 65 mi/h (I-75) and 67.1 mi/h (SR-826);
• Ramp side: right for both facilities;
• Traffic composition: 12% trucks on both freeway and ramps;
• Ramp length: 3588 ft;


• Acceleration lane length: 1500 ft;

• No shoulder available;
• Deceleration lane length: 700 ft;
• Number of ramp lanes: 2; and
Performance measures - individual facilities

The performance measures for both freeway facilities, if analyzed
independently, are presented in Exhibit 38-82 andExhibit 38-83 Exhibit 38-83.
Facility 1 (I-75) is undersaturated, while Facility 2 (SR-826) experiences
congestion in time periods 2 and 3. Ignoring the interactions between these two
facilities would lead to inaccurate estimations of performance for the upstream
facility. The merge segment (segment 2) in the SR-826 facility operates at LOS F,
and the on-ramp capacity may be affected leading to queue formation and
potential spillback.
Exhibit 38-82
Time Segment 1 Segment 2 Segment 3 Segment 4
Performance Measures for I-
period Basic Basic Diverge Basic 75 (Freeway Facility 1)
1 C C B B
2 C C C A
3 C C C A
4 B B A B
Time Segment 1 Segment 2 Segment 3 Segment 4 Segment 5 Exhibit 38-83

period Basic Merge Basic Diverge Basic Performance Measures for SR-
826 (Freeway Facility 2)
1 B C C B C
2 C F E F E
3 C F F F E
4 C C C C C
Spillback check
The analysis of SR-826 using the Freeway Facilities Oversaturated Segment
Evaluation provides the expected on-ramp queue for every time period. The first
check compares the off-ramp demand to the ramp roadway capacity, as shown
in Exhibit 38-84. The ramp queue starts to develop during time period 2. At the
end of this time period, a ramp queue length of 1188 ft is expected, yielding a
queue storage ratio of 0.33. Therefore, spillback is not expected during time
period 2. During time period 3 a ramp queue length of 5160 ft is expected with a
queue storage ratio of 1.41. Therefore, spillback will occur during time period 3.


Total
Number of Average
Exhibit 38-84 number Queue Ramp Queue
queued vehicle
Estimation of Queue Length of length length storage
vehicles in spacing
and Storage Ratio at the SR- Time queued (ft) (ft) ratio Spillback
each lane (ft)
826 On-Ramp period vehicles occurs?
[B] = [D] = [F] =

[A] [C] [E]
[A]/2 [B]*[C] [D]/[E]
1 0 0 - 0 0.00 No
2 38.3 19.15 62 1188 0.33 No

3588
3 159.1 79.55 65 5160 1.44 Yes
4 0 0 - 0 0.00 Yes
Spillback analysis
Since spillback is expected to occur, the methodology described in Appendix
A (Exhibit 38-A8 through Exhibit 38-A11) is applied to evaluate its impacts on I-
75 SB. The application of the methodology for each time period is presented
below.
Time period 1
No oversaturated conditions occur, therefore no additional calculations are
needed for this time period.
Time period 2
During time period 2, the downstream merge segment operates at LOS F and
the on-ramp capacity is expected to be reduced.
Step 1 - Calculate background density for unblocked lanes on each segment

in the case of queue spillback
The diverge segment at I-75 has 5 lanes and Regime 4 (two blocked lanes) is
expected. Therefore, when queue spillback occurs this segment operates with
two blocked lanes (lanes 1 and 2) and three unblocked lanes (lanes 3 through 5).
The capacity per lane at the diverge segment SC(3) is 2,350 pc/h/ln or 11750
pc/h. For the time step level analysis, the capacity is converted to 48.95 passenger
cars per time step (ts), Therefore, the capacity for the unblocked portion of the
segment is given by Equation 38-A11:
𝑆𝐶𝐸𝑄 𝑖, 𝑁, 𝑁𝑄 = 𝑆𝐶 𝑖, 𝑁 − 𝑁𝑄 × 𝐶𝐴𝐹
The capacity adjustment factor CAFBL is obtained from Exhibit 38-3. For a
segment with 5 directional lanes and 2 blocked lanes, an adjustment factor CAFBL
= 0.67 is applied. Therefore, the equivalent capacity of the unblocked portion is
given by:
𝑆𝐶𝐸𝑄 3, 5, 3 = 48.95 × 0.67 = 38.8𝑝𝑐/𝑡𝑠 𝑜𝑟 7872 𝑝𝑐/ℎ


The unblocked background density KBUB is calculated next. For time period
2, an expected demand of 4165.8 pc/h for the mainline is used in the calculations.
The KBUB parameter of the unblocked lanes is computed as the density of a 3-
lane basic segment with a capacity SCEQ = 7872 pc/h:
𝐾𝐵𝑈𝐵 3, 5, 3 = 30.4 𝑝𝑐/ℎ/𝑚𝑖
Step 2 - Initialize the freeway facility

When spillback occurs, the subject freeway facility is analyzed as a link-node
structure similar to the oversaturated procedure for freeway facilities. The
facility structure is also expanded to consider the ramp segments. Exhibit 38-85
illustrates the structure for the current analysis. Node 4.1 represents the interface
between the diverge segment and the ramp roadway, while node 4.2 represents
the interface between the ramp roadway and the merge at the downstream
facility.
Exhibit 38-85
Link-node Structure for
Spillback Analysis – I-75 SB
Step 2C - Determine queue influence area (QIA)

The queue influence area is obtained as function of the segment FFS, as
shown in Exhibit 38-5. Therefore, for a FFS = 65mi/h, the QIA length is equal to
1060 ft.
Step 2F - Determine initial number of vehicles at the off-ramp

The ramp speed at the expected demand is obtained as:
𝑣
𝑆 = 1 − 0.109 × ×𝑆
1000
1679 𝑚𝑖
𝑆 = 1 − 0.109 × × 55 = 44.9
1000 ℎ
Next, the ramp background density is obtained:
𝑣 1679
𝑅𝐾𝐵 = = = 37.4 𝑝𝑐/𝑚𝑖/𝑙𝑛
𝑆 44.9


The initial number of vehicles in the ramp is then computed as:

3588
𝑅𝑁𝑉 3,0,2,1 = 37.4 × × 2 = 50.8 𝑝𝑐
5280
Step 2G - Determine the capacity of the downstream terminal

The capacity of the merge is obtained by analyzing the downstream freeway
facility using the oversaturated segment evaluation procedure and aggregating
the parameter ONRO for an hourly flow rate. During this time period, the merge
capacity is constant at 13.4 pc/ts or 3217 pc/h, while the ramp demand is 14 pc/ts
or 3369 pc/h.
Given the demand and capacity at the merge, the queue in the ramp
roadway increases by 0.6 pc for every time step. Exhibit 38-86 illustrates the
ramp queue and the total number of vehicles in the ramp, considering an initial
number of 50.8 pc in the ramp at the start of the time period as previously
computed.
Exhibit 38-86
Queued Vehicles and Total
Number of Vehicles in the
Ramp – Time Period 2
Step 9A - Perform spillback analysis

The flow RF that can travel across the ramp node 4.1 and enter the ramp
roadway is obtained as the minimum of demand (RI), the ramp roadway
capacity (RC) and the constrained capacity due to a downstream queue in the
ramp (RSTG), as shown in Equation 38-A20:
𝑅𝐹 𝑖, 𝑡, 𝑝 = 𝑚𝑖𝑛 𝑅𝐼 𝑖, 𝑡, 𝑝, 𝑘 , 𝑅𝐶 𝑖, 𝑘 , 𝑅𝑆𝑇𝐺 𝑖, 𝑡, 𝑝, 𝑘
The capacity of the ramp roadway for a 2-lane ramp with FFS = 55mph, is
equal to 4,400 pc/h or 18.3 pc/ts. Therefore, the capacity of the ramp roadway is
not a constraint to ramp flow. The other potential capacity constraint RSTG is
calculated through Equation 38-A22:
𝑅𝑆𝑇𝐺 𝑖, 𝑡, 𝑝, 𝑘 = 𝑅𝐹 𝑖, 𝑡 − 1, 𝑝, 𝑘
+ 𝑅𝐾𝑄 𝑖, 𝑡, 𝑝, 𝑘 𝑥 𝑅𝐿 𝑘 𝑥 𝑅𝑁 𝑘 – 𝑅𝑁𝑉 𝑖, 𝑡 − 1, 𝑝, 𝑘
The constraint RSTG is dependent on the number of vehicles in the ramp
RNV, which increases progressively as the queue grows along the ramp. Exhibit
38-94 compares the decreasing value of RSTG with the ramp input RI during
time period 2. At the end of the time period, the capacity is still greater than
demand, therefore no spillback occurs at the end of this time period as predicted
by the queue spillback check previously described.


Exhibit 38-87
Ramp Capacity and Ramp
Inputs – Time Period 2
Since spillback does not occur, no additional calculations for the mainline are
required.
Step 30 - Calculate segment performance measures

Since spillback does not occur during this time period, the performance
measures for the mainline do not need to be recalculated. The ramp, however,
experiences queueing. Therefore, the ramp speed in this time period is
calculated using Equation 38-A61 through Equation 38-A63:
𝑅𝐹 𝑖, 𝑝, 𝑘 = 4 × 𝑅𝐹 𝑖, 𝑡, 𝑝, 𝑘 = 1679.5 pc/h/ln
1
𝑅𝐾 𝑖, 𝑝, 𝑘 = × 𝑅𝑁𝑉 𝑖, 𝑡, 𝑝, 𝑘 = 71.6 pc/mi/ln
60
𝑅𝐹 𝑖, 𝑝, 𝑘 1679.5
𝑆𝑅 𝑖, 𝑝, 𝑘 = = = 31.9mi/h
𝑅𝐾 𝑖, 𝑝, 𝑘 71.6
Time period 3
The same steps are repeated for time period 3. The ramp analysis is
summarized in Exhibit 38-88. For this time period, the ramp demand is 15.4 pc/ts,
while the merge capacity is 13.9 pc/ts. Since demand is greater than capacity, the
number of vehicles increases gradually, causing the capacity constraint RSTG to
decrease each time step. At time step 14, the value of RSTG becomes equal to the
merge capacity (13.9 pc/ts), which implies that the ramp has reached jam density
and the maximum flow that can enter the ramp is equal to the flow that departs
the ramp. Therefore, queue spillback into the mainline starts at time step 15.


Exhibit 38-88
Ramp Capacities and Ramp
Inputs – Time Period 3
After the onset of queue spillback, the number of unserved vehicles at the
exit is computed every time step through the parameter OFRUV(i,t,p). Then, the
expected length of the mainline queue OFRLQ(i,t,p) is computed based on the
number of unserved vehicles and the ramp queue density RKQ, as shown in
Equation 38-A33:
𝑂𝐹𝑅𝑈𝑉 𝑖, 𝑡, 𝑝
𝑂𝐹𝑅𝐿𝑄 𝑖, 𝑡, 𝑝 =
𝑅𝐾𝑄 𝑖, 𝑡, 𝑝
The ramp queue density RKQ is obtained using Equation 38-A21:
𝐾𝐽 – 𝑅𝐾𝐶 𝑥 𝑅𝐹 𝑖, 𝑡 − 1, 𝑝
𝑅𝐾𝑄 𝑖, 𝑡, 𝑝, 𝑘 = 𝐾𝐽–
𝑅𝐶 𝑖, 𝑡, 𝑝
𝑅𝐾𝑄 𝑖, 𝑡, 𝑝, 𝑘 = 190– 190 – 46.5 × 13.87 / 18.33 = 81.4 pc/mi/ln
Exhibit 38-89 illustrates the expected spillback queue length during time
period 3.
Exhibit 38-89
Spillback Queue Length –
Segment 3 (Diverge) – I-75
SB
The parameter OFRLQ represents the length of the queue if all unserved
vehicles were queued in a single line. Given the segment geometry (Exhibit 38-
90), the operating regimes and flow modes can be obtained as a function of
OFRLQ:


• 0 < OFRLQ ≤ 1,400 ft: Regime 1

• 1400 ft < OFRLQ ≤ 3000 ft: Regime 4, with increased turbulence
• 3000 ft < OFRLQ: Regime 4, with lane blockage (queue extends upstream
beyond the diverge)
Exhibit 38-90
Available Queue Storage –
Segment 3 (Diverge) – I-75
SB
As previously shown in Exhibit 38-89, the maximum queue length OFRLQ at

time period 3 is equal to 4696 ft. Since queues develop along lanes 1 and 2, at the
end of time period 3 the back of queue will be located 848ft upstream of the
boundary of segments 2 and 3. The length of the queue influence area (QIA) is
1060 ft, and when it is added to the back of the queue it does not reach the
upstream node of segment 2. Therefore, segment 2 capacity is not affected by the
turbulence area upstream of the queue (Exhibit 38-91).
Exhibit 38-91
Back of Queue Length,
Including QIA, at the End of
Time Period 3

The ramp speed is computed similarly to time period 2:
𝑅𝐹 𝑖, 𝑝, 𝑘 = 4 × 𝑅𝐹 𝑖, 𝑡, 𝑝, 𝑘 = 1707 𝑝𝑐/ℎ/𝑙𝑛
1
𝑅𝐾 𝑖, 𝑝, 𝑘 = × 𝑅𝑁𝑉 𝑖, 𝑡, 𝑝, 𝑘 = 108.4 𝑝𝑐/𝑚𝑖/𝑙𝑛
60
𝑅𝐹 𝑖, 𝑝, 𝑘 1707
𝑆𝑅 𝑖, 𝑝, 𝑘 = = = 21.5 𝑚𝑖/ℎ
𝑅𝐾 𝑖, 𝑝, 𝑘 108.4


For the freeway facility, performance measures are computed for the blocked
and unblocked portions of each segment.
Segment 3 (diverge) – blocked portion

Similar to the ramp, the flow through the blocked portion is aggregated for
this time period:
𝑆𝐹𝐵𝐿 𝑖, 𝑝 = 4 × 𝑡𝑖𝑚𝑒𝑠 𝑆𝐹𝐵𝐿 𝑖, 𝑡, 𝑝 = 3030 𝑝𝑐/ℎ
The average density is obtained as the sum of two separate components. The
average number of vehicles in the blocked portion of the segment is computed
as:
1
𝐾𝐵𝐿 𝑖, 𝑝 = × 𝑁𝑉(𝑖, 𝑡, 𝑝) = 51 𝑝𝑐/𝑚𝑖/𝑙𝑛
60
The increase in density due to the lane blockage ΔK is obtained as:
1
∆𝐾(𝑖, 𝑝) = ∆𝑁𝑉(𝑖, 𝑡, 𝑝) = 20.1 𝑝𝑐/𝑚𝑖/𝑙𝑛
𝑆×𝑁
The total density is then computed as:

𝐾(𝑖, 𝑝) = 𝐾𝐵𝐿(𝑖, 𝑝) + ∆𝐾(𝑖, 𝑝) = 70.1 𝑝𝑐/𝑚𝑖/𝑙𝑛
Finally, the speed in the blocked lanes is obtained through the fundamental
equation:
𝑆𝐹𝐵𝐿(𝑖, 𝑝) 3030
𝑆𝐵𝐿(𝑖, 𝑝) = = = 21.2𝑚𝑖/ℎ
𝑁(𝑖, 𝑝) × 𝐾(𝑖, 𝑝) 2 × 70.1
Segment 3 (diverge) – unblocked portion

The same process is repeated for the unblocked portion of the segment,
except the ΔK component is omitted as no queues occur in these lanes:
𝑆𝑈𝐵(𝑖, 𝑝) = 56.1𝑚𝑖/ℎ
Time period 4
During time period 4, the congestion at the downstream facility (SR-826)

dissipates, which allows the ramp to discharge at the ramp roadway capacity
(4,400 pc/h, or 18.33 pc/ts). Given the low ramp demand during this time period,
the queue can be cleared quickly (9 time steps, or 135s). After the 10th time step,
the freeway facility returns to undersaturated conditions.


EXAMPLE PROBLEM 4: ON-RAMP QUEUE SPILLBACK ANALYSIS INTO A

SINGLE-LANE ROUNDABOUT IN LOS ANGELES, CALIFORNIA
This example problem illustrates the analysis methodology when there is
spillback from an on-ramp into a single-lane roundabout. The example is based
on an existing ramp terminal at Bellflower Blvd @ Century Freeway (I-105) in Los
Angeles, California.
Example Problem Data

The traffic and geometric characteristics of this location are as follows (the
layout of the site is shown in Exhibit 38-92):
• The roundabout has one-lane approaches,
• The adjusted flow rates for all movements and O-Ds are shown in Exhibit
38-92(b),
• There are no heavy vehicles present at this location,
• U-turn movements are negligible,
• There is no pedestrian activity in the vicinity of the roundabout,
• The total length of the ramp is 1657 ft, and
• The on-ramp connecting the roundabout to the freeway is metered at a
rate cRM = 800 pc/h.
Exhibit 38-92
Schematic of the Study
Interchange for Example
Problem 4
Step 3: Determine Circulating Flow Rates

This step calculates all circulating flow rates at the roundabout. For example,
for the NB approach, the circulating flow is calculated using Equation 22-11:
𝑣 , , =𝑣 , +𝑣 , +𝑣 , = 100 + 500 + 100 = 700 𝑝𝑐/ℎ
Similarly, for the other approaches the resulting conflicting flows are:


𝑣 , , = 0 𝑝𝑐/ℎ
𝑣 , , = 300 𝑝𝑐/ℎ
Step 4: Determine Entry Flow Rates per Approach

The entry flow rate at each approach is calculated by adding the movement
flow rates that enter the roundabout.
The entry flow rates are calculated as follows:
𝑣 , , =𝑣 , +𝑣 , = 100 + 200 = 300 𝑝𝑐/ℎ
𝑣 , , = 700 𝑝𝑐/ℎ
𝑣 , , = 1600 𝑝𝑐/ℎ
Step 5: Determine the Capacity of Each Entry Lane in Passenger Car

Equivalents
By using the single-lane capacity equation (Equation 22-1), the capacity for
each entry lane is calculated as follows:
𝑐 , = 1,380𝑒 ( . × ) , , = 1,380𝑒 ( . × )( )
= 1,380 𝑝𝑐/ℎ
𝑐 , = 1,380𝑒 ( . × ) , , = 1,380𝑒 ( . × )( )
= 1,016 𝑝𝑐/ℎ
( . × ) ( . × )( )
𝑐 , = 1,380𝑒 , , = 1,380𝑒 = 676 𝑝𝑐/ℎ
Step 8: Compute the Volume-to-Capacity Ratio for Each Lane

The volume-to-capacity ratios for each entry lane are calculated using
Equation 22-16 as follows:
300
𝑥 = = 0.22
1,380
700
𝑥 = = 0.69
1,016
1,600
𝑥 = = 2.37
676
Step 12: Compute 95th Percentile Queues for Each Lane

The 95th percentile queue is first computed for each lane without considering
spillback effects. For example, the queue for the southbound approach is given as
follows (Equation 22-20):
3,600
𝑥 𝑐
𝑄 = 900𝑇 𝑥 − 1 + (1 − 𝑥) + 𝑐
,
150𝑇 3,600
⎡ 3,600 ⎤
⎢ 0.22⎥ 1,380
1,380
𝑄 , = 900(0.25) ⎢0.22 − 1 + (1 − 0.22) + = 1 𝑣𝑒ℎ
150(0.25) ⎥ 3,600
⎢ ⎥
⎣ ⎦
Similarly,
𝑄 , = 6 𝑣𝑒ℎ


𝑄 , = 121 𝑣𝑒ℎ
These values are rounded to the nearest vehicle.
Exhibit 38-93 provides the flows and resulting queues at the roundabout.
Circulating Entry Flow Volume-to- Exhibit 38-93

Capacity 95th Percentile
Approach Flow Rates Rates Capacity Flows and Queues at the
(pc/h) Queues (veh)
(pc/h) (pc/h) Ratio Roundabout of Example
SB 0 300 1380 0.22 1 Problem 4
EB 300 700 1016 0.69 6
NB 700 1600 676 2.37 121
Step 13: Maximum Throughput for each O-D Movement

To calculate the maximum throughput per movement, first the priority order
has to be defined, as shown in Exhibit 38-94. The SB is the Rank 1 leg because it is
the upstream approach to the on-ramp. The EB is the Rank 2 and the NB is the
Rank 3 approach. The capacity for each approach (calculated in Step 3) is used to
determine the maximum throughput for each approach and O-D.
Exhibit 38-94
Priority Order for the
Roundabout of Example
Problem 4
In this example, it is assumed that the exit lane towards the on-ramp can
reach an exit flow rate of 1,300veh/h.
Starting from the approach with Rank 1 (southbound approach), first the
maximum throughput for the movement that exits through the eastbound leg
(the on-ramp) is calculated as follows:
3,600 100 3,600
𝜆 , = 𝑚𝑖𝑛 𝑣 , ,𝑐 , ×𝑝 , = 𝑚𝑖𝑛 100,1380 × , Equation 38-18
ℎ 300 2.77
= 100𝑝𝑐/ℎ
where
𝜆 , = maximum throughput for the southbound-left movement (pc/h);
𝑣 , = flow rate for the southbound-left movement (pc/h);
𝑐 , = entry lane capacity for the southbound roundabout approach (pc/h);
𝑝 = percent of demand from SB approach into the on-ramp


ℎ = departure saturation headway into the on-ramp (s/veh)

Since the Rank 3 (NB) approach is the only one with a volume-to-capacity
ratio over 1, the conflicting flows and the capacity values calculated above are
valid. Then, the calculation of the maximum throughput for the remaining
movements of the approach which contribute to the conflicting flows for the
downstream approaches is as follows (Equation 38-B26):
200
Equation 38-19 𝜆 , = 𝑚𝑖𝑛 𝑣 , ,𝑐 , ×𝑝 = 𝑚𝑖𝑛 200, 1,380 × = 200𝑝𝑐/ℎ
300
where
𝜆 , = maximum throughput for the southbound-through movement (pc/h);
𝑣 , = flow rate for the southbound-through movement (pc/h);
𝑐 , = entry lane capacity for the southbound roundabout approach (pc/h);
𝑝 = percent of demand from SB approach for through movement
The maximum throughput for each approach and O-D is calculated

considering the maximum throughput on the on-ramp accounting for higher-
rank approaches:
3,600
𝜆 , = 𝑚𝑖𝑛 𝑣 , ,𝑐 −𝜆, ×𝑝 ,
ℎ
500 3,600
= 𝑚𝑖𝑛 500,1016 × , − 100 = 500 𝑝𝑐/ℎ
700 2.77
100
𝜆 , = 𝑚𝑖𝑛 𝑣 , , 𝑐 , × 𝑝 = 𝑚𝑖𝑛 100, 1,016 × = 100 𝑝𝑐/ℎ
700
3,600
𝜆 , = 𝑚𝑖𝑛 𝑣 , ,𝑐 , ×𝑝 , −𝜆 −𝜆
ℎ
1,500 3,600
= 𝑚𝑖𝑛 1,500, 678 × , − 100 − 500 = 634 𝑝𝑐/ℎ
1,600 2.77
The maximum throughput to the on-ramp is lower than the exit capacity
(1,300 veh/h), thus the northbound approach flow rate is limited by its own
approach capacity.
Step 14: Maximum Exit Flow Rate into the On-Ramp

The maximum throughput from the roundabout to the on-ramp, 𝜆 , is
calculated adding up the maximum throughput on the on-ramp from the higher-
rank approaches as follows:
𝜆 , =𝜆 , + 𝜆 , + 𝜆 , = 100 + 500 + 634 = 1,234 𝑝𝑐/ℎ
This total on-ramp demand flow rate is lower than the exit demand
(Equation 22-12), which has a rate of:
𝑣 , , =𝑣 , +𝑣 , +𝑣 , = 100 + 500 + 1500 = 2,100 𝑝𝑐/ℎ


Step 15: On-Ramp Metering Capacity

Once the saturation flow rate at the exit leg towards the on-ramp is
calculated, given the metering rate, the maximum exit flow rate into the on-ramp
is:
3600 3,600
𝑐 , = 𝑚𝑖𝑛 𝑐 , = 𝑚𝑖𝑛 800, = 800 𝑝𝑐/ℎ
ℎ 2.77
Step 16: On-Ramp Storage Ratio and Queue Spillback Length

The on-ramp storage LONR is calculated in passenger cars, considering an
average spacing of 25 ft, and given that the total length of the ramp is 1657 ft:
1,657
𝐿
= 66 𝑝𝑐 =
25
With the maximum exit flow rate into the on-ramp, the number of vehicles
that exit the roundabout through the on-ramp during a 15-minute period
analysis is obtained by the difference between the on-ramp throughput λ , and
the ramp metering rate cRM:
−𝑐 𝜆 1234 − 800
,
𝑄 = = = 108 𝑝𝑐
4 4
The queue storage ratio RQ is then calculated as the ratio between the
expected queue and the on-ramp storage:
𝑄 108
R = = = 1.63
𝐿 66
Since RQ > 1.0, there will be queues on each approach due to spillback.
Step 17: Queue Spillback Distribution per Approach

The number of vehicles queued during the 15-minute time period analysis is:
𝑄 =𝑄 −𝐿 = 42 𝑝𝑐
The queues due to the on-ramp spillback are assumed to be distributed
proportional to the demand flow rates to the on-ramp per approach and added
to the 95th percentile queues estimated for the undersaturated conditions
(Equation 22-20):
𝜆 , 100
𝑄 , =𝑄 × +𝑄 , = 42 × + 1 = 4 𝑝𝑐
𝑣 1234
𝜆 ,
𝑄 , =𝑄 × +𝑄 , = 17 + 6 = 23 𝑝𝑐
𝑣
𝜆 ,
𝑄 , =𝑄 × +𝑄 , = 22 + 121 = 142 𝑝𝑐
𝑣
Step 18: Average Delay per Approach

To estimate the average delay per approach, both the control delay and the
delay due to the on-ramp capacity limitation must be estimated.
The average control delay per approach (Equation 22-17) is:


3600
3600 × 0.22
𝑑 = + 900(0.25) 0.22 − 1 + (0.22 − 1) + 1380 +5
1380 450(0.25)
× 𝑚𝑖𝑛 0.22,1 = 4.44 𝑠/𝑣𝑒ℎ

𝑑 = 14.47 𝑠/𝑣𝑒ℎ
𝑑 = 635.86 𝑝𝑐/ℎ
The additional delay due to the on-ramp spillback (Equation 38-B37) is:
3600 2100
3600 2100 2100 ×
𝑑 = + 900(0.25) −1+ −1 + 800 800 + 5
800 800 800 450(0.25)
2100
× 𝑚𝑖𝑛 ,1
800
𝑑 = 747.94 𝑠/𝑣𝑒ℎ
Therefore, the total average delay per approach is:
100
𝑑 , =𝑑 +𝑑 × = 65.05 𝑠/𝑣𝑒ℎ
1234
500
𝑑 . =𝑑 +𝑑 × = 317.54 𝑠/𝑣𝑒ℎ
1234
634
𝑑 , =𝑑 +𝑑 × = 1020.14 𝑠/𝑣𝑒ℎ
1234


5. REFERENCES
[1] University of Florida Transportation Institute, "NCHRP 15-57 -

Highway Capacity Manual Methodologies for Corridors Involving
Freeways and Surface Streets," National Cooperative Highway
Research Program, Washington DC, 2020.
[2] L. Elefteriadou, M. Armstrong, Y. Zheng and G. Riente, "Highway

Capacity Manual (HCM) Systems Analysis Methodology," Federal
Highway Administration, Washington, DC., 2016.
[3] E. Aakre and A. Aakre, "Modeling cooperation in usignalized

intersections," in The 6th International Workshop on Agent-based
Mobility, Traffic and Transportation Models, Methodologies and
Applications (ABMTRANS), 2017.
[4] B. Robinson, L. Rodegerdts, W. Scarbrough, W. Kittelson, R.

Troutbeck, W. Brilon, L. Bondzio, K. Courage, M. Kyte, J. Mason, A.
Flannery, E. Myers and J. Bunker, "Roundabouts: An Informational
Guide," Federal Highway Administration, Washington, DC, 2000.
[5] L. Rodegerdts and G. Blackwelder, "Analytical Analysis of Pedestrian

Effects on Roundabout Exit Capacity," in National Roundabout
Conference , 2005.
[6] R. Kimber and E. Hollis, "Traffic queues and delays at road

junctions," Transport and Road Research Laboratory Report.
[7] F. Sasahara, L. Elefteriadou and S. Dong, "Lane-by-Lane Analysis

Framework for Conducting Highway Capacity Analyses at Freeway
Segments," Transportation Research Record, pp. 523-535, 2018.
[8] F. Sasahara, L. Carvalho, T. Chowdhury, Z. Jerome, L. Elefteriadou

and A. Skabardonis, "Predicting Lane-by-Lane Flows and Speeds for
Freeway Segments," Transportation Research Record, 2020.


APPENDIX A: OFF-RAMP QUEUE SPILLBACK ANALYSIS
Chapter 10, Freeway Facilities evaluates the performance of each segment

individually using standard 15-minute time periods. If any segment within the
facility yields a LOS F (v/c > 1), the analysis continues with the oversaturated
procedure, using smaller time steps.
Similarly, in order to determine whether there is queue spillback from a
freeway off-ramp, systems analysis is first conducted using 15-minute time
periods. If the analysis shows that any of the ramps are expected to experience
queue spillback, the oversaturated procedure must be used to estimate the
spillback impacts on the freeway mainline lanes, even if the segment-wide
performance is not at an LOS F.
The methodology framework for conducting a spillback check at diverge
critical points is presented in Exhibit 38-A1 and described in more detail in the
remainder of this appendix.
Exhibit 38-A1
Check Flowchart
CAPACITY CHECKS
The procedure first determines whether capacity is exceeded at any of the
critical points along the diverge section.
Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft)


Case A: Ramp Roadway

Demand at the study diverge ramp (𝑣 , as defined in Chapter 14) is
compared against the capacity of the ramp roadway using Exhibit 14-12,
replicated in Exhibit 38-A2.
Exhibit 38-A2
Capacity of Ramp Roadways
(veh/h)
Source: HCM 6th Ed. Exhibit 14-12
Case B: Ramp Terminal

Demand at the downstream urban street intersection approach is compared
against the estimated capacity of the approach. If the ramp terminal comprises
two interdependent intersections, the analyst must proceed to Chapter 23, Ramp
Terminals and Alternative Intersections. Otherwise, depending on the type of
intersection located at the end of the ramp roadway, the respective capacities are
obtained from one of the following chapters: Chapter 19, Signalized
Intersections; Chapter 20, Two-Way Stop-Control Intersections; Chapter 21, All-
Way Stop Control Intersections; Chapter 22, Roundabouts. The ramp terminal
control will generate queues even during undersaturated operations. The
recommended approach for evaluating queues is as follows:
• Signalized Intersections: Although an oversaturated approach is expected
to create longer queues that are growing in time and are more likely to
spill back into the freeway diverge, it cannot be guaranteed that the
queues at an undersaturated approach will not affect the freeway
mainline. Therefore, the methodology estimates the queue length and
compares it to the available storage length for each analysis period. The
arriving demand at the intersection may be constrained by the ramp
roadway capacity, and for this reason the ramp roadway capacity check
must be conducted first.
• Unsignalized Intersections: A LOS better than F at the intersection is not
sufficient to guarantee that spillback will not occur. For unsignalized
intersections (TWSC, AWSC and roundabouts) the user is advised to
proceed to the second step of the check methodology (comparison of
queue length).
Case C: Downstream Merge Junction

Queue spillback may also occur on freeway-to-freeway connectors, and this
is a common issue in high-demand urban interchanges. In this case, the
bottleneck is located at the downstream merge segment and occurs when the
discharge rate into the downstream merge is lower than the off-ramp demand.
Consequently, the queue may spill back into the upstream freeway lanes. In this
case, the merge capacity of the downstream freeway facility must be modeled
using the Chapter 10, Freeway Facilities analysis method. For oversaturated
conditions, the methodology estimates the queue length at the on-ramp (as
Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis


described in Chapter 25, Freeway Facilities Supplemental). This queue length

value should be used as input for queue spillback analysis as described below.
Similar to urban street intersections, the arriving demand at downstream
merge may also be constrained by the ramp roadway capacity. Therefore, the
entering ramp demand at the merge is the minimum value of the exiting flow
rate at the diverge and the ramp roadway capacity.
QUEUE LENGTH ESTIMATION

In this stage the procedure estimates the expected queue length for any
conditions where demand exceeds capacity. Three cases may occur:

Queue forms as a result of demand exceeding capacity at the entrance to the
ramp roadway and is expected to affect operations. To determine the extent of
the impact, the queue growth during each analysis period is estimated as:
Equation 38-A1 𝑄 = (𝑣 − 𝑐 ) × 𝑓 × 𝑃𝐻𝐹 × 𝑡i
where
𝑄 = queue growth during analysis period i (pc);
𝑣 = off‐ramp demand for the period (pc/h);
𝑐 = capacity of the off-ramp roadway (pc/h);
𝑓 = adjustment factor for heavy vehicle presence;
𝑃𝐻𝐹 = peak hour factor; and
𝑡 = analysis period i (h).
The ramp queue during the first time period of the analysis must be zero,
otherwise the time-space domain boundaries for the analysis need to be re-
evaluated. The accumulated queue length at the end of analysis period t is the
cumulative value of 𝑄 until 𝑡:
Equation 38-A2
𝑄 = 𝑄
where
𝑄 = accumulated queue length at the end of analysis period 𝑡 (pc);
𝑄 = queue growth during analysis period 𝑖 (pc); and
𝑡 = the current analysis period.
The Study Period is defined as “The time interval within a day for which
facility performance is evaluated, consisting of one or more consecutive analysis
periods” (Chapter 9, Glossary and Symbols). Therefore, the study period t refers
to the time boundaries defined in Step A-1 on the Freeway System Methodology,
and is composed of N analysis periods, which typically have a 15-min duration.
The maximum queue length 𝑄 during the entire analysis period is the
maximum value of 𝑄 obtained using Equation 38-A2 and is used as input for the
next stage of the spillback check procedure.


Case B: Ramp Terminal

Spillback occurs when the resulting queues from the downstream ramp
terminal intersection exceeds the available ramp storage. For all cases, the
procedure estimates the maximum throughput v at the downstream intersection
approach. That maximum throughput is limited by the capacity of the ramp
roadway, 𝑐 under Case A:
𝑣 = 𝑚𝑖𝑛(𝑣 , 𝑐 ) × 𝑓 × 𝑃𝐻𝐹 Equation 38-A3
where
𝑣 = maximum entering flow rate for the intersection approach (veh/h);
𝑣 = off‐ramp demand for the period (pc/h);
𝑐 = capacity of the off-ramp roadway (pc/h);
𝑓 = adjustment factor for heavy vehicle presence; and
𝑃𝐻𝐹 = peak hour factor;
If the off-ramp demand exceeds its capacity, the ramp roadway acts as an
upstream bottleneck and limits the demand to the intersection approach. This
step ensures that the incoming demand at intersection does not exceed the
capacity of the ramp roadway. The calculations of throughput for each
intersection type are described below.
Signalized Intersections: The methodology of Chapters 19 and 31 evaluates
the performance of individual lane groups for a subject approach. It also
estimates the back of queue length 𝑄 (Equation 31-149) or a percentile back-of-
queue length 𝑄% (Equation 31-150). In some cases, only one high-demand
movement at the intersection approach is the bottleneck that results in spillback,
yielding an unbalanced lane usage pattern at the ramp. Field observations have
shown that urban street intersection failures may occur at one lane group. As
drivers position themselves in a specific lane at the ramp to anticipate the
downstream signal, the lane usage in the ramp becomes unbalanced, as shown in
Exhibit 38-A3.
Exhibit 38-A3
Examples of Unbalanced
Ramp Lane Usage: (a)
Norfolk/VA and (b) Tampa/FL
At off-ramps with two or more lanes, the estimated queue lengths for each
intersection lane group must be associated with specific ramp lanes. Exhibit 38-
A4 illustrates an example of a typical ramp terminal for a two-lane off-ramp.
Drivers that desire to take a left turn at the intersection will position themselves
in the leftmost lane (Ramp Lane 1), while drivers who intend to turn right will


likely choose the rightmost lane (Ramp Lane 2). Analyst judgement is required to
define the grouping of intersection lane groups into ramp lanes.
Exhibit 38-A4
Spillback Occurrence by Lane
at an Off-Ramp / Weaving
Segment
By using the results of the queue estimation procedure, the number of

queued vehicles in a given ramp lane 𝑛 is estimated as follows:
Equation 38-A4
𝑄, = 𝑄 , = 𝑄%, ×𝑁
where
𝑄 , = number of queued vehicles in Ramp Lane k, during a 15-min interval;
𝑄 , = number of queued vehicles from Lane Group m associated with ramp
lane k, during a 15-min interval;
𝑄 %, = estimated back of queue length (nth percentile), as defined in Equation
31-150 (measured in veh/ln); and
𝑁 , = number of approaching lanes for Lane Group 𝑚.
For reference, Equation 31-150 can be seen below:

𝑄% = (𝑄 + 𝑄 )𝑓 % +𝑄
where
𝑄 = average back-of-queue estimate for lane group 𝑖 (veh/ln);
𝑄% = percentile back-of-queue size (veh/ln); and
𝑓 % = percentile back-of-queue factor.
Unsignalized Intersections
Each unsignalized intersection type has its own methodology to estimate
queue length. The TWSC methodology estimates the 95th percentile queue length
for minor movements with Equation 20-68, while the 95th percentile queue length
for AWSC approaches is estimated with Equation 21-33. For roundabouts, the
95th percentile queue length for a given lane is provided by Equation 22-20.
Regarding intersection lane groups and ramp lanes, the same procedure
discussed above for signalized intersections is applied.
Case C: Downstream Merge

For freeway-to-freeway connectors, the estimated queue length at the
downstream merge is estimated using the Chapter 10, Freeway Facilities
oversaturated methodology, Equation 25-21. For this specific type of connector,


the demand difference among ramp lanes can be considered negligible for the
purposes of this analysis.
QUEUE STORAGE RATIOS AND SPILLBACK CHECKS
Next, the procedure estimates the queue storage ratio (𝑅 ) for the ramp
roadway queues. If 𝑅 exceeds 1.00, then spillback is expected to occur. The
calculations for each of the three possible cases are provided below.

If the demand exceeds the capacity of the ramp roadway, this step estimates
the queue storage ratio (RQ) for the ramp roadway queues as follows:
𝐿 𝑄 Equation 38-A5
𝑅 =
𝐿 𝑁
where
Equation 38-A5 assumes all
𝑄 = maximum number of vehicles queued on the ramp (veh); lanes have the same storage.
If that is not the case, the
𝐿 = available queue storage (ft/ln); analyst should calculate the
total queue storage as a sum
𝐿 = average vehicle spacing in stationary queue (ft/veh); and of the storage of each lane.
𝑁 = number of lanes in diverge ramp.

In Case A, the bottleneck is the entry to the off-ramp, and the ramp itself
would not necessarily have a queue present. This case estimates the impacts of
the queue as it extends along the deceleration lane. The queue length upstream
of the ramp roadway (𝑄 ) is estimated based on the “leftover” demand that is
not served by the off-ramp’s available capacity:
𝑄 = (𝑣 − 𝑐 ) × 𝑓 × 𝑃𝐻𝐹 × 𝐿 × 𝑡i Equation 38-A6
where
𝑄 = length of queue beyond ramp storage distance (ft);
𝑣 = demand for the off‐ramp (pc/h);
𝑐 = capacity of the off-ramp (pc/h);
𝐿 = average vehicle spacing in stationary queue (ft/veh); and
𝑡 = analysis period i (h).
Case B: Downstream Intersection

When demand exceeds capacity at the intersection, the methodology
considers the queues for all lanes from the ramp gore to the stop bar, as well as
the channelization at the stop bar. The total storage length 𝐿 for the ramp can
be estimated as the sum of lane lengths for a 𝑖 number of different sections (a
section is defined as a uniform segment with a homogenous number of lanes) as
follows:
Equation 38-A7
𝐿 = 𝑁 ×𝐿


where
𝑁 = number of lanes in section 𝑖; and
𝐿 = length in section 𝑖 (ft).
The individual ramp storage for each of the 𝑘 lanes in the off-ramp, 𝐿 , , can
be estimated by assigning the intersection lane groups to ramp lanes, as
previously described:
Equation 38-A8
𝐿 , = 𝑁, × 𝐿
where
𝑁, = number of lanes in section 𝑖 that are associated to ramp lane 𝑘; and
𝐿 = length in section 𝑖 (ft).
Finally, the ramp queue ratio for every ramp lane 𝑘 is obtained as:
𝑄 ,
Equation 38-A9 𝑅 , =
𝐿 ,
where
𝑄 , = queue length associated to ramp lane 𝑘; and
𝐿 , = available ramp storage for ramp lane 𝑘.
Next, the total storage length is calculated. The example from Exhibit 38-A4
illustrates a common off-ramp geometry with three different sections from the
stop bar to the gore point:
• Section 1: 4 lanes with length L1 - two lanes (LG1) are associated with
ramp lane 1, and two lanes (LG2) are associated with ramp lane 2
• Section 2: 3 lanes with length L2 - one lane (LG1) is associated with ramp
lane 1, and two lanes (LG2) are associated with ramp lane 2
• Section 3: 2 lanes with length L3 - one lane (LG1) is associated with ramp
lane 1, and one lane (LG2) is associated with ramp lane 2
Therefore, the available ramp storage LR is calculated as:
𝐿 = (4 × 𝐿 ) + (3 × 𝐿 ) + (2 × 𝐿 )
The ramp storage for each ramp lane is as follows:
𝐿 , = (2 × 𝐿 ) + (1 × 𝐿 ) + (1 × 𝐿 )
𝐿 , = (2 × 𝐿 ) + (2 × 𝐿 ) + (1 × 𝐿 )


Case C: Downstream Merge

The queue storage ratio for freeway-to-freeway connections is estimated as
follows:
𝑄 × 𝐿 Equation 38-A10
𝑅 =
𝐿 𝑁
where
𝑄 = downstream on-ramp queue length (veh);
𝐿 = available queue storage distance (ft/ln);
𝐿 = average vehicle spacing in stationary queue (ft/veh); and
𝑁 = number of lanes in the diverge ramp.
The queue length at the downstream on-ramp 𝑄 is obtained from the
Freeway Facility Oversaturated Segment Evaluation procedure (Chapter 25)
through the parameter ONRQ (Equation 25-21). The parameter ONRQ(i, t, p) is
defined as the “unmet demand that is stored as a queue on the on-ramp roadway
at node i during time step t in time interval p (veh)” and is computed at every 15-
s time step. The on-ramp queue length at the end of a time period p is obtained
by the ONRQ value at the last time step of the time period p.


EVALUATION OF OFF-RAMP QUEUE SPILLBACK IMPACTS

Chapter 14 provides three LOS checks for diverge segments, and failure
(LOS F) may occur in any of the following two cases:
• the total demand flow rate on the approaching upstream freeway
segment exceeds the capacity of the upstream freeway segment;
• the off-ramp demand exceeds the capacity of the off-ramp.
Chapter 14 also provides a LOS evaluation based on the density of the ramp
influence area (Exhibit 14-3), but it only yields a LOS range of A through E;
failure due to excessive density is not considered in the methodology. The first
case of LOS F is addressed by the Oversaturated Segment Evaluation procedure
(HCM Chapter 10) and is not the focus of this methodology. The Queue Spillback
Analysis, described in this document targets the second case of LOS F, when the
off-ramp demand exceeds the capacity of the off-ramp. The methodology of this
appendix also addresses cases of spillback due to insufficient capacity at the
ramp terminal downstream of an off-ramp.
The methodology described in the first section of this Appendix presents the
necessary steps to determine whether spillback from an off-ramp is expected to
occur, based on a standard 15-min period analysis. If spillback is expected to
occur, this section provides the methodology for evaluating the impact on the
freeway performance. The approach is based on the Freeway Facilities
Oversaturated Segment Evaluation (HCM Chapter 25), where performance
measures are computed at the 15-s time step level.
Evaluation of operations along off-ramp segments

To evaluate the interaction between the freeway mainline and the
downstream off-ramp terminal, the link-node approach used by the HCM
Chapter 25 to evaluate oversaturated freeway facilities is expanded, with
additional links and nodes to represent the off-ramp segment. As shown in
Exhibit 38-A5, the mainline node for the off-ramp (Node 3) is connected to the
off-ramp segment, which has a three-node structure:
• Ramp node 3.1: interface between the diverge segment (exit lanes) and the
upstream end of the ramp proper. The volume that flows through this
node is equivalent to the amount of vehicles that are able to leave the
freeway;
• Ramp node 3.2: interface between the ramp proper and the arterial
intersection approach. The volume that flows through this node is
equivalent to the amount of vehicles that are able to leave the ramp
proper and enter the intersection;
• Ramp node 3.3: the last node in the off-ramp represents the discharge
capacity of the arterial intersection approach. The volume that flows
through this node is equivalent to the amount of vehicles that are able to
enter the intersection.


Exhibit 38-A5
Expanded Link-Node Structure
to Evaluate the Off-Ramp
Segment
The geometry of an off-ramp is seldom a homogenous road segment, and

additional lanes are frequently added closer to the arterial intersection approach.
Exhibit 38-A6 illustrates a sample off-ramp, considering its entire length from the
deceleration lane to the stop bar at the downstream signalized intersection. The
ramp roadway is the uniform ramp segment with a downstream boundary
defined by the point where additional lanes are provided. When modeling the
off-ramp geometry, the method considers the channelization at the approach as
imbalances in the turning movements may cause queues on a subset of lanes.
Exhibit 38-A6 shows a typical queue formation resulting from a left-turn
movement that operates with insufficient capacity. In this scenario, the
approaching left-turn vehicles are positioned in the leftmost lane and spillback
may occur even if not all lanes of the approach are oversaturated.
Exhibit 38-A6
Sample Geometry of an off-
Ramp Considering the Arterial
Intersection with Heavy
Demanded Left-Turn
The type of ramp terminal is an important input into the analysis. Signalized
intersections operate in cyclical patterns, and therefore those have fluctuating
queue lengths. For certain demand scenarios, this can result in queues backing
up into the freeway and then discharging multiples times within a 15-min time
period.
Stop-controlled intersections and downstream merge segments (in the case
of a freeway-to-freeway connection), on the other hand, have a more uniform
discharging rate. For cases other than signalized intersections, off-ramp queues


are assumed to develop or discharge linearly based on the relationship between

demand and capacity.
Evaluation of operations on the freeway mainline: spillback regimes

The impact of queue spillback on the freeway mainline varies as a function of
the queue length and the lanes blocked. Four spillback regimes are defined [2]:
Regime 1
The queue ends within the deceleration lane and does not spill back into the
mainline freeway (Exhibit 38-A7 (a)). During undersaturated conditions, the
deceleration lane serves as a transition zone between speeds on the mainline
(typically 55 – 75 mi/h) and advisory speeds posted along the off-ramp (typically
20 – 50 mi/h). When queues begin to form on the deceleration lane, the available
deceleration distance is reduced and speeds along the rightmost lane are
affected.
Regime 2
The queue of vehicles extends upstream beyond the deceleration lane, but
sufficient lateral clearance on the right-hand shoulder allows for additional
queue storage. In this case there is no transition zone within the deceleration lane
and drivers decelerate and join the back of the queue more abruptly, resulting in
turbulence and reduced speeds in the rightmost lane (Exhibit 38-A7 (b)). If no
lateral clearance exists immediately upstream of the deceleration lane, Regime 2
conditions are not possible. In some cases, this regime does not occur even if
storage is available; this depends on local driver behavior and is site-specific.
Regime 3
The queue extends to the rightmost lane of the freeway mainline (Exhibit 38-
A7 (c)). This may occur either when there is no shoulder available for additional
queue storage, or when drivers choose to queue in the rightmost lane once the
deceleration lane is entirely occupied. Non-exiting vehicles on the rightmost lane
are delayed or change lanes, which causes increased turbulence and reduced
speeds in both rightmost lanes.
Regime 4
The queue blocks the rightmost lane, and drivers occasionally or often use
the adjacent freeway mainline lane next to the rightmost freeway mainline lane
to force their way into the queue, blocking thus an additional lane (Exhibit 38-
A7(d)). During this regime, speed and capacity are significantly reduced. The
effects of spillback vary from site to site and from time period to time period due
to driver behavior and site geometry. Data collection at locations around the US
has shown that at some sites drivers block the adjacent lane, while at other sites
they do not, regardless of the queue spillback length at the site.


Exhibit 38-A7
Regimes
Glossary of variable definitions

This glossary defines internal variables used in the methodology for off-
ramp queue spillback evaluation. The structure of the variables is similar to the
one used in HCM Chapter 25 – Freeway Facilities Supplemental.
Facility variables
• QIA(i, p): Length of the queue influence area (ft) for segment i during time
period p, measured from the back of the queue.
Segment variables
• KBBL(i,j): background density (pc/mi/ln) at the blocked lanes in segment i,
when queue spillback occurs at a downstream segment j
• KBUB(i,j): background density (pc/mi/ln) at the unblocked lanes in
segment i, when queue spillback occurs at a downstream segment j
• LCR(i,t,p): rate of lane change maneuvers in the queue influence area
upstream of a queue from an off-ramp, for segment i during time period
p and time step t.
• LD(i,p): available deceleration lane length (ft) for segment i during time
period p. This variable is used to calculate performance measures for
ramp segments (Chapter 14 - LD.)
• MQ1(i,t,p): mainline queue length of off-ramp unserved vehicles in the
rightmost mainline lane, for segment i during time period p in time period
t.
• MQ2(i,t,p): mainline queue length of off-ramp unserved vehicles in the
rightmost mainline lane, for segment i during time period p in time period
t. If Regime 4 is not expected to occur, this parameter value is set to zero.
• NQ(i): number of blocked lanes if the off-ramp queue backs up into the
freeway mainline. This parameter is a function of the prevailing spillback
regime at segment i as provided by the analyst. The value for this
parameter is an input and can be either 1 (Regime 3 - one blocked lane) or
2 (Regime 4 – two blocked lanes);
• OFRFUP(i,t,p): flow that can exit at the closest off-ramp downstream of i
during time step t in time period p.


• OFRLQ(i,t,p): queue length of off-ramp unserved vehicles for diverge

segment i during time period p in time period t.
• OFRUV(i,t,p): number of off-ramp unserved vehicles for segment i during
time period p in time period t.
• SBKQ (i,t,p): spillback queue density for segment i during time period p in
time period t.
• SBLC(i,t,p): number of lane change maneuvers within the Queue Influence
Area at node i, during time step t in time period p.
• SBLQ(i,t,p): queue length within segment i during time period p in time
period t, caused by a downstream off-ramp bottleneck.
• SBQS(i,p): total available off-ramp queue storage (ft) for a diverge
segment i during time period p, if the subject segment has an off-ramp
bottleneck. It is calculated as a function of the available storage lengths in
the deceleration lane, shoulder and prevailing spillback regime.
• SCEQ(i,N,NQ): equivalent capacity of the unblocked portion of a segment
i with N total lanes and NQ blocked lanes.
• SL(i,p): available shoulder length (ft) for segment i during time period p. If
the value of SL is greater than zero, any off-ramp queues that exceed the
deceleration lane will occupy the shoulder before blocking mainline lanes.
• TIA(i,p): total influence area (ft) of a queue from an off-ramp bottleneck
on segment i, during time period p in time period t. It is calculated as the
sum of parameters QIA(i,t,p) and MQ(i,t,p).
Node variables
• CAFBL(i,t,p): capacity adjustment when one or more lanes of segment i are
entirely blocked during time period p in time period t. This is used to
calculate friction effects that cause through vehicles to slow down due to
the presence of a queue in the rightmost lanes.
• CAFUP(i,t,p): capacity adjustment factor of node i during time step t in
time period. This capacity adjustment factor affects approaching vehicles
within the queue influence area (QIA) upstream of an off-ramp queue.
This factor accounts for the turbulence caused by intense lane changing
within the queue influence area as vehicles adjust their position when
there is a downstream off-ramp queue.
• MFBL(i,t,p): mainline flow rate that can cross the blocked portion of node i
• MFUB(i,t,p): mainline flow rate that can cross the unblocked portion of
node i during time step t in time period p.
• MIBL(i,t,p): maximum flow desiring to enter the blocked portion of node i
• MIUB(i,t,p): maximum flow desiring to enter the unblocked portion of
node i during time step t in time period p.


• MO2BL(i,t,p): maximum number of passenger cars that can enter the

blocked portion of segment i, during time step t and time period p, due to
the presence of a queue in the downstream ramp segment.
• MO2UB(i,t,p): maximum number of passenger cars that can enter the
unblocked portion of segment i, during time step t and time period p, due
to the presence of a queue in the downstream ramp segment.
• NEXTOFR(i): index of the nearest downstream diverge segment relative
to subject node i.
• OFRDIST(i): distance (ft) from node i to the start of the deceleration lane
at the nearest downstream off-ramp.
• OFRPCT(i,j): percent of the off-ramp demand at segment j over the
mainline entering volume at segment i.
Ramp variables
• RC(i,p): capacity of the ramp proper (pc/h) during time period p in time
period t. Capacity values for the ramp proper are provided in HCM
Exhibit 14-12.
• RF(i,t,p,k): flow (pc/ts) that can enter the ramp proper at segment i during
time period p in time period t and level k.
• RI(i,t,p,k): maximum flow (pc/ts) desiring to enter the off-ramp on
segment i during time period p in time period t and level k, including
queues accumulated from previous time periods.
• RKB(i,t,p,k): ramp proper queue density (pc/mi/ln) for segment i during
time period p in time period t and level k.
• RL(i): length of ramp proper (ft) for segment i.
• RN(i): number of ramp lanes for segment i.
• RNV(i,t,p,k): maximum number of passenger cars within the ramp of
segment i at the end of time step t during time period p and level k. The
number of vehicles is initially based on the calculations of Chapters 12, 13,
and 14, but, as queues grow and dissipate, input–output analysis updates
these values during each time step.
• RSTG(i,t,p,k): maximum number of passenger cars that can enter the ramp
level k of segment i, during time step t and time period p, due to the
presence of a queue in the downstream ramp segment.
• RUV(i,t,p,k): number of unserved vehicles at the entrance of the ramp
proper of segment i at the end of time step t during time period p and
level k. Any values of RUV greater than zero indicate the occurrence of
queue spillback from an off-ramp.


Intersection (ramp terminal) variables

• ID (i,t,p,k): discharge capacity (pc/ts) for intersection movement k in
segment i during time period p in time period t.
• IF(i,t,p): flow (pc/ts) that can enter the intersection on segment i, level k,
during time period p in time period t.
• II(i,t,p,k): maximum flow (veh/ts) desiring to enter the intersection on
segment i, level k, during time period p in time period t, including queues
accumulated from previous time periods.
• IL(i,k): storage length of movements at intersection of segment i, for level
k (ft)
• INV(i,t,p,k): number of vehicles at the intersection of segment i, for level k
at the end of time step t during time period p
• IO(i,t,p): flow (pc/ts) that can be discharged from the intersection on
segment i, level k, during time period p in time period t.
• ISTG(i,k): total available storage length at intersection of segment i, for
level k (ft)
• IUV (i,t,p,k): number of unserved vehicles at the entrance of the
intersection of segment i, for level k, at the end of time step t during time
period p


Evaluation of operations on the freeway mainline: step-by-step

methodology description
The methodology for evaluating off-ramp queue spillback is integrated to the
core methodology for Freeway Facilities Oversaturated Segment Evaluation
(HCM Chapter 25). Exhibit 38-A8 through Exhibit 38-A11 show the core
methodology, highlighting additions and changes to address off-ramp queue
spillback.
Exhibit 38-A8
Freeway Facilities
Oversaturated Segment
Evaluation Procedure,
Adapted for Off-Ramp Queue
Spillback Evaluation


Exhibit 38-A9
Freeway Facilities
Spillback Evaluation -
Continued


Exhibit 38-A10
Freeway Facilities
Continued


Exhibit 38-A11
Freeway Facilities
Continued


Step 1 - Calculate background density for unblocked lanes on each segment in

the case of queue spillback
The first step in the Oversaturated Segment Evaluation procedure computes
a background density (KB), for each segment at the start of each time period,
defined as the expected density when there is no queueing on the segment. It is
used as a reference to estimate how many vehicles occupy a given segment at
undersaturated conditions, creating an initial reference point for oversaturated
analyses.
When Regime 3 or Regime 4 occur, there is blockage of one or more freeway
lanes in the affected segments, and the through vehicles aim to move to the
unblocked lanes. The capacity of the unblocked lanes must be calculated at the
initialization step, to be used as a reference value.
For a segment i with N lanes, a subset NQ of lanes will be blocked when
spillback occurs (NQ = 1 for Regime 3 and NQ = 2 for Regime 4). Therefore, the
capacity of the unblocked lanes will be equivalent to a similar segment with (N -
NQ) lanes, adjusted for the impact of the blockage using a capacity adjustment
factor CAFBL. The values of CAFBL are equal to the Incident Capacity Adjustment
Factors of Chapter 11, Freeway Reliability Analysis (Exhibit 11-23), as there are
currently no data available to accurately assess the impacts of blockage due to
spillback. These values may be conservative, as during incidents capacities may
be further reduced due to the presence of police vehicles. Exhibit 38-A12 presents
the recommended values for 𝐶𝐴𝐹 .
Directional Lanes 1 Blocked Lane 2 Blocked Lanes Exhibit 38-A12
2 0.70 N/A Capacity Adjustment Factors
3 0.74 0.51 for Lane Blockage (CAFBL) as
4 0.77 0.50 a Function of the Number of
5 0.81 0.67 Directional Lanes and the
6 0.85 0.75 Number of Blocked Lanes
7 0.88 0.8
8 0.89 0.84
The equivalent capacity SCEQ of segment 𝑖, with 𝑁 lanes and 𝑁𝑄 blocked

lanes, is estimated as:
𝑆𝐶𝐸𝑄(𝑖, 𝑁, 𝑁𝑄) = 𝑆𝐶(𝑖, 𝑁 − 𝑁𝑄) × 𝐶𝐴𝐹 Equation 38-A11
Exhibit 38-A13 presents an example of a basic 4-lane directional segment

operating in Regime 4 (2 blocked lanes). The capacity of the unblocked lanes will
be equivalent to the capacity of a 2-lane basic segment with a capacity
adjustment factor CAFBL = 0.50 (4 directional lanes with 2 blocked lanes).
Exhibit 38-A13
Equivalent Segment Capacity
for Unblocked Lanes When
Lane Blockage Occurs
For the segment of Exhibit 38-A13, capacity at ideal conditions is:

• 𝑐 = 2,400 𝑝𝑐/ℎ (Capacity per lane) or
• 𝑆𝐶 = 9,600 𝑝𝑐/ℎ (Segment capacity)


When Regime 4 occurs (2 blocked lanes), the equivalent capacity 𝑆𝐶𝐸𝑄 is

obtained as the equivalent capacity of a 2-lane segment multiplied by a
corresponding 𝐶𝐴𝐹 of 0.5 (Exhibit 38-A12):
𝑆𝐶𝐸𝑄 = 2 × 2,400 × 0.5 = 2,400 𝑝𝑐/ℎ
Next, the unblocked queue density KBUB is calculated. This parameter
estimates the queue density of the uncongested portion of a given segment
operating under a two-pipe regime due to a queue spillback from a downstream
off-ramp. To estimate this value, the method first determines the ratio of the
Expected Demand (ED) that will move to the uncongested side of the segment.
When queue spillback occurs in a diverge segment j, the parameter OFRPCT(j) is
defined as the percent of the off-ramp demand over the mainline entering
volume 𝑣 :
Equation 38-A12
𝑣 (𝑗)
𝑂𝐹𝑅𝑃𝐶𝑇(𝑗) =
𝑣 (𝑗)
For any segment i, upstream of segment j and affected by the off-ramp
spillback from segment j, the ratio of vehicles traveling towards the off-ramp at
segment i is given by OFRPCT(j), while the ratio of vehicles traveling through in
the unblocked lanes is given by (1- OFRPCT(j)). Therefore, the unblocked queue
density KBUB at any segment i upstream of an off-ramp spillback in a segment j
is given by:
Equation 38-A13 𝐾𝐵𝑈𝐵(𝑖, 𝑗) = 𝐾𝐵 𝐸𝐷(𝑖) × 1 − 𝑂𝐹𝑅𝑃𝐶𝑇(𝑖) , 𝑆𝐶𝐸𝑄(𝑗)
where
KBUB(I, j)= background density at the unblocked lanes in segment i, when queue
spillback occurs at the downstream segment
ED(i) = expected demand at segment i , as defined in HCM Chapter 25
𝑂𝐹𝑅𝑃𝐶𝑇(𝑖)= rate of off-ramp flow and mainline flow at segment i
KB(v, c) = density at a segment with demand flow rate v and capacity c, as
provided by HCM Chapters 12 (basic), 13 (weaving) and 14 (merge
and diverge)

These calculations are performed at the start of the analysis, to prepare the
flow calculations for the first time step and specify return points, such as
background density (KB), for later time steps. This subsection presents the
additional parameters required for queue spillback analysis.
(a) Number of mainline blocked lanes

The number of mainline blocked lanes is stored in the parameter NQ(i) and is
determined by the prevalent queue spillback regime as provided by the analyst.
If the back of an off-ramp queue is calculated to reach the freeway mainline, two
possible spillback regimes may occur:
• Regime 3: blockage of one lane in the freeway mainline → Set NQ(i) = 1
• Regime 4: blockage of two lanes in the freeway mainline → Set NQ(i) = 2


The analyst should select one of these two regimes based on prevailing
driver behavior at the site and in the vicinity of the site.
(b) Shoulder length

The available shoulder length must be input by the analyst for queue
spillback analysis and is stored under the parameter SL(i) for oversaturated
calculations.
(c) Deceleration lane length

The deceleration lane length is provided by the analyst for the analyses of
diverge segments and is stored under the parameter LD(i) for oversaturated
calculations.
(d) Spillback queue storage length

The maximum storage length for off-ramp queues on segment i is computed
as a function of the segment length L(i), the deceleration lane length LD(i) and
the number of queued lanes NQ(i). Exhibit 38-A14 provides guidance on
measuring each of the components required for Regimes 3 and 4.
Exhibit 38-A14
Maximum Off-Ramp Queue
Storage Length at Diverge
Segments with Occurrence of
(a) Regime 3 Queue Spillback
And (b) Regime 4 Queue
Spillback, when no Shoulder is
Available
Exhibit 38-A15 illustrates queue length measurements for special cases of

queue spillback, when a shoulder is present, but its storage length is not
sufficient to accommodate the unserved vehicles. Regime 3A (Exhibit 38-A15(a))
occurs when there is blockage of one mainline lane in addition to the shoulder.
Regime 4A (Exhibit 38-A15(b)) occurs when there is blockage of two mainline
lanes in addition to the shoulder.
Exhibit 38-A15
Maximum Off-Ramp Queue
Storage Length at Diverge
Segments with Occurrence of
(A) Regime 3a Queue
Spillback and (B) Regime 4a
Queue Spillback, when
Shoulder is Available
Step 2A - Model off-ramp geometry

The three-level node structure for the off-ramp shown in Exhibit 38-A5 must
be modeled to reflect the geometric characteristics of the site, as illustrated in


Exhibit 38-A6. This is accomplished by setting a “branch” structure, where a

node can connect to multiple links downstream. If a node is connected to more
than one downstream link, the flow through the node will be constrained by the
downstream link with the highest queue storage ratio.
The ramp structure must be modeled from the downstream end towards the
upstream end:
• For the most downstream location provide one node for each lane group
or movement at the approach;
• For the next upstream change in alignment provide one node for each
ramp proper lane connecting to a distinct lane group downstream.
The data structure used in the methodology computations should be
adjusted according to this “branch” structure. Most parameters in the
Oversaturated Segment Evaluation methodology are computed as a 3-
dimensional array (i, t, p), where i is the segment index in the freeway facility
and t refers to a specific time step within a given time period p. In the case of
two-lane ramps that need to be evaluated independently, a new dimension k will
be added to the ramp parameter arrays to account for the specific lane under
analysis. Lanes are numbered right from left; therefore, k=1 stands for the
rightmost lane and k=2 for the leftmost lane of the ramp.
Example 1 – In this example, there is only one lane connecting the freeway
exit to the entry leg of the downstream roundabout. Therefore, only one node is
required at each location (single branch structure, with k=1 in all nodes), as
shown in Exhibit 38-A16.
Exhibit 38-A16
Node Structure for Example 1
Example 2 – A single-lane ramp connects with a stop-controlled T-

intersection ramp terminal (Exhibit 38-A17). The intersection node is comprised
of two branches (k=2), while the ramp proper has only one lane (k=1). Each
movement of the intersection (LT and RT) is represented by a node, and when
there is a queue on either one of the movements, the one with the longest length
will constrain the flow of vehicles from the ramp proper.


Exhibit 38-A17
Example 3 – A two-lane ramp connects with a signalized intersection ramp

terminal (Exhibit 38-A18). Both the intersection and the ramp proper nodes
comprise of two branches each (k=2). At the downstream end, one node is
defined for each lane group at the intersection (LT and RT). According to the
ramp geometry, left-turning drivers will be positioned along ramp lane 2, while
right-turning drivers will be located along ramp lane 1. Therefore, two nodes are
also defined at the upstream location. If the queue storage ratio for any of the
ramp lanes reaches 1, vehicle flow in the respective upstream node will be
constrained, resulting in queue spillback on the freeway mainline.
Exhibit 38-A18
Step 2B - Determine spillback regime for each diverge segment

Field observations [1] have shown that locations that experience recurring
queue spillback always have the same type of spillback regime when the queue
extends beyond the deceleration lane (Regime 3 or 4). Regime 4 occurs often at
ramp junctions with a lane drop. At these locations, the exiting traffic can access
the off-ramp with a single lane change. Therefore, drivers are more likely to wait
until they are closer to the exit to change lanes, blocking the adjacent through
lane. However, not all lane drop exits experience a Regime 4 queue spillback.
Regime 4 occurs more frequently in locations with more aggressive driver


behavior. Local information and driver behavior should be taken into

consideration in determining the prevailing regime at a given site.
For operational analyses of existing locations, it is recommended that the
analyst provides the expected spillback regime based on observed field
conditions. For planning level purposes where no field data is available, Exhibit
38-A19 provides the expected queue spillback regime as a function of the number
of exiting lanes and driver aggressiveness.
Ramp Driver Aggressiveness

Exhibit 38-A19
Geometry Low Medium High
Default Spillback Regimes as a
Function of Ramp Geometry Diverge Regime 3 Regime 3 Regime 3
and Driver Aggressiveness
Lane Drop Regime 3 Regime 4 Regime 4

Chapter 14 provides the following definition for the ramp influence area for
off-ramps operating under steady conditions:
“For right-hand off-ramps, the ramp influence area includes the deceleration lane(s)
and Lanes 1 and 2 of the freeway for a distance of 1,500 ft upstream of the diverge point.”
When there is queue spillback in one or more freeway lanes, drivers would
react to the presence of the queue further upstream resulting in increasing lane
changes and additional turbulence upstream of the ramp influence area (Exhibit
38-A20). In this step the methodology estimates the length of the Queue
Influence Area (QIA), measured upstream from the back of queue.
Exhibit 38-A20
Queue Influence Area with
Increased Turbulence
The length of Queue Influence Area is based on time needed for arriving
drivers to react to partial lane blockage and adjust their speeds and positions.
Research [1] has shown that traffic speeds upstream of the back of queue are
negatively affected at a headway distance of 10.95s. Therefore, the influence area
represents the distance traversed by a vehicle during 10.95s with a speed
consistent with the traffic stream.
The length of the QIA is estimated as a function of the segment free-flow
speed (FFS), as shown in Exhibit 38-A21. The exact location of the QIA varies as a
function of the queue length. The QIA values are shorter than the ramp
influence distance of 1,500 ft. However, the two concepts are very different and
are used differently in analyzing ramp operations: the ramp influence area is
used to analyze undersaturated conditions, while the QIA is used to analyze
oversaturated conditions. Since drivers can only detect a downstream queue
visually, they have shorter times to react when compared to the presence of


undersaturated off-ramps, where signing and navigation information is

provided in advance and allows drivers to adjust their position earlier.
Segment FFS (mi/h) Queue Influence Area (ft)

Exhibit 38-A21
50 810 Queue Influence Area as
55 900 Function of the Segment FFS
60 980
65 1060
70 1140
75 1220
When Regimes 3 or 4 occur and lane blockage is present in the mainline, the
estimated QIA is added to the queue length to determine the extent of spillback
effects. If an upstream node is located within the combined length of the queue
and QIA, capacity adjustment factors must be applied to account for the
spillback effects.
Step 2D - Determine ramp proper capacity and speed

The first off-ramp parameter to be determined is its capacity (RC), defined as
function of the ramp free-flow speed and is obtained from HCM Exhibit 14-12,
replicated below in Exhibit 38-A22.
Exhibit 38-A22
Capacity of Ramp Proper for
Off-Ramps
The RC is compared to the off-ramp demand, and if the demand-to-capacity

ratio is greater than 1.0 then spillback is expected to occur.
Determining the speed-flow relationship at the ramp proper is also critical
for the analysis. Ramp speeds can be obtained through the following equation:
𝑣 Equation 38-A14
𝑆 = 1 − 0.109 × ×𝑆
1000
where
𝑆 = ramp speed (mi/h);
The speed-flow relationship for ramps is linear and speed decreases with
higher ramp flows, as presented in Exhibit 38-A23. The maximum allowed
values of vR are bounded by ramp capacity, consistent with guidance provided
by Chapter 14 – Merge and Diverge segments (Exhibit 14-12).


Exhibit 38-A23
Speed-flow Curves for
Freeway Ramps
The ramp density at capacity (RKC) is not necessarily equal to 45 pc/mi/ln as

assumed for freeway mainline lanes. This parameter is required to evaluate the
queue density at the ramp proper when operating in oversaturated conditions.
The ramp density at capacity can be found by dividing the capacity by speed.
Exhibit 38-A24 summarizes the values of RKC as a function of the Ramp FFS.
Exhibit 38-A24 Ramp FFS (mi/h) Capacity (pc/h/ln) RKC (pc/mi/ln)

Ramp Density at Capacity as a
55 2200 40.0
Function of Ramp FFS
50 2100 42.0
45 2100 46.7
40 2000 50.0
35 2000 57.1
30 1900 63.3
25 1900 76.0
20 1900 90.0
15 1800 120
Step 2E - Determine intersection storage capacity

The storage capacity at the intersection, ISTG, is obtained as the sum of the
available storage of every lane group, multiplied by the number of lanes. If the
off-ramp has multiple branches at the intersection (k > 1), then the available
storage capacity must be computed for each branch k individually. This
distinction is necessary to evaluate cases with unbalanced demands at the
intersection, when the queues developed in one oversaturated movement may
extend upstream and block the throughput of all movements at the off-ramp.
ISTG is estimated as:
𝑀
Equation 38-A15 𝐼𝑆𝑇𝐺(𝑖, 𝑝, 𝑘) = 𝑁𝑚 𝑥 𝐿𝑚 𝑥𝐿
𝑚
where
Nm = number of lanes serving movement m at the intersection
Lm = storage length for movement m at the intersection (ft)
N = number of movements at the approach
Lh = average vehicle spacing in stationary queue (ft/veh) (HCM Equation
31-155)



The computation of the number of vehicles in the facility at every time step is
critical for deriving performance measures of oversaturated freeway facilities.
Similar to the Freeway Facilities Oversaturated Segment Evaluation
methodology, the estimation of the number of vehicles in the ramp during
oversaturated conditions requires a reference value for undersaturated
conditions to be computed during the initialization steps.
First, the initial number of vehicles on the ramp during undersaturated
conditions is determined as an initial reference point. The density at an off-ramp
segment can be obtained by dividing the off-ramp flow rate (vR) by its speed (SR,
obtained through Equation 38-A15). Then, the total number of vehicles is
obtained by multiplying the ramp density by the ramp length (RL) and number
of lanes (RN), as follows
𝑣 ,
𝑅𝑁𝑉(𝑖, 0,0, 𝑘) = 𝑥 𝑅𝐿(𝑖, 𝑘)𝑥 𝑅𝑁(𝑖, 𝑘)
𝑆
where
𝑅𝑁𝑉(𝑖, 0,0, 𝑘)) = number of vehicles in the ramp proper at the initialization step
IN(i,k) = off-ramp demand at the first time period in the analysis (pc/h)
𝑄 = off-ramp free-flow speed (mi/h)
The initial number of vehicles in the intersection approach are also

determined as an initial reference point, as follows:
𝐼𝑁𝑉(𝑖, 0, 𝑝, 𝑘) = 𝐼𝑁(𝑖, 𝑘) 𝑥 𝑄 Equation 38-A16
where
𝐼𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘)=numberof vehicles at the intersection of segment 𝑖, for level 𝑘 at the
end of time step 𝑡 during time period 𝑝
𝐼𝑁(𝑖, 𝑘) = number of lanes serving the subject approach 𝑘; and
𝑄 = back-of-queue length for the subject approach 𝑘 (veh).
The back-of-queue length 𝑄 is estimated using equations corresponding to

the intersection type at the ramp terminal (Exhibit 38-A25).
Intersection type Reference Equation Exhibit 38-A25

Reference HCM Equations for
Signalized 31-149
Back-of-Queue Length
TWSC 20-68
Estimation
AWSC 21-33
Roundabout 22-20
At signalized intersections, due to their cyclic nature, queues form and

discharge at different times for different movements. Therefore, a reference point
within the cycle must be selected as a starting point in the methodology. The
methodology assumes pretimed signalization or converts actuated control to the
equivalent pretimed pattern. Typical signalized intersections at ramp terminals
have the off-ramp approach as the minor movement, with a start of green on the


right side of the barrier (Exhibit 38-A26). It is recommended setting a reference

point at the onset of green for phases 3 and 7, as the back-of-queue lengths at this
time can be easily estimated using the methodology of Section 4, HCM Chapter
31.
Exhibit 38-A26
Selection of a Cycle Reference
Point to Determine the Initial
Number of Vehicles Within the
Approach

The methodology to evaluate the capacity of the terminal is specific to each
intersection type and relies mostly on the respective HCM chapters (19 through
23).
Signalized Intersections
For a signalized intersection approach, the capacity for each movement at
each time step is a function of the signal phase sequence and the capacities of the
individual movements at the intersection. Exhibit 38-A27 illustrates a sample
signalized intersection approach from an off-ramp, with two lane groups: left-
turn (Phase 3) and right turn (Phase 8).


Exhibit 38-A27
Sample Signalized
Intersection Approach from an
Off-Ramp
Input Parameters
The required parameters to evaluate the capacity of a ramp terminal capacity
are generally the same required for standard signalized intersection analyses, as
listed in Exhibit 19-11.
Arrival type: Chapter 19 of the HCM (Exhibit 19-14) provides guidelines for
selecting the appropriate Arrival Types based on the characteristics of arterial
operations, such as quality of progression and coordination. For an off-ramp
approach to the intersection, vehicles arrivals can be considered random.
Therefore, Arrival Type 3 (random arrivals) is recommended to analyze the off-
ramp approach at a signalized ramp terminal.
Phase duration and effective green time: The duration of each phase at the signal
can be fixed (pre-timed control), or variable (semi-actuated or actuated control).
For the former case, phase duration is known. For the latter, an average phase
duration is estimated as described in Section 2 of HCM Chapter 31 – Signalized
Intersections Supplemental. The effective green time g for each phase can then be
computed according to HCM Equation 19-3:
𝑔 =𝐷 −𝑙 −𝑙 Equation 38-A17
where
𝑔 = effective green time (s)
𝐷 = phase duration (s)
𝑙 = start-up lost time = 2.0 (s)
𝑙 = clearance lost time = 𝑌 + 𝑅 – 𝑒 (s)
Converting approach capacity from time periods to time steps

The standard signalized intersection analysis is performed in 15-min periods,
while the queue spillback evaluation requires a 15-second approach compatible
with the Freeway Facilities oversaturated methodology. Therefore, an
adjustment is necessary to calculate the capacities of each movement in 15-
second intervals.
The cycle length C can be divided into n time steps, with a duration of 15 s
each seen in Exhibit 38-A28. If an integer number of time steps is not obtained,


the difference is included in the first time-step of the next cycle. Then, green
times for each time step from 1 to n are computed. This procedure must be
repeated for every time step within the 15 minutes time period, resulting in a
total of 900/15 = 60 time-steps.
Exhibit 38-A28
Conversion of Green Times to
Time Steps
The capacity ID for each approach and for each time step, is then obtained by
multiplying its respective green time by its capacity, as shown:
Equation 38-A18 𝐼𝐷(𝑖, 𝑡, 𝑝, 𝑘) = 𝑁 𝑠 𝐺𝑇(𝑖, 𝑡, 𝑝, 𝑚) × 𝑓
Where
𝑁 = number of lanes serving movement k
𝑠 = saturation flow rate for movement k (veh/h/ln)
𝐺𝑇(𝑖, 𝑡, 𝑝, 𝑚) = green time for each movement m (s)
The green time parameter GT(i,t,p,m) measures the available green time for a
given intersection movement m, downstream of a freeway segment i, in time step
t and time period p. It can range from 0 (when the movement has red through the
entire time step length) to 15 (movement has green through the entire time step
length).
The heavy vehicle factor fHV needs to be applied to the equation for
intersection discharge to make the units used in intersection capacity (veh/h)
consistent with the flow rates used in uninterrupted flow methods (pc/h).
Step 2H - Determine reference index for next downstream off-ramp

This step is essential for building the computational engine for this
procedure, but it is not important for understanding the overall methodology.
The Freeway Systems methodology uses the parameter OFRF(i,t,p) to store the
off-ramp flow rate at diverge segment i. When a segment upstream of an off-
ramp is evaluated for queue spillback, the off-ramp flow rate must be referenced
in order to estimate the incoming flows for the blocked and non-blocked lanes.
Therefore, a new variable NEXTOFR(i), is introduced to reference the index of
the closest diverge segment downstream of segment i. This is illustrated in


Exhibit 38-A29, where the node (i+2) represents a diverge segment with an off-
ramp flow 𝑣 . When the queue extends upstream to node i, the approaching flow
𝑣 is segregated into two groups: the exiting vehicles that will join the back of the
queue, and the through vehicles that will use the non-blocked lanes.
Exhibit 38-A29
Illustration of Mainline Flow
Rate Split into Blocked and
Unblocked Lanes
For nodes 𝑖 and 𝑖 + 1, the closest downstream off-ramp is located at node

(i+2), therefore the following parameter is computed:
𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖) = 𝑖 + 2
The use of the parameter NEXTOFR facilitates referencing diverge segments
downstream of a given segment 𝑖 and will be used for the spillback analysis
procedure described over the next section.

This is a new step in the Freeway Facilities Analysis method (Exhibit 38-A8).
In this step, spillback effects in a diverge segment are determined after the off-
ramp flow OFRF is determined (steps 7/8).
(a) Determine ramp input, RI

The ramp input, RI, represents demand, and it is the number of vehicles that
wish to travel through the ramp proper node during a given time step. It takes
into account the off-ramp demand, OFRF (as defined in the Freeway Facilities
Oversaturated methodology) and the number of off-ramp unserved vehicles
from the previous time step, RUV. The OFRF parameter already takes into
consideration any bottleneck segments upstream of the diverge that may meter
the off-ramp demand (HCM Equations 25-23 through 25-25). The RI is calculated
as:
𝑅𝐼(𝑖, 𝑡, 𝑝) = 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) + 𝑅𝑈𝑉(𝑖, 𝑡 − 1, 𝑝) Equation 38-A19
where
OFRF(I, t, p) = flow that can exit the off-ramp 𝑖 during time step 𝑡 in time period 𝑝
RUV(I, t, p, k)= number of unserved vehicles at the off-ramp exit at segment 𝑖, during
time step 𝑡 in time period 𝑝
Calculate flow to the off-ramp and number of unserved vehicles

The ramp maximum flow RF represents capacity, i.e., the number of vehicles
that are able to enter the ramp proper by crossing the boundary node between
the diverge segment and the ramp proper. It is calculated as the minimum of
three variables: RI, RC and RSTG.


Equation 38-A20 𝑅𝐹(𝑖, 𝑡, 𝑝) = 𝑚𝑖𝑛 𝑅𝐼(𝑖, 𝑡, 𝑝, 𝑘), 𝑅𝐶(𝑖, 𝑘), 𝑅𝑆𝑇𝐺(𝑖, 𝑡, 𝑝, 𝑘)

The parameters RI and RC have been previously defined. The parameter
RSTG represents the maximum number of vehicles that can enter the ramp due
to a queue inside the ramp proper. The calculations follow the same approach
taken by the Mainline Output 2 (MO2) parameter (Equation 25-11). It starts by
calculating the maximum number of vehicles allowed on the ramp at a given
ramp queue density RKQ:
Equation 38-A21 (𝐾𝐽 – 𝑅𝐾𝐶)𝑥 𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
𝑅𝐾𝑄(𝑖, 𝑡, 𝑝, 𝑘) = 𝐾𝐽–
𝑅𝐶(𝑖, 𝑡, 𝑝)
The calculation of RKQ takes an approach similar to the calculation of the
mainline queue density KQ (Equation 25-10), with the following remarks on the
inputs:
• The jam density parameter KJ uses the same value adopted for the
mainline calculations
• The ramp density at capacity RKC is determined based on the ramp FFS
(Exhibit 38-A24)
• The parameters SF (segment flow) and SC (segment capacity) from
Equation 25-10 are replaced with RF (ramp flow, previously defined) and
RC (ramp capacity, previously defined)
The maximum ramp storage constraint RSTG is then calculated using an
approach similar to the Mainline Output 2 (MO2) parameter from the
Oversaturated segment evaluation procedure. This constraint limits the number
of vehicles able to enter the off-ramp due to the presence of a queue within the
ramp proper. RTTG is calculated as:
Equation 38-A22 𝑅𝑆𝑇𝐺(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝑅𝐾𝑄(𝑖, 𝑡, 𝑝, 𝑘)𝑥 𝑅𝐿(𝑘)𝑥 𝑅𝑁(𝑘)
− 𝑅𝑁𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘)
Next, the number of unserved vehicles at the ramp entrance RUV is
calculated. For each time step, the number of unserved vehicles is computed as
the value from the previous time step, plus the difference between demand (RI)
and throughput (RF) at the ramp node. RUV is calculated as:
Equation 38-A23 𝑅𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝑈𝑉(𝑖, 𝑡 − 1, 𝑝 , 𝑘) + 𝑅𝐼(𝑖, 𝑡, 𝑝, 𝑘) − 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘)
where
K = number of different branches at the intersection
If there are multiple branches k at the ramp proper (two lane ramps), RI and
RF are compared for each branch k to obtain RUV for each branch k. The total
number of unserved vehicles at the ramp RUV(i,t,p) is then obtained as the sum
of RUV for each lane:
Equation 38-A24 𝑅𝑈𝑉(𝑖, 𝑡, 𝑝) = 𝑅𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘)
(b) Calculate approach input, II

The intersection approach input II is the number of vehicles that wish to
travel through the intersection node during a given time step, i.e., its demand. It


takes into account the off-ramp flow RF and the number of unserved vehicles on
the approach from the previous time step IUV. II is calculated as:
𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) + 𝐼𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A25
(c) Calculate maximum ramp output

The maximum allowable ramp output (RO) is calculated as a function of the
available storage space within the intersection approach, minus the number of
vehicles present at the previous time step and the number of vehicles discharged
(IDC) in the present time period. RO is estimated as:
𝑅𝑂(𝑖, 𝑡, 𝑝, 𝑘) = 𝐼𝑆𝑇𝐺(𝑖, 𝑘) − 𝐼𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝐼𝐷𝐶(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A26
(d) Calculate intersection approach flow and number of unserved

vehicles
The intersection flow IF represents the number of vehicles that are able to
cross the boundary node between the ramp proper and the intersection (i.e., its
capacity). It is computed as the minimum value between the number of vehicles
that wish to enter the intersection and the maximum number of vehicles allowed
to enter the intersection due to the available queue storage in the intersection:
𝐼𝐹(𝑖, 𝑡, 𝑝, 𝑘) = 𝑚𝑖𝑛 𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘), 𝑅𝑂(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A27
If the number of vehicles trying to enter the intersection exceeds the amount
of vehicles allowed to enter the intersection, then the number of total unserved
vehicles must be computed and considered in the intersection input II during the
next time period:
𝐼𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 𝐼𝑈𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘) − 𝑅𝑂(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A28
(e) Update number of vehicles at the ramp terminal intersection

The number of vehicles at the intersection, NV, is updated every time step
based on the NV from the previous time step, plus the number of vehicles that
enter the intersection approach minus the number of vehicles that are
discharged. The maximum allowable total number of vehicles is function of the
available storage at the intersection, ISTG. NV is calculated as:
𝐼𝑁𝑉(𝑖, 𝑡, 𝑝) = 𝐼𝑁𝑉(𝑖, 𝑡 − 1, 𝑝) + 𝐼𝐹(𝑖, 𝑡, 𝑝, 𝑘) − 𝐼𝐷𝐶(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A29
(f) Calculate number of unserved vehicles at the off-ramp

The number of unserved vehicles, OFRUV, at the entrance of the ramp
proper is updated every time step as the difference between the number of
vehicles that wish to enter the ramp proper (RI) and the flow through the ramp
node (RF):
𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡, 𝑝) = 𝑅𝐼(𝑖, 𝑡, 𝑝) − 𝑅𝐹(𝑖, 𝑡, 𝑝) Equation 38-A30
(g) Calculate intersection approach output

The intersection flow, IO, represents the actual number of vehicles
discharging from the intersection approach. It is computed as the minimum
value between the intersection discharge capacity and the sum of number of
vehicles present in the intersection and the intersection input demand:
Equation 38-A31


𝐼𝑂(𝑖, 𝑡, 𝑝, 𝑘) = 𝑚𝑖𝑛 𝐼𝐷𝐶(𝑖, 𝑡, 𝑝, 𝑘), 𝐼𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘)
(h) Update number of vehicles at the ramp proper

The number of vehicles at the ramp proper, RNV, at the end of each time
step is calculated based on the number of vehicles from the previous time step
plus the number of vehicles that entered the ramp minus the number of vehicles
that left the ramp:
Equation 38-A32 𝑅𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝑁𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) − 𝐼𝐹(𝑖, 𝑡, 𝑝, 𝑘)
(i) Determine the back-of-queue length and spillback regime

Field observations have shown that off-ramp queues blocking mainline lanes
are typically not stationary. These queues usually consist of a platoon of closely
spaced vehicles moving at very low speeds (< 15mph). The spacing between
vehicles is also longer than the average vehicle spacing in stationary queues,
represented in the HCM by Lh (Equation 31-155). Therefore, the density of the
spillback queue follows the queue density at the ramp (RKQ, as previously
defined), which allows the estimation of the queue length OFRLQ. This
parameter estimates the total queue length upstream of the off-ramp if all
unserved vehicles formed a single queue:
Equation 38-A33 𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡, 𝑝)
𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) =
𝑅𝐾𝑄 (𝑖, 𝑡, 𝑝)
Next, the mainline queue length, SBLQ, is compared to the available
spillback queue storage for the prevalent spillback regime for the given time
step, as follows:
If OFRLQ = 0 → Regime 0
If 0 < OFRLQ ≤ LD → Regime 1
If SBLQ > LD :
If SL(i,p) > 0:
If OFRLQ < (LD + SL) → Regime 2
Else: Regime 3 / 4
Finally, the queue length in the mainline lanes MQ1 (lane 1) and MQ2 (lane
2) are obtained as a function of the expected spillback regime. The total queue
length OFRLQ minus the available storage lengths at the deceleration lane and
shoulder computes the queue length that the associated blockage.
If the site experiences Regime 3:
𝑀𝑄1(𝑖, 𝑡, 𝑝, 𝑘) = 𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝, 𝑘) − 𝐿𝐷(𝑖)– 𝑆𝐿(𝑖)
Equation 38-A34
𝑀𝑄2(𝑖, 𝑡, 𝑝, 𝑘) = 0

𝑀𝑄1(𝑖, 𝑡, 𝑝) = 𝑀𝑄2(𝑖, 𝑡, 𝑝) = [𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) − 𝐿𝐷(𝑖)– 𝑆𝐿(𝑖) ] / 2
Equation 38-A35
(a) Check for impacts on upstream nodes
The freeway nodes upstream of a congested off-ramp may be affected by
spillback as queues grow. When this occurs, the methodology calculates the


length of the queue in the upstream segment. The length of the queue within the
subject segment will then be used to evaluate whether the capacity of any
upstream node is affected by the queue.
For upstream segments that may be affected by spillback, the queue length
within the segment (measured from its downstream end) must be computed and
stored in the parameter SBLQ. This check is performed for every node upstream
of a congested off-ramp (Exhibit 38-A30).
Exhibit 38-A30
Procedure for Evaluating the
Impact of Queue Spillback on
Upstream Nodes and
Determination of the Queue
Length within Upstream
Segments
When queue spillback occurs in a downstream off-ramp, the length of the

mainline queue measured from the start of the deceleration lane is known from
the previous step. If a given segment has any queues blocking one or more lanes,
three possible scenarios may occur at the node (Exhibit 38-A31):
1. Lane blockage: Queues extend through the entire segment and reach
the upstream node, causing the subject node to operate in a two-pipe
regime. The blocked lanes operate in a congested regime, with their
capacity constrained by the off-ramp capacity. The unblocked lanes,
on the other hand, operate at uncongested conditions with a small
reduction in capacity due to the friction of through vehicles passing
along congested lanes. For the through lanes, an adjustment factor
CAFBL is applied. This condition occurs when the Spillback Queue
length SBLQ(i) is equal or greater than the Segment Length L(i).


2. Increased turbulence: Queues extend partially through the segment

and the upstream node is located within the Queue Influence Area
(QIA). This region is characterized by intense turbulence as vehicles
quickly perform lane changes to adjust their position reacting to the
queue ahead, and all lanes in node i have their capacity reduced by
an adjustment factor CAFUP. This condition occurs when the sum of
the Spillback Queue length SBLQ(i) and the Queue Influence Area
QIA(i) is equal or greater than the segment length L(i).
3. No effect: Queues extend partially through the segment, but the
upstream node is located within the Queue Influence Area (QIA).
For this condition, no capacity adjustment factors are applied to the
node i. This condition occurs when the sum of the Spillback Queue
length SBLQ(i) and the Queue Influence Area QIA(i) is smaller than
the segment length L(i).
Exhibit 38-A31
Illustration of Different
Impacts of an off-Ramp
Queue at Node i: (a) Lane
Blockage, (b) Increased
Turbulence and (c) No Effect
(b) Calculate capacity adjustment factors

Based on how upstream nodes are affected as described under Step 6B (Lane
Blockage, Increased Turbulence or No Effect), the corresponding impacts on
capacity are computed in this step. This section describes the calculations of
capacity adjustments depending on how upstream nodes are affected.
Lane blockage adjustment factor

When one or more lanes are blocked, the subject node is analyzed as a two-
pipe operation, with a congested flow in one or more lanes of the ramp side and
uncongested flow in the remaining lanes.
The capacity of these lanes is equal to the number of queued vehicles
discharged at the downstream segment. The flow rate attempting to cross the
node through the congested lanes is equal to the off-ramp flow rate (OFRF) at the
closest downstream off-ramp.
Increased turbulence adjustment factor

When a node falls under the Increased Turbulence case (Exhibit 38-A31b), all
lanes are affected by the turbulence caused by the intense lane changing. In this
case, an adjustment factor CAFUP is applied uniformly to the node capacity:
.
Equation 38-A36 𝐶𝐴𝐹𝑈𝑃(𝑖, 𝑡, 𝑝) = 1 − 0.52 × 𝐿𝐶𝑅(𝑖, 𝑡, 𝑝)


The parameter LCR estimates the rate of lane change maneuvers performed
by vehicles within the Queue Influence Area trying to adjust their position when
spillback occurs. Vehicles traveling towards the exit ramp will move to the
shoulder lane attempting to join the back of the queue, while vehicles traveling
through will move to the median lanes in order to avoid the queue. Therefore,
the lane change rate LCR is computed as:
𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝) Equation 38-A37
𝐿𝐶𝑅(𝑖, 𝑡, 𝑝) =
𝑆𝐹(𝑖, 𝑡, 𝑝)
The parameter SBLC estimates the number of lane change maneuvers

performed by vehicles within the Queue Influence Area trying to adjust their
position when spillback occurs. Vehicles traveling towards the exit ramp will
move to the shoulder lane attempting to join the back of the queue, while
vehicles traveling through will move to the median lanes in order to avoid the
queue.
In order to compute SBLC for a given node, the number of vehicles driving
toward the off-ramp must be estimated for each freeway lane. For each lane 𝑖, the
parameter pi represents the percent of the off-ramp demand 𝑣 traveling on the
subject lane. In order to estimate the values of pi as a function of the distance
from the off-ramp to the subject node, the following steps and assumptions are
used:
(a) Within the influence area (1,500 ft from the exit point), the off-ramp
demand flow rate 𝑣 is entirely positioned in the two rightmost
lanes, according to the guidance provided in HCM Chapter 14.
Therefore, the sum of the off-ramp flow rate percentages in the ramp
influence area p1,R and p2,R is equal to 1. The methodology to estimate
lane-by-lane flow distribution in freeway segments allows the
estimation of the Lane Flow Ratio (LFR) for lanes 1 and 2. The
proportion between p1,R and p2,R can then be estimated as follows:
𝐿𝐹𝑅
𝑝 , = Equation 38-A38
𝐿𝐹𝑅 + 𝐿𝐹𝑅
𝐿𝐹𝑅
𝑝 , =
𝐿𝐹𝑅 + 𝐿𝐹𝑅
(b) According to the guidance provided in HCM Chapter 14, the
influence of ramps rarely extends beyond 8,000 ft. Therefore, for any
nodes located beyond 8,000 from the off-ramp, the distribution of pi
is taken as equal among all N freeway lanes:
1 Equation 38-A39
𝑝 =
𝑁
(c) At intermediate distances from the off-ramp ranging between
1,500 ft and 8,000 ft, the distribution values of pi can be obtained
through linear interpolation between the cases previously described.


Exhibit 38-A32
Distribution of pi as Function
of Distance from the Off-
Ramp Exit, for a 3-Lane
Segment
The value of pi as function of the distance from off-ramp exit can then be
obtained through the following equation:
1
Equation 38-A40 − 𝑝 , 𝑅 × (𝑑 − 1,500)
𝑝 =𝑝, + 𝑁
6500
As the lane-by-lane distribution of the off-ramp flow is known, the number
of lane change maneuvers, SBLC, can then be estimated. For Regime 3 cases (one
blocked lane), the number of lane changes is obtained as follows:
Equation 38-A41 𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝) = 𝑣 (1 − 𝑝 ) + (𝑖 − 1) × 𝑣 𝑝
The equation adds the number of through vehicles in lane 1 that move to
lane 2 to avoid the queue and the number of exiting vehicles in the remaining
lanes that adjust their position to join the back of the queue, multiplied by the
necessary number of lane changes. Exhibit 38-A33 illustrates an example of the
proposed equation applied to a 4-lane segment.
Exhibit 38-A33
Illustration of Lane Change
Maneuvers Within the Queue
Influence Area in a 4-Lane
Segment With Regime 3
For Regime 4 cases, the following equation is applied to obtain SBLC:
Equation 38-A42 𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝) = 2 × 𝑣 (1 − 𝑝 ) + 𝑣 (1 − 𝑝 ) + (𝑖 − 2) × 𝑣 𝑝
Exhibit 38-A34 illustrates an example of the proposed equation applied to a

4-lane segment.
Exhibit 38-A34
Illustration of Lane Change
Maneuvers Within the Queue
Influence Area in a 4-Lane
Segment With Regime 4


Step 9 - Calculate mainline input

The Oversaturated Segment Evaluation procedure computes the Mainline
Input (MI) for each node, in every time step. It is defined as the maximum flow
desiring to enter the subject node during the current time step.
An adjustment is necessary when the subject node is operating in a two-pipe
regime, as the blocked and unblocked portions will be subject to different input
demands. Since exiting and through drivers segregate when approaching a
queue, the mainline input demand in the blocked side consists of the off-ramp
demand, while the remaining demand will move to the unblocked portion.
When node i operates in a two-pipe regime, the Mainline Input (MI)
parameter is split into two components: MIUB, representing the mainline input
in the unblocked lanes, and MIBL, representing the mainline input joining the
back of the queue. These parameters are computed as follows:
𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑂𝐹𝑅𝐹(𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖), 𝑡, 𝑝) Equation 38-A43
𝑀𝐼𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝐼(𝑖, 𝑡, 𝑝) − 𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝) Equation 38-A44
Step 12 - Calculate on-ramp maximum output

If there is a merge segment upstream of an off-ramp bottleneck, the capacity
of on-ramp output may be affected due to the blockage caused by the spillback
queue. The Oversaturated Segment evaluation procedure calculates the on-ramp
maximum output through HCM Equation 25-18, based on a series of potential
constraints that include ramp metering, the on-ramp capacity, the capacity of the
merge, or the presence of downstream queues. At high demands on both the
freeway and the on-ramp, zipper merge (one-to-one) is expected to occur.
Therefore, a new capacity constraint is added to Equation 25-18, included in the
equation below in bold font and illustrated in Exhibit 38-A35:
𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝)
Equation 38-A45
𝑅𝑀(𝑖, 𝑡, 𝑝)
⎧
𝑂𝑁𝑅𝐶(𝑖, 𝑡, 𝑝)
⎪
⎪ 𝑀𝐹(𝑖 + 1, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪ ⎧𝑚𝑖𝑛 − 𝑀𝐼(𝑖, 𝑡, 𝑝)
𝑀𝑂3(𝑖, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪ ⎪
⎪ 𝑆𝐶(𝑖, 𝑡, 𝑝)
= 𝑚𝑖𝑛( ⎪
⎨𝑚𝑎𝑥( 𝑚𝑖𝑛 𝑀𝐹(𝑖 + 1, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪ ⎨ 𝑀𝑂3(𝑖, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪ ⎪ 2𝑁(𝑖, 𝑝)
⎪ ⎪ 𝑹𝑭(𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊), 𝒕, 𝒑))
⎪ ⎪
⎩ ⎩ 𝟐 × 𝑵𝑸 𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊)


Exhibit 38-A35
Impact of a queue spillback
on the discharge capacity of
an upstream on-ramp
If one or more lanes are blocked due to a downstream off-ramp bottleneck,

the throughput in Lane 1 will be equal to the maximum exit throughput in the
congested off-ramp if the site operates in Regime 3, or 50% of the maximum exit
throughput in the off-ramp, if it operates in Regime 4. It is assumed that the on-
ramp and the flow arriving from the upstream on Lane 1 contribute equally to
the downstream Lane 1 flow, and thus the on-ramp maximum output, in this
case, is assumed to be half of the downstream throughput in Lane 1.
Step 21 - Calculate mainline output (2)

The Oversaturated Segment Evaluation methodology calculates the
maximum number of vehicles, MO, that can exit a node, constrained by a
downstream bottleneck or by merging on-ramp traffic. Among the potential
constraints to calculate MO, the Mainline Output 2 accounts for the growth of
queues on a downstream segments, eventually limiting the maximum number of
vehicles that can enter it.
When there is a queue in a downstream segment caused by a downstream
off-ramp bottleneck, the segment is expected to operate under two distinct
densities (Exhibit 38-A36). Therefore, the total number of vehicles in the
downstream segment takes into account two different density values: the ramp
queue density (RKB), prevailing at the queued area in red, and the background
density (KB), prevailing in the remaining area of the segment (blue).
Exhibit 38-A36
Illustration of Different
Density Values Within One
Diverge Segment
If there are no spillback effects, the segment operates with a uniform density.
In this case, the constraints for the unblocked and blocked portions (MO2UB and
MO2BL, respectively) are calculated proportionately to the number of unblocked
and blocked lanes:


1 − 𝑁𝑄(𝑖) Equation 38-A46

𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) ×
𝑁(𝑖)
𝑁𝑄(𝑖)
𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) × Equation 38-A47
𝑁(𝑖)
If node i operates under Increased Turbulence (node is in the Queue
Influence Area), the unblocked portion of segment i will operate similar to a
regular segment. Therefore, the component MO2UB is equal to MO2 but
proportional to the number of lanes in the unblocked portion:
1 − 𝑁𝑄(𝑖) Equation 38-A48
𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) ×
𝑁(𝑖)
For the blocked portion of segment i, the parameter is calculated as equal to
MO2 proportional to the number of lanes in the blocked portion plus an
additional number of vehicles due to the presence of a partial queue. This
additional number of vehicles is obtained by the bold terms in the following
equation, which takes into account the difference between the queue spillback
density (RKQ) and the segment queue density (KQ), multiplied by the queue
length:
𝑁𝑄(𝑖)
𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) × + 𝑆𝐵𝐿𝑄(𝑖, 𝑡 − 1, 𝑝) × 𝑁𝑄(𝑖, 𝑡 − 1, 𝑝) Equation 38-A49
𝑁(𝑖)
× [𝑅𝐾𝑄(𝑂𝐹𝑅𝑁𝐸𝑋𝑇(𝑖), 𝑡 − 1, 𝑝) − 𝐾𝑄(𝑖 − 1, 𝑡 − 1, 𝑝)]
If node i experiences lane blockage, the values of queue density must be
computed for both the unblocked (KQUB) and blocked (KQBL) portions of
segment i. For the unblocked portion, the queue density KQUB is calculated
similarly to Equation 25-10, but the inputs for segment flow (SF) and segment
capacity (SC) are replaced by their equivalent parameters SFUB and SCEQ:
𝐾𝑄𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝐾𝐽 − [(𝐾𝐽 − 𝐾𝐶)] × 𝑆𝐹𝑈𝐵(𝑖, 𝑡 − 1, 𝑝)]/𝑆𝐶𝐸𝑄(𝑖, 𝑝) Equation 38-A50
The queue density for the blocked portion is computed as equal to the ramp
queue density:
𝐾𝑄𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑅𝐾𝑄(𝑂𝐹𝑅𝑁𝐸𝑋𝑇(𝑖), 𝑡 − 1, 𝑝) Equation 38-A51
With the queue density values for both the blocked and unblocked portions
known, the MO2 components MO2BL and MO2UB can be computed:
𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑆𝐹𝑈𝐵(𝑖, 𝑡 − 1, 𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) Equation 38-A52
+ 𝐾𝑄𝑈𝐵(𝑖, 𝑡, 𝑝) × 𝐿(𝑖) × 𝑁(𝑖, 𝑝) − 𝑁𝑄(𝑖, 𝑝) − 𝑁𝑉(𝑖, 𝑡 − 1, 𝑝)

𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑆𝐹𝐵𝐿(𝑖, 𝑡 − 1, 𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) Equation 38-A53
+ [𝐾𝑄𝐵𝐿(𝑖, 𝑡, 𝑝) × 𝐿(𝑖) × 𝑁𝑄(𝑖, 𝑝)] − 𝑁𝑉(𝑖, 𝑡 − 1, 𝑝)
Step 22 - Calculate mainline flow

The Oversaturated Segment Evaluation procedure computes the Mainline
Flow through a subject node as the minimum of several variables, as presented
in HCM Equation 25-16. If the node experiences spillback, the calculation of
Mainline Flow must consider the flow through both the blocked and the
unblocked portions of the node. Therefore, the Mainline Flow (MF) parameter is
split into two components in an approach similar to the Mainline Input: the


component MFUB represents flow across the node in the unblocked lanes, while
the component MFBL represents the flow across the node in the blocked lanes.
For both components, the resulting flow is computed as the minimum value
between input and the maximum allowed flow.
For MFUB, the maximum allowed flow is equal to the capacity of unblocked
lanes in the downstream segment, represented by the parameter SCEQ as
computed in the initialization step:
Equation 38-A54 𝑀𝐹𝑈𝐵(𝑖) = 𝑚𝑖𝑛 𝑀𝐼𝑈𝐵(𝑖, 𝑡, 𝑝), 𝑆𝐶𝐸𝑄(𝑖, 𝑡, 𝑝), 𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝)
For MFBL, the maximum allowed flow is equal to the flow allowed to enter
the nearest downstream off-ramp RF, as presented in the following equation:
Equation 38-A55 𝑀𝐹𝐵𝐿(𝑖) = 𝑚𝑖𝑛(𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝), 𝑅𝐹(𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖), 𝑡, 𝑝, 𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝))
Next, the Mainline Flow MF through node i is computed as the sum of the
blocked and unblocked portions, as follows:
Equation 38-A56 𝑀𝐹(𝑖, 𝑡, 𝑝) = 𝑀𝐹𝑈𝐵(𝑖, 𝑡, 𝑝) + 𝑀𝐹𝐵𝐿(𝑖, 𝑡, 𝑝)
Step 25 - Update number of vehicles in the blocked portion of the segment

The number of vehicles in the blocked portion NVBL during increased
turbulence is updated based on the number of vehicles in the previous time step
and considers the number of vehicles that are able to leave the current and
upstream segment :
𝑁𝑉𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑁𝑉𝐵𝐿(𝑖, 𝑡 − 1, 𝑝) + 𝑀𝐹𝐵𝐿(𝑖 − 1, 𝑡, 𝑝) Equation 38-A57

+ 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝) − 𝑀𝐹𝐵𝐿(𝑖, 𝑡, 𝑝)
− 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝)

The aggregated segment flow for a 15-min time period is obtained as the
sum of flows for every time step (HCM Equation 25-30):
𝑇
Equation 38-A58 𝑆𝐹(𝑖, 𝑝) = 𝑆𝐹(𝑖, 𝑡, 𝑝)
𝑆
Similarly, the aggregated off-ramp ramp is aggregated at a 15-min time

period:
𝑇
Equation 38-A59 𝑂𝐹𝑅𝐹(𝑖, 𝑝) = 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝)
𝑆
The additional density in the queued lanes is obtained by aggregating the

additional number of vehicles ΔNV(i,t,p) in the off-ramp queue:
1
Equation 38-A60 ∆𝐾(𝑖, 𝑝) = ∆𝑁𝑉(𝑖, 𝑡, 𝑝)
𝑆×𝑁
Similar to the mainline, the flow in the ramp roadway is also aggregated:


𝑇
𝑅𝐹(𝑖, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A61
𝑆
The aggregated density at the ramp is calculated as the average of the

number of vehicles inside the ramp along the time period:
1
𝑅𝐾(𝑖, 𝑝, 𝑘) = 𝑅𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘) Equation 38-A62
𝑆
Finally, the speed at the ramp for a time period p is obtained by dividing the
total ramp flow in the time period by its average density:
𝑅𝐹(𝑖, 𝑝, 𝑘) Equation 38-A63
𝑆𝑅(𝑖, 𝑝, 𝑘) =
𝑅𝐾(𝑖, 𝑝, 𝑘)


APPENDIX B: ON-RAMP QUEUE SPILLBACK ANALYSIS
Queue spillback into an urban street intersection may occur when the
freeway merge segment has insufficient capacity to process the ramp’s demand.
Spillback may also occur in cases of ramp metering. This appendix presents the
methodology for determining whether spillback will occur from an on-ramp into
the upstream intersection.
The methodology considers signalized intersections, two-way stop-
controlled intersections, all-way stop controlled intersections, and roundabouts.
The procedure first estimates the demand approaching the on-ramp (determined
based on the upstream intersection’s configuration), and then estimates the
capacity of the off-ramp. The Chapter 10, Freeway Facilities methodology for
oversaturated conditions can estimate the resulting queue length, however, the
user must input the on-ramp demand flow rate.
The methodology framework for conducting this spillback check is presented
Exhibit 38-B1 .
Exhibit 38-B1
Procedure for Detecting
Spillback Occurrence at an
On-Ramp
Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft)


DEMAND ESTIMATION
The first step in the methodology calculates the entering demand flow rate at
the on-ramp (𝑣 ), as a function of the upstream intersection configuration and
operations. Under low demand conditions, the on-ramp demand flow rate is
calculated as the sum of the demands on each of the intersection approaches that
discharge into the ramp. However, if any of these movements is operating over
capacity, the total throughput to the ramp will be constrained by the capacity of
these oversaturated movements. Hence, this check ensures that the on-ramp
demand is not overestimated. The analysis approach for each of four intersection
types is presented next.
Case A: Signalized intersections

The throughputs of a signalized intersection are highly dependent on several
parameters such as phasing sequences, actuation, cycle lengths, and permitted-
protected phasing, among others. The methodology of this chapter identifies the
movements that discharge to the on-ramp and their operational characteristics
(permitted or protected). For example, typical diamond interchanges will include
a left-turn movement, a right-turn movement and a through movement (which
will typically have negligible flow).
The on-ramp demand 𝑣 is computed as the sum of the throughputs of each
movement that discharges into the on-ramp. The throughput of a given
movement i is obtained as the minimum value of its demand and capacity:
𝑣 = min(𝑣 , 𝑐 )
Equation 38-B1
where
𝑣 = on-ramp demand (veh/h);
𝑣 = demand for movement 𝑖 at the intersection (veh/h);
𝑐 = demand for movement 𝑖 at the intersection (veh/h);
𝑁 = number of intersection movements that discharge into the on-ramp
If all movements operate below capacity, the on-ramp demand is obtained as
the sum of the movement demands. If any of the ramp terminal movements that
discharge into the on-ramp operates over capacity, the total throughput to the
on-ramp will be lower than the sum of the corresponding intersection
movements.
Unsignalized Movements
In the case of unsignalized movements discharging into the on-ramp, the
demand for these movements must also be compared to their capacity. The
potential capacity cp,i of an unsignalized movement can be computed by
aggregating its saturation flow rates at different phases throughout a cycle.
If the unsignalized movement is free-flowing and there are no other
conflicting movements discharging to the on-ramp, its saturation flow rate sFF is
obtained by HCM Equation 19-8, with the applicable adjustment factors applied:
Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis


𝑠 =𝑠 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓
Equation 38-B2
Where
𝑠 = saturation flow rate for unsignalized movement during free-flow
(veh/h/ln);
𝑠 = base saturation flow rate (pc/h/ln)
All other adjustment factors are as described in Equation 19-8.
If the unsignalized movement must yield to a conflicting movement
discharging to the on-ramp, the permitted saturation flow rate sp is calculated
based on HCM equation 31-100:
𝜆 𝑒 ,
𝑠 =
1−𝑒 ,
Where:
𝑠 = permitted saturation flow rate for unsignalized movement (veh/h/ln);
𝜆 = throughput of the conflicting movement (veh/h/ln)
𝑡 = critical headway = 4.5 (s);
𝑡 = follow-up headway = 2.5 (s)
The throughput of the conflicting movement 𝜆 is determined as a function

of the flow profile of the respective conflicting movement. The effective green (𝑔)
of the conflicting movement is divided into a queue service time (𝑔 ) and a green
extension time (𝑔 ), each with a specific flow profile:
• If the conflicting movement occurs during the queue service time
(𝑔 ), 𝜆 is equal to the saturation flow rate s of the conflicting
movement;
• If the conflicting movement occurs during the green extension time
(𝑔 ), 𝜆 is equal to the arrival flow rate during the green 𝑞 (Equation
19-32) of the conflicting movement.
Case B – Two-Way Stop Controlled (TWSC) intersections

The TWSC intersection analysis is based on the calculation of the potential
capacities of each movement, based on factors such as priority order, conflicting
flow, and critical gap. With very few adjustments, estimating the on-ramp
throughput from this intersection type is a relatively straightforward task.
The procedure first identifies the movements that discharge to the on-ramp
and their respective ranks (priority orders). The evaluation of freeway-arterial
interactions assumes that for TWSC interchanges the urban street will always be
the major street.
Exhibit 38-B2 illustrates a typical TWSC intersection at a freeway
interchange, where movements discharging into the on-ramp are numbered


according to their ranks, using the default numbering of Chapter 20 (Exhibit 20-
1).
Exhibit 38-B2
Schematic of Movements
Turning to an On-Ramp from
a TWSC Intersection
Similarly to signalized intersections, there are three movements turning into

the ramp, and their respective flows are discussed below:
1. Rank 1 Movement (Right Turn from the Major Street): This movement is
considered unimpeded, experiencing zero delay. The only physical
constraint able to limit the throughput of this movement is its saturation
flow rate if demand is very high. Therefore, the maximum throughput λRT
(veh/h) for this right-turn movement is given by:
𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑠 )
Equation 38-B3
where
𝜆 = departure rate from major street right turn into the on-ramp (veh/h);
𝑣 = demand flow rate for the major street right turn; and
𝑠 = saturation flow rate for a right-turn movement (veh/h).
2. Rank 2 Movement (Left Turn from the Major Street): The maximum
throughput for this movement is limited by its potential capacity (𝑐 , ), as
defined in Equation 20-36. Therefore, the maximum throughput (veh/h)
for this left-turn movement is given by:
𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑐 , ) Equation 38-B4
where
𝜆 = departure rate from the major-street left-turn into the on-ramp (veh/h);
𝑣 = demand flow rate for the major street left turn; and
𝑐 , = potential capacity for the major street left turn (veh/h).


3. Rank 3 Movement (Through Movement from the Minor Street): Similar to rank
2 movements, the maximum throughput for this movement is limited by
its potential capacity (𝑐 , ), as defined in Equation 20-47. Therefore, the
maximum throughput λTh (veh/h) for this through movement is given by:
Equation 38-B5 𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑐 , )
where
𝜆 = departure rate from the minor street through into the on-ramp (veh/h);
𝑣 = demand flow rate for the minor street through; and
𝑐 , = potential capacity for the minor street through (veh/h).
Finally, the total on-ramp demand flow rate 𝑣 can be estimated as follows:
𝑣 =𝜆 + 𝜆 + 𝜆
Equation 38-B6
where
𝜆 = departure rate from major street right turn into the on-ramp (veh/h)
(Equation 38-B3);
𝜆 = departure rate from the major-street left-turn into the on-ramp (veh/h)
(Equation 38-B4); and
𝜆 = departure rate from the minor street through into the on-ramp (veh/h)
(Equation 38-B5).
Case C – All-Way Stop Controlled (AWSC) intersections

The AWSC methodology uses departure headways (ℎ ) for each approach,
making the calculation of the on-ramp flow straightforward. Exhibit 38-B3
illustrates the movements discharging into an on-ramp from an AWSC
intersection.
Exhibit 38-B3
an AWSC Intersection


The on-ramp demand flow rate can be obtained directly from the departure
headways of the three movements combined:
3600 3600 3600
𝑣 = + + Equation 38-B7
ℎ , ℎ , ℎ ,
where
𝑣 = on-ramp flow rate (veh/h);
ℎ , = departure headway for the major street right turn(s);
ℎ , = departure headway for the major street left turn(s); and
ℎ , = departure headway for the minor street through(s).
Case D: Roundabouts
The Roundabouts methodology is based on the calculation of the potential
capacities of each approach, based on three main variables: the critical and the
follow-up headways, and the circulating flow (Equation 22-21 through Equation
22-23). Both critical and follow-up headway values can be obtained from Chapter
33. The methodology considers each approach independently. To analyze
roundabouts within a system it is first necessary to estimate the on-ramp
throughput from a roundabout.
The procedure first identifies the movements that discharge to the on-ramp
and their respective ranks (priority orders). Exhibit 38-B4 illustrates a typical
roundabout, where movements discharging into the on-ramp are numbered
according to their ranks. In contrast to other types of intersections, the approach
furthest from the on-ramp has priority as it enters the circulating stream without
any significant conflicting traffic (other than occasional U-turns). The operation
of each of these movements is as follows:
Exhibit 38-B4
a Roundabout


Rank 1 Movement (Left-Turn from the Third Upstream Approach from the On-
Ramp):
This movement has priority over the other movements because it enters the
circulating stream first. Also, because the on-ramp does not have an approach
into the roundabout, this movement is most often unopposed by the circulating
stream (except for occasional U-turns in the intersection). Therefore, the
maximum throughput 𝜆 (veh/h) for this left-turn movement is given by:
Equation 38-B8 𝜆 = 𝑚𝑖𝑛(𝑣 ,𝑐 )
where
𝜆 = departure rate from the third upstream approach into the on-ramp
(veh/h);
𝑣 = demand flow rate for the third upstream approach into the on-ramp;
and
𝑐 = potential capacity for the approach (veh/h).
Rank 2 Movement (Through from the Second Upstream Approach, Most Likely an
Off-Ramp):
The maximum throughput for this movement is limited by the upstream
approach departure rate and its own potential lane capacity (𝑐 ), as defined in
Equations 22-21 through 22-23. Therefore, the maximum throughput 𝜆 veh/h)
for this through movement is given by:
where
𝜆 = departure rate from the second upstream approach into the on-ramp
(veh/h);
𝑣 = demand flow rate for the second upstream approach into the on-ramp
(veh/h); and
Rank 3 Movement (Right-Turn for the First Upstream Approach):

Similar to rank 2 movements, the maximum throughput for this movement is
limited by the immediately upstream approach and its own potential capacity
(c3 ), as defined in Equation 22-21 through Equation 22-23. Therefore, the
maximum throughput 𝜆 (veh/h) for this right-turn movement is given by:
where
𝜆 = departure rate from the first upstream approach into the on-ramp
(veh/h);
𝑣 = demand flow rate for the first upstream approach into the on-ramp;
and
Finally, the total on-ramp demand flow rate 𝑣 can be estimated as follows:


𝑣 =𝜆 + 𝜆 + 𝜆 Equation 38-B11
The total on-ramp demand flow rate can be calculated by the same method
for roundabouts with a higher number of approaches.
CAPACITY ESTIMATION
Capacity at the on-ramp must be estimated in order to predict the occurrence
of queue spillback. Three cases may occur:
Case 1: Ramp Metering is Active

In this case, the metering rate is a required user input (veh/h) and is stored in RM(i,t,p) is defined in Chapter
25 as the maximum allowable
the existing variable 𝑅𝑀(𝑖, 𝑡, 𝑝), as defined in Chapter 25. The maximum output rate of an on-ramp meter at
flow rate 𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) that can enter the merge point takes into consideration the the on-ramp node i during time
interval p, measured in veh/h.
ramp metering rate as one of its possible constraints (Equation 25-18) and is RM(i,t,p) is also one of the
properly adjusted if the ramp metering becomes the restricting factor to the on- inputs used in calculating the
maximum on-ramp output
ramp discharge. 𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) is defined as follows: (Equation 25-18)
“𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) - maximum output flow rate that can enter the merge point from on-
ramp 𝑖 during time step t in time interval 𝑝; it is constrained by Lane 1 (shoulder lane)
flow on segment 𝑖 and the segment 𝑖 capacity or by a queue spillback filling the mainline
segment from a bottleneck further downstream, whichever governs”
Case 2: No Ramp Metering, Oversaturated Merge Segment

In this case, the ramp merge capacity can be computed by aggregating the
ONRO parameter into a 15-minute period and then converted into an hourly
flow rate.
Case 3: No Ramp Metering, Undersaturated Merge Segment

This case does not require any adjustments to the Chapter 10 - Freeway
Systems methodology.


EVALUATION OF ON-RAMP QUEUE SPILLBACK IMPACTS

This section describes the methodological modifications required to address
the occurrence of queue spillback from an on-ramp. The occurrence of queue
spillback affects each type of intersection differently. The methods outlined here
address signalized intersections, two-way stop-controlled (TWSC) intersections,
all-way stop-controlled (AWSC) intersections, and roundabouts.
Exhibit 38-B5 presents the core methodology for evaluating the performance
of signalized intersections, with proposed modifications to address impacts from
an on-ramp queue spillback. New steps and modified steps to the methodology
are described in the following paragraphs.


Exhibit 38-B5
Methodology With
Adjustments to Address On-
Ramp Queue Spillback

The volume of vehicles that enters a freeway on-ramp is a function of the
demands and capacities of each individual intersection movements that
discharge into the ramp. A typical signalized intersection within a diamond
interchange is shown in Exhibit 38-B6, with three movements discharging into
the on-ramp (SBL, EBT and NBR).


Exhibit 38-B6
Typical Signalized Intersection
Ramp Terminal in a Diamond
Interchange
The total throughput from the intersection into the on-ramp λONR is the sum
of the throughput from each of the contributing movements:
Equation 38-B12 𝜆 =𝜆 + 𝜆 + 𝜆
The throughput for each movement i is the minimum value of its demand
and capacity:
Equation 38-B13 𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑐 )
where
vi = demand flow rate for intersection movement i (veh/h)
ci = capacity for intersection movement i (veh/h), as provided by Equation
19-16
Unsignalized movements, which are common for right-turn movements to
the on-ramp, are unrestricted. The capacity of these movements can be estimated
as the saturation flow rate (Equation 19-8), with an adjustment factor for right
turns fRT (Equation 19-13).
If all movements at the intersection are undersaturated, (vi ≤ ci for every i),
then Equation 38-B12 is simplified and the total on-ramp demand throughput
λONR is as follows:
Equation 38-B14
𝜆 = 𝑣𝑖
𝑖
Step 7B. Obtain merging capacity using freeway facilities methodology

This step computes the merging capacity into the freeway cmerge. Three
potential bottlenecks can limit the on-ramp discharge into the freeway:
• Capacity of the on-ramp (Exhibit 14-12)
• Capacity at the merge segment, when oversaturated conditions occur at
the freeway facility;
• An active ramp metering RM
The procedure to obtain cmerge is presented in Exhibit 38-B7. The freeway
facility must be analyzed using the Freeway Facilities methodology (Chapter 10)


to evaluate whether the merging capacity is constrained by oversaturated

conditions in the mainline. If the freeway facility is undersaturated (LOS A-E),
the merging capacity cmerge takes the minimum value between the on-ramp
capacity and the ramp metering rate, if present.
If the freeway facility is oversaturated (LOS F), the Oversaturated Segment
Evaluation procedure described in Chapter 25 can provide the maximum on-
ramp output ONRO, computed at a time-step level (15 seconds). The merging
capacity cmerge can then be computed by aggregating the parameter ONRO to an
hourly flow rate:
𝑇 Equation 38-B15
𝑐 = 𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝)
𝑆
where
ONRO(I, t, p) = maximum output flow rate that can enter the merge point from on-
ramp 𝑖 during time step t in time interval p
T = number of time steps in 1 h (integer). T is set as a constant of 240 in the
computational engine, or equal to four times the value of S;
S = number of computational time steps in an analysis period (integer).
𝑆 is set as a constant of 60 in the computational engine, corresponding
to a 15-s interval and allowing a minimum segment length of 300 ft;
and
t = time step index.


Exhibit 38-B7
Step 7B - Estimation of
Merging Capacity in a
Freeway Ramp
Step 7C. Plot Queue Accumulation Polygon for the On-Ramp

In this step, a Queue Accumulation Polygon (QAP) must be built for the on-
ramp, considering the throughput from all contributing movements within the
cycle. Exhibit 38-B8 illustrates a sample intersection which will be used to
describe this step.
The application of this methodology requires that the first analyzed time
period is undersaturated. Based on this requirement, the QAP starts with zero
vehicles inside the on-ramp. The on-ramp QAP for this example is provided in
Exhibit 38-B9. The cycle starts with the SBL green discharging into the on-ramp
at a throughput rate λSBL, while the on-ramp discharges to the freeway merge at a
rate cmerge. Therefore, the number of vehicles within the on-ramp grows at a rate
equal to (λSBL - cmerge). When the number of vehicles along the on-ramp reaches
the maximum ramp storage length LONR, vehicles from the intersection can only
be discharged to the on-ramp at the same the rate they are discharged from the
on-ramp into the freeway. The number of vehicles within the on-ramp is then


maintained and it is equal to LONR until the end of the green for the SBL
movement. At the end of the SBL green, the vertical difference between the
projected number of vehicles (dashed line) and the actual number of vehicles
inside the on-ramp represent the number of unserved vehicles for the SBL
approach. This additional queue can be considered in a multiperiod analysis for
the signalized intersection or interchange, using the methods provided in
Chapter 23 – Ramp Terminals and Alternative Intersections.
Exhibit 38-B8
Sample Intersection for
Calculation of a QAP for the
On-Ramp
The slope of the red line connecting the number of vehicles in the end and
start of the green represent the reduced capacity of the SBL movement due to
queue spillback. For the remainder of the cycle, the NBR movement discharges
at a constant rate into the on-ramp, as this is an unsignalized movement. Given
that the discharge capacity cmerge is greater than the on-ramp demand λNBR, the
vehicles along the on-ramp are discharged to the freeway until the on-ramp is
cleared. Therefore, the NBR movement does not have its capacity affected by
queue spillback.
This procedure can be applied for both pretimed and actuated control types,
since the core methodology can address both controller types. If the signal is
actuated, the average phase duration lengths are applied, as obtained in Step 6.
Step 7D. Calculate adjusted capacities for the affected movements

Based on the on-ramp QAP developed in the previous step, the adjusted
capacity cSP must be calculated for every movement affected by the queue
spillback. For the example of Exhibit 38-B9, the adjusted capacity for the SBL


movement cSBL,SP can be obtained from the QAP as the slope of the red line (cSBL,SP
- cmerge) as follows:
𝑁(𝑔 ) − 𝑁(0)
Equation 38-B16 𝑐 −𝑐 −
,
𝑔
where
N(g ) = number of queued vehicles along the on-ramp at t = g1 (end of green
for phase 1);
N(0) = number of queued vehicles along the on-ramp at t = 0 (start of the
cycle);
G = effective green time for phase 1
Exhibit 38-B9
On-Ramp Queue
Accumulation Polygon During
Queue Spillback
The adjusted capacity of the SBL movement cSBL,SP is then computed as:
𝑁(𝑔 ) − 𝑁(0)
Equation 38-B17 𝑐 , =𝑐 +
𝑔
If the queue develops and fully discharges during every cycle, then
subsequent cycles will have the same discharge. However, if there are residual
queues at the on-ramp by the end of the cycle, the QAP must then be plotted
again for the following cycle with an initial queue equal to the number of queued
vehicles in the end of the present cycle. This process must be then repeated for a
number of cycles N= 900/C, sufficient to analyze the entire 15-minute period.
The adjusted capacity for each movement is estimated as the average of the
discharge rates during each cycle.
Step 8. Determine delay

The calculations for obtaining delay at the intersection approaches do not
need to be modified. The only change required is replacing the input value of the
demand-to-capacity ratio X (Equation 19-17) for the adjusted value Xsp, estimated
using the adjusted capacity due to spillback:


𝑣
𝑋 = Equation 38-B18
𝑐
Two-Way Stop-Controlled (TWSC) Intersections

The operation of TWSC intersections is based on determining the priorities of
movements arriving at the intersection. Minor street movements have lower
priority and must stop before entering the intersection. Left-turning drivers from
the major street must yield to oncoming major-street through or right turning
traffic, but they are not required to stop in the absence of oncoming traffic.
The methodologies for evaluating the operations of TWSC intersections are
based on gap acceptance theory. Drivers from lower priority movements must
select a suitable gap in order to proceed through the intersection. According to
previous research [3], during oversaturated conditions and when queue spillback
occurs drivers show cooperative behavior, with higher priority vehicles often
yielding to those with lower priority, as illustrated in Exhibit 38-B10. In such
cases, the gap acceptance model is no longer valid, and a new approach must be
used to evaluate the intersection performance.
Exhibit 38-B10
Illustration of Cooperative
Behavior in Unsignalized
Intersections With Queue
Spillback
When queue spillback occurs at a TWSC intersection the maximum

throughput to the on-ramp (exit capacity) is constrained by the discharge capacity
of the freeway merge. It is assumed that during oversaturated conditions the
intersection movements that discharge to the on-ramp share the exit capacity
proportionately to their demands.
Exhibit 38-B11 presents the core methodology for evaluating the
performance of TWSC intersections, with proposed modifications to address
impacts from an on-ramp queue spillback. New steps and modified steps to the
methodology are described in the following paragraphs.


Exhibit 38-B11
TWSC intersections Core
Methodology With

The throughput to the on-ramp is calculated using the approach described in
Step 7A of the queue spillback analysis for signalized intersections (Exhibit 38-
B5). The total throughput from the intersection into the on-ramp λONR is the sum
of the throughput from each of the contributing movements. For each movement


i discharging into the on-ramp, the throughput is the minimum value of its
demand and its movement capacity:
𝜆 = 𝑚𝑖𝑛 𝑣 , 𝑐 , Equation 38-B19
where
vi = demand flow rate for movement i
cm,j = movement capacity for movement i (Equations 20-36, 20-37 and 20-40).
This step computes the merging capacity into the freeway cmerge. The
procedure described in Step 7B of the queue spillback analysis for signalized
intersections (Exhibit 38-B5) is applied.

While signalized intersections operate in a cyclical pattern, stop-controlled
intersections have relatively uniform patterns of demand and capacity within a
time period. Therefore, the 15-minute aggregated demand and capacity values
are assumed to be constant, and the growth and discharge of queues are
assumed to be linear.
The queue accumulation polygon is used to illustrate the development of
queues along the on-ramp (Exhibit 38-B12). For a given time period of T minutes
(typically T=15), the intersection yields a throughput λONR to the ramp (Step 5B),
while the merge has capacity cmerge. If λONR > cmerge, then queues will develop
along the on-ramp until the number of vehicles reach the maximum ramp
storage LONR, when queue spillback begins. When that occurs, the maximum rate
of vehicles that can enter the on-ramp is limited by the merging capacity cmerge for
the rest of the time period.
Exhibit 38-B12
On-ramp Queue Accumulation
Polygon – TWSC Intersection
From this relationship shown in Exhibit 38-B12 the spillback time TSB is
defined as the amount of time within a time period when spillback is active:


𝐿 − 𝑁(0)
Equation 38-B20 𝑇 =𝑇−
𝜆 −𝑐
where
TSB = time period with active spillback (minutes)
T = duration of analysis time period (minutes)
LONR = available queue storage at on-ramp (veh)
N(0) = number of queued vehicles along the on-ramp at t = 0 (start of the
cycle);
cmerge = merging capacity of the on-ramp (veh/h)
λ from the intersection into the on-ramp (veh/hr)
Estimating the spillback time TSB is critical to the methodology, as the
aggregated calculations of capacity for each movement depend on the amount of
time that the intersection operates under queue spillback.

In this step, the capacities of the movements affected by spillback are
obtained and then aggregated to a time period level. When on-ramp queue
spillback occurs at an intersection, movements discharging towards the on-ramp
switch to a cooperative approach instead of the priority-based regular operation.
When there is queue spillback, the maximum throughput to the on-ramp is
equal to the merging capacity cmerge. This capacity is then used by all movements
traveling into the on-ramp. The capacity of each affected movement i during
spillback ci,SB is obtained proportionally to its demand flow rate:
𝑐 ×𝑣
Equation 38-B21
𝑐 , =
∑ 𝑣
where
c , = capacity during spillback for movement i (veh/h)
V = demand flow rate for movement i (veh/h)
C = merging capacity of the on-ramp (veh/h)
N = number of movements at the intersection discharging into the on-ramp
Finally, the adjusted capacity of each affected movement ci,EQ is obtained as a
function of the amount of time within the time period when spillback was
present. The adjusted capacity considers the proportion of time there is blockage
during queue spillback and consists of the aggregation, at a time period level, of
movement capacities cm,i (which is observed during undersaturated conditions)
and spillback capacities cSB,i,(which is observed during oversaturated conditions):
Equation 38-B22 𝑐 , ×𝑇 + 𝑐𝑚,𝑖 × (𝑇 − 𝑇 )
𝑐 , =
𝑇
where
c , = adjusted capacity for movement i (veh/h)


C , = capacity during spillback for movement i (veh/h)

V = demand flow rate for movement i (veh/h)
C = merging capacity of the on-ramp (veh/h)
When queue spillback lasts for the entire time period T (for example, in a
multi-period analysis), the spillback time TSB is equal to T, and the capacity of
each movement i is obtained as the capacity during spillback and Equation 38-
B22 becomes:
𝑐 , =𝑐 ,
Equation 38-B23
Step 11. Compute movement control delay

The average control delay is obtained using Equation 20-64 replacing the
movement capacity cm,i by the adjusted capacity cEQ,i:
⎡ 3600 𝜆 ⎤
× Equation 38-B24
3600 ⎢ 𝑣 𝑣 𝑐 , 𝑐 , ⎥
𝑑 = + 900𝑇 ⎢ −1+ −1 + ⎥+5
𝑐 , 𝑐 , 𝑐 , 450𝑇
⎢ ⎥
⎣ ⎦


ALL-WAY STOP-CONTROLLED (AWSC) INTERSECTIONS

The methodology to evaluate queue spillback into AWSC intersections
follows the approach developed for TWSC intersections. As shown in Exhibit 38-
B13, after the capacities of individual movements during undersaturated
conditions are computed (Step 12), the process described for TWSC intersections
is performed by new steps 13A through D.
Exhibit 38-B13
AWSC Intersections Core
Methodology With
The only step in the methodology that differs from the TWSC (13D) is
described below.
Step 13D – Compute spillback departure headway

The AWSC methodology calculates the delay for each approach based on its
departure headway instead of capacity. The estimated spillback capacity (cSB,i) is
converted to a spillback headway hSB through the following equation:
3600
Equation 38-B25 ℎ =
𝑐 ,
ROUNDABOUT RAMP TERMINALS

The core methodology presented in Chapter 22 – Roundabouts is shown in
Exhibit 38-B14. The additional steps proposed to the methodology are marked in
blue. Each of the steps added and modified is discussed in the following


paragraphs. This methodology is applicable only to single-lane roundabouts.

Exhibit 22-9 and Exhibit 38-B15 provide the required input data and potential
data sources for roundabout motorized vehicle analysis.
Exhibit 38-B14
Roundabouts Methodology
With Adjustments to Address
On-Ramp Queue Spillback


Required Data and Units Potential Data Source Suggested Default

Onramp Data
Exhibit 38-B15 On-ramp metering rate (veh/h) Design plans, Field data Must be provided
Required Data and Potential On-ramp storage length LONR(ft) Field data Must be provided
Data Sources – Roundabout Roundabout Data
Spillback Evaluation Departure saturation headway
Field data 3s/veh
into the on-ramp hs (s/veh)
Step 13 – Compute the maximum throughput into the on-ramp for

every movement
The maximum throughput into the on-ramp per movement is calculated
using the roundabout priority order in a counterclockwise order starting from
the most upstream approach from the on-ramp exit leg. The Rank 1 approach
(Exhibit 38-B16) is the one whose flow has the highest priority, given it enters the
circulating stream upstream of all other approaches). The next priority
movement is the Rank 2 approach, and the last is the Rank 3 approach.
Exhibit 38-B16
Priority Order for a
Roundabout Upstream of an
On-Ramp
Next, the methodology calculates the capacity of the roundabout’s exit lane
into the on-ramp. Previous research ( [4] [5]) suggests that the capacity of an exit
lane, accounting for pedestrian and bicycle traffic in a typical urban area, is in the
range of 1,200 to 1,300 vehicles per hour. Starting from the approach with Rank
1, and proceeding counterclockwise with the rest of the approaches, the capacity
for each approach is used to determine the maximum throughput for every
movement discharging to the on-ramp.
Rank 1 – SB approach. The Rank 1 approach has priority over the other
movements connecting to the on-ramp because it enters the circulating stream
first. Also, because the on-ramp does not have an approach into the roundabout,
the Rank 1 movement is most often unopposed by the circulating stream (except
for occasional U-turns along the arterial). Therefore, the maximum throughput
λSB-ONR (veh/h) for this left-turn movement is limited by its own lane capacity (cSB)
and the maximum throughput to the on-ramp, and it is given by:
3,600
Equation 38-B26 𝜆 = 𝑚𝑖𝑛 𝑣 ,𝑐 ×𝑝 ,
ℎ


where
λSB- rate from the SB approach into the on-ramp (veh/h)
vSB- flow rate for the SB approach into the on-ramp (veh/h)
cSB = lane capacity for SB approach (veh/h) (HCM Equation 22-21)
pSB- of demand from SB approach into the on-ramp
hs = departure saturation headway into the on-ramp (s/veh)
Rank 2 – EB approach. The maximum throughput for this Rank 2 movement

is limited by its own lane capacity (cEB), as defined in HCM Equations 22-21
through 22-23, and the maximum throughput after considering the departure
rate of the upstream Leg 1. Therefore, the maximum throughput λEB-ONR (veh/h)
for this movement is given by:
3,600
𝜆 = 𝑚𝑖𝑛 𝑣 ,𝑐 ×𝑝 , −𝜆 Equation 38-B27
ℎ
where
λEB- rate from the EB approach into the on-ramp (veh/h)
vEB- flow rate for the EB approach into the on-ramp (veh/h)
cEB = lane capacity for EB approach (veh/h) (HCM Equation 22-21)
pEB- of demand from the EB approach into the on-ramp,
Rank 3 – NB approach. Similar to rank 2 movements, the maximum

throughput for the NBR (i.e., NB-ONR) movement is limited by its own lane
capacity (𝑐 ), as defined in HCM Equation 22-21 through Equation 22-23, and
the maximum throughput to the on-ramp after considering departure rates from
the upstream approaches. Therefore, the maximum throughput (λNB-ONR) for this
right-turn movement is given by:
3,600
𝜆 = 𝑚𝑖𝑛 𝑣 ,𝑐 ×𝑝 , −𝜆 −𝜆 Equation 38-B28
ℎ
where
λNB- rate from the NB approach into the on-ramp (veh/h)
vNB- flow rate for the NB approach into the on-ramp (veh/h)
cNB = lane capacity for NB approach (veh/h) (HCM Equation 22-21)
pNB- of demand from the NB approach into the on-ramp
The total on-ramp demand flow rate can be similarly calculated if there are
additional approaches to the roundabout.


Step 14 – Calculate the throughput into the on-ramp

The maximum throughput from the roundabout to the on-ramp, 𝜆 is
calculated as:
Equation 38-B29 𝜆 =𝜆 + 𝜆 + 𝜆
Step 15 – Compute on-ramp merging capacity and compare to the

maximum throughput to the on-ramp
The calculation of the on-ramp merging capacity follows the exact same
procedure used in Step 7B of the methodology developed for queue spillback
into Signalized Intersections (Exhibit 38-B5). The maximum number of vehicles
that can merge into the on-ramp cmerge (estimated using Equation 25-18) is
compared to the maximum throughput from the roundabout to the on-ramp, 𝜆 .
If cmerge ≤ λONR, then spillback is not expected to occur, and no adjustments are
necessary in the procedure. If cmerge > λONR, queues will develop along the on-
ramp, and spillback may occur if the queue storage is insufficient. The analyst
must then proceed to Step 17 to evaluate the on-ramp Queue Storage Ratio to
evaluate whether spillback will occur.
Step 17 – Determine the on-ramp storage ratio and queue spillback

length
With the exit flow rate into the on-ramp (λ ), the expected queue length
QONR along the on-ramp during a 15-minute period analysis is:
−𝑐𝜆
Equation 38-B30 𝑄 =
4
If a multi-period analysis is performed, the queue length for the current time
period p must be added to the queue length obtained from the previous time
period:
Equation 38-B31 −𝑐𝜆 , ,
𝑄 , =𝑄 , +
4
The on-ramp storage ratio is calculated by dividing the available on-ramp
storage LR (ft) by the average vehicle spacing , 𝐿 (Equation 31-155):
𝐿 ×𝑄
Equation 38-B32 𝑅 =
𝐿
If the on-ramp storage ratio (R ) is greater than 1, queues will form along
each approach due to spillback. The value of RQ corresponds to the specific
analysis period. If congestion is expected, but RQ < 1 for a single analysis period,
multi-period analysis may have to be conducted.
Step 18 – Compute the queue spillback distribution per approach

When spillback occurs, the total number of vehicles queued during a 15-
minute time period analysis (𝑄 ) is calculated as:
Equation 38-B33 𝑄 =𝑄 −𝐿 ×𝐿
These queues are assumed to be distributed proportional to the demand flow
rates to the on-ramp per approach and added to the 95th percentile queues
estimated for the undersaturated conditions (Equation 22-20):


𝜆
𝑄 , =𝑄 × +𝑄 , Equation 38-B34
𝜆
𝜆
𝜆
𝜆
𝜆
Where
𝑄 , = queue due to the on-ramp spillback on 𝑖 approach (veh)
λ, = maximum throughput for 𝑖 approach into the on-ramp (veh)
𝑄 , = 95th percentile queue on 𝑖 approach (veh)
Step 19. Calculate the average control delay per approach

To estimate the average delay per approach, the delay due to the on-ramp
capacity limitation is estimated and added to the approach control delay
calculated in Step 9 (Chapter 22). As indicated in Chapter 22, it is recommended
to estimate the approach average control delay through Equation 22-17.
Equation 22-17 assumes no residual queue at the start of the analysis period.
If queue spillback occurs, the average control delay is significantly affected by
the analysis period length. However, Chapter 22 – Roundabouts does not
provide a multiperiod analysis method. Therefore, the delay results may not be
accurate when there is a queue at the start of the analysis period.
However, an iterative process that carries over queues from one time period
to the next may be considered [6]. The additional delay (in sec/veh) due to the
on-ramp spillback is calculated as follows:
⎡ 3600 𝜆 ⎤
×
3600 ⎢𝜆 𝜆 𝑐 𝑐 ⎥ Equation 38-B37
𝑑 = + 900𝑇 ⎢ −1+ −1 + ⎥+5
𝑐 𝑐 𝑐 450𝑇
⎢ ⎥
⎣ ⎦
𝜆
× 𝑚𝑖𝑛 ,1
𝑐
where
c =merging capacity of the on-ramp (veh/h);
λ = exit flow rate into the on-ramp (veh/h); and
t = time period (h) (T = 0.25 h for a 15-min analysis).


APPENDIX C: LANE-BY-LANE ANALYSIS FOR FREEWAY

FACILITIES
LANE-BY-LANE FLOW MODELS BY SEGMENT TYPE

The lane flow ratio (LFR) model for each lane is estimated as a function of the
logarithm of the segment volume-capacity ratio (v/c). Additional details on the
development of the model is available in [1]. The LFR equation is applied to
each lane in the segment except for the leftmost lane, which is estimated as the
remaining flow, to ensure the sum of the flow shares from each lane always
equals 100%. The equations estimating LFR are as follows:
𝑣
Equation 38-C1 𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 +𝑏
𝑐
Equation 38-C2 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅
where
𝑎 = multiplicative calibration parameter (Equation 38-C3, Equation 38-C5,
and Equation 38-C7);
𝑏 = additive calibration parameter (Equation 38-C4, Equation 38-C6, and
Equation 38-C8);
𝐿𝐹𝑅 = share of the total flow on lane 𝑖, where 𝑖 ranges from 1 to n-1 (n = total
number of segment lanes);
𝐿𝐹𝑅 = share of the total flow on the leftmost lane (lane n); and
𝑣/𝑐 = volume/capacity ratio 0 < ≤ 1 .
The model in Equation 38-C1 and Equation 38-C2 can be applied for basic,
merge, diverge and weaving segments. For merge and diverge segments, the
share of flow is estimated at the area upstream of the ramp. For weaving
segments, the share of flow is estimated at the mainline upstream the on-ramp.
Volume and capacity are given in veh/h. The calibration parameters 𝑎 and 𝑏
applicable in the analysis of basic segments are as follows:
Equation 38-C3 𝑎 =𝑎 +𝐺×𝑎 +𝑡×𝑎 +𝑛×𝑎
Equation 38-C4 𝑏 =𝑏 +𝐺×𝑏 +𝑡×𝑏 +𝑛×𝑏
For merge and diverge segments, the 𝑎 and 𝑏 parameters are as follows, with
additional coefficients 𝑎 and 𝑏 to address ramp demand:
𝑣
Equation 38-C5 𝑎 =𝑎 +𝐺×𝑎 +𝑡×𝑎 +𝑛×𝑎 + ×𝑎
1,000
𝑣
Equation 38-C6 𝑏 =𝑏 +𝐺×𝑏 +𝑡×𝑏 +𝑛×𝑏 + ×𝑏
1,000
where
𝑎 = multiplicative calibration parameter;
Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft)

𝑎 = empirical constant (Exhibit 38-C1);

𝑎 = empirical coefficient due to impact of grade (Exhibit 38-C1);
𝑎 = empirical coefficient due to impact of access point density (Exhibit 38-
C1);
𝑎 = empirical coefficient due to impact of trucks (Exhibit 38-C1);
𝑎 = empirical coefficient due to impact of ramp flow (Exhibit 38-C1);
𝑏 = additive calibration parameter;
𝑏 = empirical constant (Exhibit 38-C1);
𝑏 = empirical coefficient due to impact of grade (Exhibit 38-C1);
𝑏 = empirical coefficient due to impact of access point density(Exhibit 38-
C1);
𝑏 = empirical coefficient due to impact of trucks (Exhibit 38-C1);
𝑏 = empirical coefficient due to impact of ramp flow (Exhibit 38-C1);
𝐺 = grade (%);
𝑛 = access point density – number of ramps half a mile upstream and half
mile downstream;
𝑡 = truck percentage (%); and
𝑣 = ramp flow (vph).
The adjustment factors for the weaving segments address the effect of
weaving-specific properties:
𝑣 , 𝑣 , 𝐿
𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + ×𝑎 + ×𝑎 + ×𝑎 Equation 38-C7
1,000 1,000 1,000
+ 𝑉𝑅 × 𝑎
𝑣 , 𝑣 , 𝐿
𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + ×𝑏 + ×𝑏 + ×𝑏 Equation 38-C8
1,000 1,000 1,000
+ 𝑉𝑅 × 𝑏
where
𝑎 = empirical coefficient due to impact of interchange density; Interchange density, according
to Chapter 13, is the number
𝑎 = empirical coefficient for length of the weaving segment (Exhibit 38- of interchanges within 3 mi
upstream and downstream of
C2); the center of the subject
weaving segment divided by 6,
𝑎 = empirical coefficient for off-ramp flow (Exhibit 38-C2); in interchanges per mile
(int/mi).
𝑎 = empirical coefficient for on-ramp flow (Exhibit 38-C2);
𝑎 = empirical coefficient for volume ratio (Exhibit 38-C2);
𝐼𝐷 = interchange density, as defined in Chapter 13;
𝑏 = empirical coefficient due to impact of interchange density;
𝑏 = empirical coefficient for length of the weaving segment (Exhibit 38-
C2);
𝑏 = empirical coefficient for off-ramp flow (Exhibit 38-C2);
𝑏 = empirical coefficient for on-ramp flow (Exhibit 38-C2);
Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities

𝑏 = empirical coefficient for volume ratio (Exhibit 38-C2);

𝐿 = length of the weaving segment (ft);
𝑉𝑅 = volume ratio (weaving volume/total volume);
𝑣 , = off-ramp flow (veh/h);
𝑣 , = on-ramp flow (veh/h); and
The remaining factors have been defined previously.
The empirical constants (𝑎 , 𝑏 , and the calibration parameters 𝑎 and 𝑏) are
specific for each combination of segment type, lane number and total number of
lanes. The values for basic, merge and diverge segments are presented in Exhibit
38-C1, and the values for weaving segments are presented in Exhibit 38-C2.
Exhibit 38-C1 Lane

Parameter
Basic Segment Lanes Diverge Segment Lanes Merge Segments Lanes
Adjustment Factors for Lane # 2 3 4 2 3 4 2 3 4
Flow Distribution on Basic, 𝑎 0.18 0.027 0.068 0.0097 -0.075 0.31 0.015 0.0029 -0.077
Merge and Diverge Segments 𝑏 0.52 0.27 0.22 0.44 0.27 0.25 0.59 0.28 0.24
𝑎 0.024 0.021 -0.011 0.0097 0.0077 -0.034 0.015 -0.0029 -0.0030
𝑎 -0.048 -0.0036 -0.0021 -0.0093 0.00080 -0.057 -0.0093 -0.0029 0.011
𝑎 -0.095 -0.0083 -0.059 -0.0097 0.014 -0.028 -0.0047 -0.0029 0.014
L1
𝑏 0.0030 0.0097 -0.034 -0.0098 -0.0081 -0.00016 0.020 0.031 0.040
𝑏 0.008 -0.0029 0.0024 0.0078 0.0014 -0.019 -0.014 -0.0018 -0.027
𝑏 0.0013 0.032 -0.035 0.00057 0.031 0.0052 -0.040 -0.042 -0.041
𝑎 -0.21 -0.067 -0.0087 -0.035 -0.10 0.026
𝑏 -0.13 0.013 -0.021 -0.070 -0.030 0.0091
𝑎 -0.063 -0.025 0.0096 0.29 -0.0082 -0.080
𝑏 0.31 0.29 0.34 0.25 0.38 0.24
𝑎 -0.0060 0.0015 -0.0096 -0.035 -0.0082 0.00048
𝑎 0.0011 0.00027 -0.00054 -0.052 -0.00082 0.013
𝑎 0.0037 -0.0085 -0.0096 -0.030 -0.0026 0.018
L2
𝑏 -0.017 -0.024 -0.0019 0.0019 0.0079 -0.019
𝑏 0.0024 -0.00036 0.00089 -0.0041 -0.00048 -0.0067
𝑏 0.01 -0.041 0.0052 0.0044 -0.0060 0.0010
𝑎 -0.048 -0.0065 -0.12 -0.033
𝑏 -0.073 -0.0091 -0.039 -0.013
𝑎 -0.045 0.27 0.029
𝑏 0.28 0.25 0.25
𝑎 -0.0017 -0.036 -0.0017
𝑎 0.0021 -0.044 -0.0058
𝑎 0.0081 -0.034 -0.0068
L3
𝑏 0.011 0.0034 0.00060
𝑏 -0.0011 0.0092 0.014
𝑏 0.015 0.0016 0.018
𝑎 0.021 -0.079
𝑏 -0.0064 -0.041
The calibrated values for weaving segments are presented in Exhibit 38-C2.

Para- 2-Lane Exhibit 38-C2

meter Segments 3-Lane Segments 4-Lane Segments Adjustment Factors for Lane
L1 L1 L2 L1 L2 L3 Flow Distribution on Weaving
𝑎 0.99 0.64 0.48 -0.13 0.0048 0.12 Segments
𝑏 0.40 0.40 0.33 0.24 0.26 0.27
𝑎 -0.21 -0.28 0.11 0.13 -0.0048 -0.12
𝑎 -0.12 -0.055 -0.033 -0.012 -0.0048 0.019
𝑎 0.13 0.0037 -0.035 -0.0025 -0.0048 -0.12
𝑎 0.022 0.075 -0.090 0.072 -0.031 -0.011
𝑎 -0.19 -0.036 0.017 -0.13 0.030 0.051
𝑎 -0.20 0.098 -0.031 0.056 0.0020 -0.041
𝑎 0.0080 0.024 0.089 -0.11 -0.0045 0.12
𝑏 0.069 -0.40 0.039 -0.030 0.045 0.041
𝑏 0.0032 -0.051 0.0045 -0.0043 -0.011 -0.0043
𝑏 -0.016 0.40 -0.020 -0.0067 -0.0050 -0.0026
𝑏 -0.048 -0.14 0.0047 0.065 -0.0089 -0.038
𝑏 0.040 0.039 -0.047 0.063 -0.015 -0.037
𝑏 -0.011 0.15 0.0050 -0.030 0.011 0.020
𝑏 0.078 0.40 0.018 -0.14 0.040 0.15
Notes: The number of lanes parameter represents the freeway section upstream of the weave.
Lanes connecting the on-ramp and off-ramp are not included.
LFR distribution as function of demand-to-capacity ratio

As discussed in the previous section, LFR is obtained as a function of a series
of operational factors. From these, the most influencing factor is the demand-to-
capacity ratio, as research [7] shows that LFR distributions follow typical
patterns depending on the number of lanes.
Exhibit 38-C3 demonstrates that, for 2-lane segments, flow distribution
follows a “scissors” pattern, with the flow highly concentrated in lane 1 during
free-flow conditions. As the demand flow rate for the segment increases, flow
gradually migrates to lane 2. During oversaturated conditions, flow is more
concentrated in lane 2.

Exhibit 38-C3
LFR Distribution for a Sample
2-Lane Segment
(Minneapolis/MN)
Next, Exhibit 38-C4 illustrates the LFR distribution for a 3-lane freeway
segment. At low demand most of the flow of 3-lane segments is concentrated in
the center lane (lane 2), followed by lanes 1 and lane 3. As demand increases, lane
flow distribution increases in lane 3, while decreasing in lanes 1 and 2.
Exhibit 38-C4
3-Lane Segment (Tampa/FL)
Exhibit 38-C5 shows the LFR distribution for 4-lane segments. At free-flow
conditions, lanes 2 and 3 carry the majority of flow. Lane 4 is typically underused
during undersaturated conditions, but for higher demands it carries the majority
of flow.
Exhibit 38-C5
4-Lane Segment (Tampa/FL)
The flow distribution patterns shown in the previously exhibits for basic
segments are also observed in merge, diverge and weaving segments. Additional

factors such as ramp volume, grade, truck percentage influence the boundary
values and slopes of the curves, but does not change the typical LFR distribution
as function of v/c.
Checking for Negative Flows and Lane Capacities

After lane flow ratios are obtained, a two-step check must be performed to
ensure the estimated flow distribution is reasonable. The first check identifies
any estimated negative flows. This issue is more likely to occur in the leftmost
lane, as the flows on this lane are obtained by the difference between the total
segment flow and the sum of estimated flows in the other lanes. Therefore, if
flows on the remaining lanes are overestimated the resulting flow in the leftmost
lane may become negative. Exhibit 38-C6 illustrates the procedure for this check.
Exhibit 38-C6
Check for Negative Lane
Flows
The variables in Exhibit 38-C6 are defined as follows:

𝑖 = index for the subject lane;
𝐿𝐹𝑅 = lane flow ratio on lane i;
𝑣 = flow rate on lane i;
∆ = negative flow on lane i, to be relocated to all other lanes k ≠ i
𝑘 = index for a subject lane to where flow is being relocated
𝑣 = flow rate on lane k;
𝑛 = number of lanes in the segment
The second check compares the estimated flow by lane with the respective
lane capacities to ensure no lane operates with a demand-to-capacity ratio
greater than 1. The procedure is illustrated in Exhibit 38-C7. If any lane is
estimated to operate above its capacity, the flow in this given lane is constrained
by the capacity value and the exceeding demand is moved to the adjacent lane.

Exhibit 38-C7
Check for Lane Capacity
The variables in Exhibit 38-C7 are defined as follows:

𝑖 = index for the subject lane;
𝑐 = capacity for lane i;
𝑣 = flow rate on lane i;
∆ = exceeding flow on lane i, to be relocated to the adjacent lane
𝑛 = number of lanes in the segment
SPEED FLOW CURVES BY LANE AND BY SEGMENT TYPE

This section presents the models used to obtain speed-flow curves for each
lane in a freeway segment, as a function of two key inputs: free-flow speed (FFS)
and lane capacity. The first part discusses the estimation of lane FFS, while the
second presents models for obtaining lane capacities. The last part provides the
speed-flow models obtained as a function of lane FFS and lane capacities.
Lane FFS
Field observations have shown that speeds differ among lanes, and they are
typically lower in shoulder lanes and higher in median lanes.
Models were developed to estimate individual lane FFS by applying a
multiplying factor xFFS to the segment FFS. Exhibit 38-C8 summarizes the
recommended multipliers which are provided as a function of the segment type
and the number of lanes in the segment. As shown, when the number of lanes
increases, the range of FFS multipliers increase as well (i.e. there are lower
speeds in the shoulder lanes and higher speeds on the median lanes). For 2-lane
segments, merge and diverge segments have a higher difference in FFS between
the two lanes when compared to basic segments. For 3-lane segments, basic
segments show the highest FFS range, while merge segments have more uniform
lane FFS. As for 4-lane segments, merge segments show the highest FFS range,
followed by basic and merge segments yield similar results.

Segment Number of FFS Multiplier (xFFS) Exhibit 38-C8

Type Lanes L1 L2 L3 L4 Multipliers to Estimate Lane
2 lanes 0.965 1.032 - - FFS from Segment FFS
Basic 3 lanes 0.934 1.010 1.087 -
4 lanes 0.924 0.989 1.028 1.079
2 lanes 0.964 1.044 - -
Merge 3 lanes 0.955 1.015 1.045 -
4 lanes 0.935 0.991 1.036 1.091
2 lanes 0.961 1.035 - -
Diverge 3 lanes 0.943 1.024 1.068 -
4 lanes 0.933 0.975 1.018 1.074
2 lanes 0.969 1.018 - -
Weaving 3 lanes 0.968 1.023 1.062 -
4 lanes 0.910 0.988 1.053 1.110
The free-flow speed for each lane i is then computed as follows:

𝐹𝐹𝑆 = 𝐹𝐹𝑆 ×𝑥 Equation 38-C9
where
𝐹𝐹𝑆 = free-flow speed for lane i (mi/h);
𝐹𝐹𝑆 = adjusted free-flow speed for the segment average (mi/h) (Equation 12-
5).
𝑥 = FFS multiplier (Exhibit 38-C8);
Capacity for Speed Flow Curves by Lane

Similar to free-flow speeds, capacities differ among lanes, and they are
typically lower in shoulder lanes and higher in median lanes. Center lanes
typically have values similar to the segment average.
For weaving segments, capacity distributions were observed to be
significantly more complex and the breakdown method does not provide reliable
results. Capacity is assumed uniform for all lanes within a weaving segment,
obtained by Equation 13-5 (based on a maximum density of 43 pc/h/ln):
𝑐 =𝑐 − [438.2 (1 + 𝑉𝑅) . ] + (0.0765 𝐿 ) + (119.8𝑁 ) Equation 38-C10
where
𝑐 = capacity (per lane) of the weaving segment under equivalent ideal
conditions (pc/h/ln);
𝑐 = capacity (per lane) of a basic freeway segment with the same FFS as the
weaving segment under equivalent ideal conditions (pc/h/ln).
𝑉𝑅 = volume ratio;
𝐿 = length of weaving segment (ft); and
𝑁 = number of lanes from which weaving maneuvers may be made with
either one or no lane changes.
Exhibit 38-C9 presents the percent distribution of the total segment capacity
across lanes, defining a capacity multiplier xc for each combination of segment
type and number of lanes.

Segment Number of Capacity Multiplier (xc)

Exhibit 38-C9
Type Lanes L1 L2 L3 L4
Capacity of Individual Lanes
2 lanes 0.44 0.56
as a Percentage of Segment
Capacity, by Segment Type Basic 3 lanes 0.25 0.35 0.40
and Number of Lanes 4 lanes 0.19 0.25 0.28 0.28
2 lanes 0.42 0.58
Merge 3 lanes 0.23 0.36 0.41
4 lanes 0.21 0.24 0.25 0.30
2 lanes 0.42 0.58
Diverge 3 lanes 0.26 0.34 0.40
4 lanes 0.21 0.24 0.27 0.28
* Lane capacity on weaving segments is assumed to be equal across all lanes (Equation 38-C10)
The segment capacities measured from field data may not be equal to the
estimated capacities using HCM methodologies. According to the HCM
Equation 12-6, the base capacity can be estimated as:
Equation 38-C11 c = min[2200 + 10 × (FFS − 50), 2400]
The adjusted capacity of a segment is obtained through Equation 12-8:
Equation 38-C12 c = 𝑐 × 𝐶𝐴𝐹
The capacity for each lane i is computed as:

Equation 38-C13 𝑐 =𝑐 ×𝑁×𝑥
where
𝑐 = capacity of lane i (pc/h/ln);
𝑐 = adjusted capacity for the segment average (pc/h/ln) (Equation 12-8).
𝑁 = number of lanes in the segment
𝑥 = capacity multiplier (Exhibit 38-C9);
Field measurements of capacity have been found to be lower than HCM

estimates [8]. Such differences can result in overestimating the overall
performance of a segment. Therefore, it is recommended that capacity
adjustment factors (CAFs) are applied to adjust the estimated capacities to local
conditions.
With flow, capacity and FFS by lane determined, HCM equations can be
used to estimate the speeds on individual lanes. Segment-wise inputs of flow,
capacity and FFS are based on the field measurements, and the methods
previously described are applied to estimate their distribution among individual
lanes.
Speed on each lane i is determined as:
𝑐
Equation 38-C14 𝐹𝐹𝑆 − (𝑣 − 𝐵𝑃 )
𝑆 = 𝐹𝐹𝑆 − 45
(𝑐 − 𝐵𝑃 )
where
𝐵𝑃 = breakpoint value on lane i (pc/h/ln) (Equation 38-C15);
𝑐 = capacity on lane i (pc/h/ln) (Equation 38-C13);

𝐹𝐹𝑆 = free-flow speed on lane i(mi/h);

𝑆 = speed (mi/h) on lane i; and
𝑣 = demand flow rate on lane i (pc/h/ln), with 𝑣 = 𝑣 × 𝐿𝐹𝑅 .
This model is applied to individual lanes, as the three key parameters (𝐹𝐹𝑆, 𝑐
and 𝑣 ) are input by lane. The breakpoint value (𝐵𝑃) is also determined for each
lane:
𝐵𝑃 = [1000 + 40 × (75 − 𝐹𝐹𝑆 )] × 𝐶𝐴𝐹 Equation 38-C15
where
𝐵𝑃 = breakpoint value (pc/h/ln);
𝐹𝐹𝑆 = adjusted free-flow speed (mi/h); and
𝐶𝐴𝐹 = capacity adjustment factor.

APPLICATION EXAMPLES
Example 1 - Diverge Segment from Example Problem 1

This section presents an application of the LFR model for a freeway segment
extracted from Example Problem 1 (O-D Based Travel Time Estimation for I-75
NB Freeway in Gainesville, FL). A 3-lane diverge segment (segment 16 of the
freeway facility) was selected for lane-by-lane analysis, with the following input
data:
• Grade (𝐺): 1%;
• Heavy vehicles (𝑡): 2%;
• PHF = 1.0
• Access point density (𝑛): 1 adjacent ramp;
• Mainline hourly demand volume (𝑉): 4848 veh/h;
• Capacity adjustment factor (CAF): 1.0
• Off-ramp demand (𝑣 ): 960 veh/h; and
• Measured segment capacity (𝑐): 2400 pc/h/ln (7200 veh/h).
The mainline hourly demand volume (veh/h) is first converted to a demand

flow rate under equivalent base conditions, with a fHV = 0.969:
𝑉 4848
𝑣= = = 5003.1 pc/h
𝑃𝐻𝐹 × 𝑓 1.0 × 0.969
The flow ratio for lane 1 (right lane) is obtained by the following equation:
𝑣
𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 +𝑏
𝑐
The calibration parameters 𝑎 and 𝑏 for lane 1 are obtained as follows:
𝑣
𝑎 =𝑎 +𝐺×𝑎 +𝑡×𝑎 +𝑛×𝑎 + ×𝑎
1000
960
𝑎 = −0.075 + 1 × 0.0077 + 2 × 0.0008 + 0 × 0.014 + × (−0.067)
1000
𝑎 = −0.116
𝑣
𝑏 =𝑏 +𝐺×𝑏 +𝑡×𝑏 +𝑛×𝑏 + ×𝑏
1000
960
𝑏 = 0.26667 + 1 × (−0.00810) + 2 × 0.00140 + 1 × 0.03129 +
1000
× 0.01324
𝑏 = 0.296
The flow rate on lane 1 can then be obtained by:
5003
𝐿𝐹𝑅1 = −0.116 × 𝑙𝑛 + 0.296 = 𝟎. 𝟑𝟓𝟎
7200
The same procedure is applied to obtain the flow rate on lane 2, using the
respective coefficients from Exhibit 38-C1:
𝑣
𝑎 =𝑎 +𝐺×𝑎 +𝑡×𝑎 +𝑛×𝑎 + ×𝑎
1000

960
𝑎 = 0.0096 + 1 × (−0.00960) + 2 × (−0.00054) + 1 × (−0.0096) +
1,000
× (−0.048)
𝑎 = −0.0568
𝑣
𝑏 =𝑏 +𝐺×𝑏 +𝑡×𝑏 +𝑛×𝑏 + ×𝑏
1000
960
𝑏 = 0.34 + 1 × (−0.0019) + 2 × (0.00089) + 1 × 0.0052 + × (−0.073)
1,000
𝑏 = 0.275
5003
𝐿𝐹𝑅 = −0.0568 × 𝑙𝑛 + 0.275 = 𝟎. 𝟐𝟗𝟔
7200
Finally, the flow rate on the leftmost lane (lane 3) can be obtained as:
𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.350 − 0.296
𝐿𝐹𝑅 = 𝟎. 𝟑𝟓𝟒
Lane flows can be obtained by multiplying the segment demand by

respective LFR values for each lane:
𝑣 = v × 𝐿𝐹𝑅 = 5003.1 × 0.350 = 1753.2 pc/h/ln
𝑣 = v × 𝐿𝐹𝑅 = 5003.1 × 0.296 = 1482.6 pc/h/ln
𝑣 = v × 𝐿𝐹𝑅 = 5003.1 × 0.354 = 1767.3 pc/h/ln
Speed calculations
Individual free-flow speeds for each lane can be obtained by multiplying the
segment FFS (75.4 mi/h) by the corresponding multipliers (Exhibit 38-C6) as
follows:
𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 0.943 = 75.4 × 0.943 = 71.1 mph
𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 1.024 = 75.4 × 1.024 = 77.2 mph
𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 1.064 = 75.4 × 1.068 = 80.5 mph
Applying factors to the segment capacity, individual lane capacities can be

obtained as follows:
𝑐 = 𝑐 × 0.26 = 7200 × 0.26 = 1872 pc/h
𝑐 = 𝑐 × 0.34 = 7200 × 0.34 = 2448 pc/h
𝑐 = 𝑐 × 0.40 = 7200 × 0.40 = 2880 pc/h
Breakpoint values for each lane can be obtained:

BP1 = [1000+ 40 x (75‐FFS1)] x CAF2 = [1000+ 40 x (75‐71.10)] x 1 = 1156 pc/h
BP2 = [1000+ 40 x (75‐FFS2)] x CAF2 = [1000+ 40 x (75‐77.21)] x 1 = 911.6 pc/h
BP3 = [1000+ 40 x (75‐FFS3)] x CAF2 = [1000+ 40 x (75‐80.23)] x 1 = 778.9 pc/h
Average speed of each lane can be obtained by applying Equation 38-C9 to

each lane:

𝑐
𝐹𝐹𝑆 − (𝑣 − 𝐵𝑃 )
𝑆 = 𝐹𝐹𝑆 − 45
(𝑐 − 𝐵𝑃 )
1872
71.1 − (1753.2 − 1156)
𝑆 = 71.1 − 45 = 50.6 mi/h
(1872 − 1156)
2448
77.2 − (1482.6 − 911.6)
𝑆 = 77.2 − 45 = 74.1 mi/h
(2448 − 911.6)
2880
80.5 − (1767.3 − 778.9)
𝑆 = 80.5 − 45 = 76.8 mi/h
(2880 − 778.9)
The obtained speed-flow curves for each lane are presented and compared to
the segment-wise curve in Exhibit 38-C10:
Exhibit 38-C10
Comparison of Speed-Flow
Curves for Each Lane and for
the Segment
Example 2 - Weaving Segment

This section presents an application of the LFR model for a weaving segment
(Exhibit 38-C11) to estimate the upstream lane flow shares.
Exhibit 38-C11
Example of LFR Calculation for
a Weaving Segment
The following input data is provided:

• Number of lanes within the weave (𝑁): 5;
• Number of upstream lanes (NUP ): 4;
• Grade (𝐺): -0.5%;
• Heavy vehicles (𝑡): 3.3%;

• Interchange density (𝐼𝐷): 0.67;

• Weaving length (𝐿 ): 3920 ft;
• Upstream mainline demand flow rate (𝑣 ): 4512 veh/h;
• On-ramp demand flow rate (𝑣 , ): 428 veh/h;
• Freeway-to-freeway demand (𝑣 ): 3312 veh/h;
• Freeway-to-ramp demand (𝑣 ): 1200 veh/h;
• Ramp-to-freeway demand (𝑣 ): 404 veh/h;
• Ramp-to-ramp demand (𝑣 ): 24 veh/h;
• Off-ramp flow rate (𝑣 , ): 1224 veh/h;
• Number of weaving lanes (𝑁 ): 2 lanes;
• Measured segment free-flow speed (FFS): 70 mi/h; and
• PHF = 1.0.
The heavy-vehicles adjustment factor can be estimated as (for 𝐸 = 2)
1 1
𝑓 = = = 0.968
1 + 𝑃 (𝐸 − 1) 1 + 0.03(2 − 1)
The weaving and non-weaving demands can be adjusted to flow rates under
ideal conditions. Because the demands are estimated based on 15-minute
intervals, it is assumed that PHF is equal to 1.
𝑉
𝑣=
𝑃𝐻𝐹 × 𝑓
24
𝑣 = = 24.8 𝑝𝑐/ℎ
1 × 0.968
404
𝑣 = = 417.3 𝑝𝑐/ℎ
1 × 0.968
1200
𝑣 = = 1,239.6 𝑝𝑐/ℎ
1 × 0.968
3312
𝑣 = = 3,421.3 𝑝𝑐/ℎ
1 × 0.968
The weaving and non-weaving flows are given by:
𝑣 =𝑣 +𝑣 = 1,239.6 + 417.3 = 1,656.9 𝑝𝑐/ℎ
𝑣 =𝑣 +𝑣 = 24.8 + 3,421.3 = 3,446.1 𝑝𝑐/ℎ
The volume ratio can be computed as:
𝑣 1,656.9
𝑉𝑅 = = = 0.325
𝑣 1,656.9 + 3,446.1
The capacity for a weaving segment is given by the minimum between the
density-capacity (𝑐 , from HCM Equation 13-5) and weaving-demand-capacity
(𝑐 , from HCM Equation 13-7):
𝑐′ =𝑐 − [438.2(1 + 𝑉𝑅) . ] + (0.0765𝐿 ) + (119.8𝑁 )
𝑐 = 2,400 𝑝𝑐/ℎ

𝑐′ = 2,400 − [438.2(1 + 0.325) . ] + (0.0765 × 3,920) + (119.8 × 2)

= 2,252.3 𝑝𝑐/ℎ/𝑙𝑛
𝑐 = 𝑐′ ×𝑓 = 2,252.3 × 0.968 = 2,180.4 𝑣𝑒ℎ/ℎ/𝑙𝑛
2,400 2,400
𝑐′ = = = 7,391.5 𝑝𝑐/ℎ
𝑉𝑅 0.325
𝑐′ ×𝑓 7,391.5 × 0.968
𝑐 = = = 1,788.8 𝑣𝑒ℎ/ℎ/𝑙𝑛
𝑁 4
𝑐 = 𝑚𝑖𝑛(𝑐 ,𝑐 ) = 𝑚𝑖𝑛(2,180.4, 1,788.8) = 1,788.8 𝑣𝑒ℎ/ℎ/𝑙𝑛
The estimated capacity is 1,788.8 veh/h/ln. The flow ratio for lane 1 (right
lane) is obtained by the following equation:
𝑣
𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 +𝑏
𝑐
The calibration parameters 𝑎 and 𝑏 for lane 1 are obtained as follows:
𝑣 , 𝑣 , 𝐿
𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + ×𝑎 + ×𝑎 + ×𝑎
1000 1000 1000
+ 𝑉𝑅 × 𝑎
𝑎 = −0.13 + (−0.5) × 0.13 + (3.3) × (−0.012) + 0.67 × (−0.0025) + ×
,
, ,
0.072 + × (−0.13) + × (0.056) + 0.325 × (−0.11)
, ,
𝑎 = −0.1843
𝑣 , 𝑣 , 𝐿
𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + ×𝑏 + ×𝑏 + ×𝑏
1000 1000 1000
+ 𝑉𝑅 × 𝑏
𝑏 = 0.24 + (−0.5) × (−0.03) + (3.3) × (−0.0043) + 0.67 × (−0.0067) +
, ,
× 0.065 + × 0.063 + × (−0.03) + 0.32 × (−0.14)
, , ,
𝑏 = 0.1790
The flow rate on lane 1 is estimated as:

4,512
𝐿𝐹𝑅 = −0.1843 × 𝑙𝑛 + 0.1790
4 × 1,788.8
𝐿𝐹𝑅 = 𝟎. 𝟐𝟔𝟒
The same procedure is applied to estimate the flow rate on lane 2, using the
𝑣 , 𝑣 , 𝐿
𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + ×𝑎 + ×𝑎 + ×𝑎
1000 1000 1000
+ 𝑉𝑅 × 𝑎
𝑎 = 0.0048 + (−0.5) × (−0.0048) + (3.3) × (−0.0048) + 0.67 × (−0.0048)
428 1224 3920
+ × (−0.031) + × (0.03) + × (0.002) + 0.325
1000 1000 1000
× (−0.0045)

𝑎 = 0.0176
𝑣 , 𝑣 , 𝐿
𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + ×𝑏 + ×𝑏 + ×𝑏
1000 1000 1000
+ 𝑉𝑅 × 𝑏
𝑏 = 0.26 + (−0.5) × (0.045) + (3.3) × (−0.011) + 0.67 × (−0.005) + ×
(−0.0089) + × (−0.015) + × (0.011) + 0.325 × 0.04
𝑏 = 0.2271

4512
𝐿𝐹𝑅 = 0.0176 × 𝑙𝑛 + 0.2271
4 × 1788.8
𝐿𝐹𝑅 = 𝟎. 𝟐𝟏𝟗
The same procedure is applied to obtain the flow rate on lane 3, using the
𝑣 , 𝑣 , 𝐿
𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + ×𝑎 + ×𝑎 + ×𝑎
1000 1000 1000
+ 𝑉𝑅 × 𝑎
428
𝑎 = 0.12 + (−0.5) × (−0.12) + (3.3) × 0.019 + 0.67 × (−0.12) +
1000
1224 3920
× (−0.011) + × 0.051 + × (−0.041) + 0.325 × 0.12
1000 1000
𝑎 = 0.0985
𝑣 , 𝑣 , 𝐿
𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + ×𝑏 + ×𝑏 + ×𝑏
1000 1000 1000
+ 𝑉𝑅 × 𝑏
𝑏 = 0.27 + (−0.5) × 0.041 + (3.3) × (−0.0043) + 0.67 × (−0.0026) + ×
,
, ,
(−0.038) + × (−0.037) + × 0.0198 + 0.325 × 0.15
, ,
𝑏 = 0.3010
4,512
𝐿𝐹𝑅 = 0.0985 × 𝑙𝑛 + 0.3010
4 × 1,788.8
𝐿𝐹𝑅 = 𝟎. 𝟐𝟓𝟔
Finally, the flow rate on the leftmost lane (lane 4) can be obtained as:
𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.256 − 0.219 − 0.264
𝐿𝐹𝑅 = 𝟎. 𝟐𝟔𝟏
Example 3 – Basic Segment

A 2-lane basic segment was modeled, and the lane-by-lane performance is
compared to field data (CA-1 NB – Santa Cruz/CA). Field measured parameters
are as follows:
• Free-flow speed: 69.1 mph;
• Capacity: 3993 veh/h (1996.5 veh/h/ln);
• % Heavy vehicles: 1.7; and

• Grade: 3% (rolling).
By applying the multiplying factors obtained in Exhibit 38-C8 to the segment
FFS, individual FFS can be obtained as follows:
𝐹𝐹𝑆1 = 𝐹𝐹𝑆 × 0.965 = 69.1 × 0.965 = 66.68 𝑚𝑝ℎ
𝐹𝐹𝑆2 = 𝐹𝐹𝑆 × 1.032 = 69.1 × 1.032 = 71.31 𝑚𝑝ℎ
Next, lane capacities are obtained by applying the multiplying the factors
obtained in Exhibit 38-C9 to the capacity as follows:
𝑐1 = 𝑐 × 44% = 3993 × 44% = 1757 𝑣𝑒ℎ/ℎ
𝑐2 = 𝑐 × 56% = 3993 × 56% = 2236 𝑣𝑒ℎ/ℎ
For comparison purposes, HCM methods would obtain the following
theoretical capacity:
𝑐 = [2200 + 10 × (𝐹𝐹𝑆 – 50)] × 𝑓𝐻𝑉 = [2200 + 10 × (69.1 − 50) )] × 0.967
= 2312 𝑣𝑒ℎ/ℎ/𝑙𝑛
Therefore, the recommended CAF for this location is obtained by
dividing the field-measured by the theoretical values of capacity:
𝑐 1996.5
𝐶𝐴𝐹 = = = 0.864
𝑐 2312
Next, the breakpoint values for each lane can be obtained:
𝐵𝑃1 = [1000 + 40 × (75 − 𝐹𝐹𝑆1)] × 𝐶𝐴𝐹 = [1000 + 40 × (75 − 66.68)] × 0.864
𝐵𝑃1 = 995 𝑣𝑒ℎ/ℎ
𝐵𝑃2 = [1000 + 40 × (75 − 𝐹𝐹𝑆2)] × 𝐶𝐴𝐹 = [1000 + 40 × (75 − 71.31)] × 0.864

𝐵𝑃2 = 857 𝑣𝑒ℎ/ℎ
Flows on each lane can be obtained by applying the model described in

Equation 38-C1 to the flow rate entering the segment. Next, speeds on individual
lanes can be obtained using the speed-flow relationship described in Equation
38-C8. For this location, a sample of 14690 observations (15-min each) was
randomly selected, and then predicted values were compared to field data as
shown in Exhibit 38-C12.

Exhibit 38-C12
Field × Predicted Speed-Flow
Curve for (a) Lane 1 and (b)
Lane 2 (CA-1 NB – Santa
Cruz/CA)
As observed, the individual speed-flow models can replicate field conditions

with good accuracy. Naturally, the oversaturated portion of the speed-flow curve
cannot be addressed by the model, as this is already a limitation of the existing
method.

APPENDIX B
Off-Ramp Queue Spillback Check
The current methodology for Freeway Facilities analysis (HCM Chapter 10) evaluates the performance
of each segment individually using standard 15-minute time periods. If any segment within the facility
yields a LOS F and/or a v/c ratio greater than 1.0, the analysis continues with the oversaturated procedure,
using smaller time steps.
Similarly, in order to determine whether there is queue spillback from a freeway off-ramp, the analysis
is first conducted using 15-minute time periods. If the analysis shows that any of the ramps are expected to
experience queue spillback, the oversaturated procedure must be used to estimate the spillback impacts on
the freeway mainline lanes, even if the segment-wide performance is not at a LOS F and/or a v/c ratio
greater than 1.0.
The methodology framework for conducting a spillback check at diverge critical points is presented in
Figure B-1 and described in more detail in the remainder of this section.
232

Figure B-1. Procedure for identifying spillback occurrence at an off-ramp/weaving segment
Step 1 - Capacity Checks

The first step in the methodology determines whether capacity is exceeded at any of the critical points
along the diverge section:
Case A – Ramp proper

Demand at the study diverge ramp (vR, as defined in HCM Chapter 14) is compared against the capacity
of the ramp proper (cR) using HCM Exhibit 14-12, replicated in Figure B-2.
233


Figure B-2. Capacity of ramp roadways (pc/h)
Case B – Downstream intersection

Demand at the downstream arterial intersection approach is compared against the estimated capacity of
the approach. Depending on the type of intersection located at the end of the ramp proper, the respective
capacities are obtained from one of the following chapters: Signalized Intersections (HCM Chapter 19);
Two-Way Stop-Control Intersections (HCM Chapter 20); All-Way Stop Control Intersections (HCM
Chapter 21); Roundabouts (HCM Chapter 22); Ramp Terminals and Alternative Intersections (HCM
Chapter 23). The recommended approach for each case is as follows:
Signalized Intersections. The operation of a signalized intersection will yield queues even when the
operation is undersaturated. Although an oversaturated approach is expected to create longer queues that
are growing in time and are more likely to spill back into the freeway diverge, it cannot be guaranteed that
the queues at an undersaturated approach will not affect the freeway mainline. Therefore, the methodology
estimates the queue length and compares it to the available storage length for each analysis period. The
arriving demand at the intersection may be constrained by the ramp proper capacity, and for this reason the
ramp proper capacity check must be conducted first.
Unsignalized Intersections. Similar to signalized intersections, the approaches of an unsignalized

intersection yield queues even during undersaturated conditions. Therefore, a LOS better than F at the
intersection is not sufficient to guarantee that spillback will not occur. For unsignalized intersections
(TWSC, AWSC and roundabouts) the user is advised to proceed to the second step of the check
methodology (comparison of queue length).
Case C – Downstream merge junction

Queue spillback may also occur on freeway-to-freeway connectors, and this is a common issue in high-
demand urban interchanges. In this case, the bottleneck is located at the downstream merge segment and
occurs when the discharge rate into the downstream merge is lower than the off-ramp demand.
Consequently, the queue may back up into the upstream freeway lanes. In this case, the merge capacity of
the downstream freeway facility must be modeled using the current HCM methodology for freeway
facilities. For oversaturated conditions, the methodology estimates the queue length at the on-ramp (as
described in Chapter 25 – Freeway Facilities Supplemental). This queue length value should be used as
input for queue spillback analysis as described below.
Similar to arterial intersections, the arriving demand at downstream merge may also be constrained by
the ramp proper capacity. Therefore, the entering ramp demand at the merge is the minimum value of the
exiting flow rate at the diverge and the ramp proper capacity.
234

Step 2 – Queue Length Estimation

In the second step, the procedure estimates the expected queue length for any conditions where demand
exceeds capacity. Three cases may occur:

In cases of demand exceeding capacity of the ramp proper, the bottleneck is the entry to the off-ramp,
and the ramp proper would not necessarily have a queue present. If Case A occurs, bottleneck is expected
to occur and no additional calculations are necessary at this step.
Case B – Downstream intersection

Spillback occurs when the resulting queues from the downstream intersection ramp terminal exceed the
available ramp storage. For all cases, the first step is to estimate the maximum throughput v at the
downstream intersection approach. That maximum throughput must not exceed the capacity of the ramp
proper, cR under Case A:
𝑣 = min 𝑣 , 𝑐 ×𝑓 × 𝑃𝐻𝐹 × 𝑓 (Equation B-1)
Where:
v = maximum entering flow rate for the intersection approach (veh/h)
vR = off‐ramp demand for the period (pc/h)
cR = capacity of the off-ramp roadway (pc/h)
fHV = adjustment factor for heavy vehicle presence
fp = adjustment factor for driver population
If the off-ramp demand exceeds its capacity, the ramp proper acts as an upstream bottleneck, and limits
the demand to the intersection approach. This step ensures that the incoming demand at intersection does
not exceed the capacity of ramp proper. The calculations of throughput for each intersection type are
described below.
Signalized Intersections. The current methodology described in Chapters 19 and 31 evaluates the
performance of individual lane groups for a subject approach. It also estimates the back of queue length Q
(HCM Equation 31-149) or a percentile back-of-queue length Q% (HCM Equation 31-150). In some cases,
only one high-demand movement at the intersection approach is the bottleneck that results in spillback,
yielding an unbalanced lane usage pattern at the ramp. Field observations have shown that arterial
intersection failures may occur at one lane group as drivers position themselves in a specific lane at the
ramp to anticipate the downstream signal, the lane usage in the ramp becomes unbalanced, as shown in
Figure B-3.
235

Figure B-3. Examples of unbalanced ramp lane usage: (a) Norfolk, VA and (b) Tampa, FL
At off-ramps with two or more lanes, the estimated queue lengths for each intersection lane group must
be associated with specific ramp lanes. Figure B-4 illustrates an example of a typical ramp terminal. It is
expected that drivers that desire to take a left turn at the intersection will position themselves in the leftmost
lane ramp (Ramp Lane 2), while drivers who intend to turn right will likely choose the rightmost lane at the
ramp (Ramp Lane 1). Analyst judgement is required to define the grouping of intersection lane groups into
ramp lanes.
Figure B-4. Off-ramp geometry with additional lanes at the arterial approach
By using the results of the queue estimation procedure, the number of queued vehicles in a given ramp
lane n is estimated as follows:
QL,k= ∑ QLG,m = Q%, LGn x NLGm (Equation B-2)
Where:
QL,k = number of queued vehicles in ramp lane k, during a 15-min interval
QLG,m = number of queued vehicles from lane group m associated with ramp lane k, during a 15-min
interval
Qn%,LGm = estimated back of queue length (nth percentile), as defined in HCM Equation 31-150 (measured
in veh/ln)
NLGm = number of approaching lanes for lane group m
236

Unsignalized Intersections. Each unsignalized intersection type has its own methodology to estimate
queue length. The TWSC methodology estimates the 95th percentile queue length for minor movements
with Equation 20-68, while the 95th percentile queue length for AWSC approaches is estimated with
Equation 21-33. For roundabouts, the 95th percentile queue length for a given lane is provided by Equation
22-20. Regarding intersection lane groups and ramp lanes, the same procedure discussed above for
signalized intersections is applied.
Case C – Downstream merge

For freeway-to-freeway connectors, the estimated queue length at the downstream merge is estimated
using the freeway facilities oversaturated methodology, Equation 25-21. For this specific type of connector,
the demand difference among ramp lanes can be considered negligible for the purposes of this analysis.
Step 3 – Queue Storage Ratios and Spillback Checks

The third step is to estimate the queue storage ratio (RQ) for the ramp proper queues. If RQ exceeds 1.00,
then spillback is expected to occur. The calculations for each of the three possible cases is as follows:

In cases of demand exceeding the capacity of the ramp proper, the bottleneck is the entry to the off-ramp,
and the ramp itself would not necessarily have a queue present. This case estimates the impacts of the queue
as it extends along the deceleration lane. The queue length upstream of the ramp proper (QSP) is estimated
based on the “leftover” demand that is not served by the off-ramp’s available capacity:
𝑄 = 𝑣 −𝑐 ×𝑓 × 𝑃𝐻𝐹 × 𝑓 × 𝐿 × 𝑡i (Equation B-3)
Where:
QSP = length of queue beyond ramp storage distance (ft)
vR = off‐ramp demand for the period (pc/h)
cR = capacity of the off-ramp roadway (pc/h)
fHV = adjustment factor for heavy vehicle presence
PHF = peak hour factor
fp = adjustment factor for driver population
ti = analysis period i (h)
Case B – Downstream Intersection

In cases of demand exceeding capacity at the intersection, the methodology considers the queues for all
lanes from the ramp gore to the stop bar, as well as the channelization at the stop bar. The total storage
length LR for the ramp can be estimated as the sum of lane lengths for i number of different sections (a
section is defined as a uniform segment with a homogenous number of lanes) as follows:
𝐿 = ∑ 𝑁 𝑥𝐿 (Equation B-4)
Where:
Ni = number of lanes in section i
Li = section i length (ft)
237

The individual ramp storage for each of the k lanes in the off-ramp, LR,k, can be estimated by assigning
the intersection lane groups to ramp lanes, as previously described:
𝐿 , = ∑ 𝑁, 𝑥𝐿 (Equation B-5)
Where:
Ni,k = Number of lanes in section i that are associated to ramp lane k
Li = Section i length (ft)
Finally, the ramp queue ratio for every ramp lane k is obtained as:
,
𝑅 , = (Equation B-6)
,
Where:
QL,k = queue length associated to ramp lane k
LR,k = available ramp storage for ramp lane k
Next, the total storage length is calculated. Figure B-4 illustrates a common off-ramp geometry with three
different sections from the stop bar to the gore point:
• Section 1: 4 lanes with length L1: two lanes (LG1) are associated with ramp lane 1, and two lanes
(LG2) are associated with ramp lane 2
• Section 2: 3 lanes with length L2: two lanes (LG1) are associated with ramp lane 1 and one lane
(LG2) is associated with ramp lane 2, and
• Section 3: 2 lanes with length L3: one lane (LG1) is associated with ramp lane 1, and one lane
(LG2) is associated with ramp lane 2
Therefore, the available ramp storage LR is calculated as:
LR = (4 x L1) + (3 x L2) + (2 x L3)
The ramp storage ratio for each ramp lane is as follows:
LR,1 = (2 x L1) + (2 x L2) + (1 x L3)

LR,2 = (2 x L1) + (1 x L2) + (1 x L3)
Case C – Downstream Merge

The queue storage ratio for freeway-to-freeway connections is estimated as follows:
∗
𝑅 = (Equation B-7)
Where:
onramp queue length (veh)
LR = available queue storage distance (ft/ln)
Lh = average vehicle spacing in stationary queue (ft/veh)
N = number of lanes in the diverge ramp
238

Example Problem 1 – Queue spillback from a downstream signalized intersection
The exit ramp at I-95 SB to SW 25th Rd (Miami, FL) has a signalized intersection ramp terminal (Figure
A-5). The off-ramp has two lanes and the signalized approach from the ramp (WB) has three lanes (one
shared left-through, one through, and one shared through-right), as shown in Figure B-5.
Figure B-5. Study site for example problem 1 (off-ramp queue spillback check - Miami, FL)
The geometry of the approach, the channelization at the stop bar and the segment lengths are shown in
Figure B-6.
Figure B-6. Signalized approach geometry for example problem 1 (off-ramp queue spillback check
- Miami, FL)
Queues from each lane group are assigned as indicated in Table B-1:
Table B-1. Assignment of lane group queues to ramp lanes
Lane group Ramp Lane

LG 1 (WB T-R) L1
LG 2 (WB T)
L2
LG 3 (WB L-T)
239

The signalized intersection performance was estimated using HCM methods (Chapter 19 – Signalized
Intersections), and the 95th percentile back-of-queue lengths were calculated as shown in Figure B-7.
Figure B-7. Back-of-queue length estimation for intersection approach using HCM methodology
(off-ramp queue spillback check – Miami, FL)
240

The 95th percentile queues to each ramp lane are:

QL,1 = Q95%,LG1 = 1196.5 ft
QL,2 = Q95%,LG2 + Q95%,LG3 = 1200.8 + 1532.3 = 2733.1 ft
Available queue storage on each ramp lane are:

LR,1 = = 400*1 + 1000*1 = 1,400 ft
LR,2 = 400*2 + 1000*1 = 1,800 ft
The ramp storage ratio for each of the two ramp lanes is:
RQ,1 = 1,196/1,400 = 0.85 < 1 → No spillback expected
RQ,2 = 2,733/1,800 = 1.51 > 1 → Spillback is expected
It is concluded that spillback will occur due to the higher demand on ramp lane 2 (connected to the left
and through movements). The expected queue length beyond the gore is 2733 – 1,800 = 933 ft.
Given the length of the deceleration lane (LD = 450 ft), the queue will extend to the freeway mainline.
241

Example Problem 2 – Queue Spillback from a Downstream Merge (Freeway-to-Freeway)
A freeway-to-freeway two-lane ramp is evaluated for queue spillback (I-75 SB to SR-826 SB – Miami,
FL). The schematic of the study site is shown in Figure B-8.
Figure B-8. Study site for example problem 2 (freeway-to-freeway queue spillback check, Miami-FL)
This freeway-to-freeway connector is modeled as two separate freeway facilities. The upstream freeway
(I-75) is modeled with a diverge section that is connected to the downstream freeway (SR-826). The detailed
geometry, including turning movements and segment lengths, are shown in Figure B-9.
Figure B-9. Geometry for the study site of example problem 2: (a) I-75 and (b) SR-826
A multi-period analysis considering AM peak hour traffic volume (6.00 AM-7.30 AM) is conducted for
both facilities for six time periods (15 min each). The free-flow speed was measured as 63.5 mph for I-75
and 67.3 mph for SR-826. There are 12.1% trucks along the ramp, and the ramp length is 3,588 ft. The
exiting demand from the diverge is equal to the entering demand at the merge for undersaturated conditions;
however, the throughput at the two locations may not be the same if demand exceeds capacity at either
location. The results of the analysis for the SR-826, where the queue originates, are shown in Figure B-10.
242

Figure B-10. Summary of analysis results for SR-826
243

As shown, segments 1 and 3 (boundary basic segments) in SR-826 are operating at LOS C and D
respectively for the entire analysis period. On the other hand, the merge section operates at LOS F each
during the third and fourth time periods. Thus, there is a queue present at the ramp starting from the third
time period. The estimated on-ramp queue for each time period is provided using the Freeway Facilities
method (Table B-2). The queue is assumed to be distributed evenly among the ramp lanes. The length of
the queue along the ramp during each time period is estimated to be greater than the length of the ramp. As
shown in Table B-2, the available queue storage length is insufficient (Queue storage ratio > 1), therefore
queue spillback is expected to occur at the diverge segment of I-75.
Table B-2. Estimation of queue length at the SR-826 on-ramp
Total Number of Average

Ramp
Number of queued vehicle Queue length Queue
Time length Spillback
queued vehicles in length (ft) storage ratio
period (ft) occurs?
vehicles each lane (ft)
[A] [B] = [A]/2 [C] [D] = [B]*[C] [E] [F] = [D]/[E]

1 0 0 0 0.00 No
2 0 0 0 0.00 No
3 1002 501 13,727 3.83 Yes
27.4 3588
4 1860 930 25,482 7.10 Yes
5 2065 1032.5 28,291 7.88 Yes
6 2099 1049.5 28,756 8.01 Yes
244

APPENDIX C
Freeway Off-Ramp – Queue Spillback Analysis
1. Introduction
The HCM (Chapter 14) provides three LOS checks for diverge segments, and failure (LOS F) may occur
in any of the following two cases:
• the total demand flow rate on the approaching upstream freeway segment exceeds the capacity of
the upstream freeway segment;
• the off-ramp demand exceeds the capacity of the off-ramp.
The HCM methodology also provides a LOS evaluation based on the density of the ramp influence area
(Exhibit 14-3), but it only yields a LOS range of A through E; failure due to excessive density is not
considered in the methodology. The first case of LOS F is addressed by the Oversaturated Segment
Evaluation procedure (HCM Chapter 10) and is not the focus of this methodology. The Queue Spillback
Analysis, described in this document targets the second case of LOS F, when the off-ramp demand exceeds
the capacity of the off-ramp. The methodology of this appendix also addresses cases of spillback due to
insufficient capacity at the ramp terminal downstream of an off-ramp.
The methodology described in Appendix A - Off-ramp Spillback Check presents the necessary steps to
determine whether spillback from an off-ramp is expected to occur, based on a standard 15-min period
analysis. This appendix provides the methodology for evaluating operations when spillback occurs. The
approach is based on the Freeway Facilities Oversaturated Segment Evaluation (HCM Chapter 25), where
performance measures are computed at the 15-s time step level.
Section 2 introduces the basic link-node structure that is applied to model off-ramp segments in the
methodology. Section 3 presents the concept of spillback regimes as a function of the off-ramp queue.
Section 4 presents a glossary with the definition of all parameters used in the procedure. Section 5 presents
the methodology to evaluate the impacts of an off-ramp queue spillback, and discusses each step and the
respective calculations.
2. Evaluation of operations along off-ramp segments

To evaluate the interaction between the freeway mainline and the downstream off-ramp terminal, the
link-node approach used by the HCM Chapter 25 to evaluate oversaturated freeway facilities is expanded,
with additional links and nodes to represent the off-ramp segment. As shown in Figure C-1, the mainline
node for the off-ramp (Node 3) is connected to the off-ramp segment, which has a three-node structure:
• Ramp node 3.1: interface between the diverge segment (exit lanes) and the upstream end of the
ramp proper. The volume that flows through this node is equivalent to the amount of vehicles that are
able to leave the freeway;
• Ramp node 3.2: interface between the ramp proper and the arterial intersection approach. The
volume that flows through this node is equivalent to the amount of vehicles that are able to leave the
ramp proper and enter the intersection;
245

• Ramp node 3.3: the last node in the off-ramp represents the discharge capacity of the arterial
intersection approach. The volume that flows through this node is equivalent to the amount of vehicles
that are able to enter the intersection;
Figure C-1 – Expanded link-node structure to evaluate the off-ramp segment
The geometry of an off-ramp is seldom a homogenous road segment, and additional lanes are frequently
added closer to the arterial intersection approach. Figure C-2 illustrates a sample off-ramp, considering its
entire length from the deceleration lane to the stop bar at the downstream signalized intersection. The ramp
proper is the uniform ramp segment with a downstream boundary defined by the point where additional
lanes are provided. When modeling the off-ramp geometry, the method considers the channelization at the
approach as imbalances in the turning movements may cause queues on a subset of lanes. Figure C-2 shows
a typical queue formation resulting from a left-turn movement that operates with insufficient capacity. In
this scenario, the approaching left-turn vehicles are positioned in the leftmost lane and spillback may occur
even if not all lanes of the approach are oversaturated.
Figure C-2 – Sample geometry of an off-ramp considering the arterial intersection with heavy
demanded left-turn
246

The type of ramp terminal is an important input into the analysis. Signalized intersections operate in
cyclical patterns, and therefore those have fluctuating queue lengths. For certain demand scenarios, this
can result in queues backing up into the freeway and then discharging multiples times within a 15-min time
period.
Stop-controlled intersections and downstream merge segments (in the case of a freeway-to-freeway
connection), on the other hand, have a more uniform discharging rate. For cases other than signalized
intersections, off-ramp queues are assumed to develop or discharge linearly based on the relationship
between demand and capacity.
3. Evaluation of operations on the freeway mainline: spillback regimes

The impact of queue spillback on the freeway mainline varies as a function of the queue length and the
lanes blocked. Four spillback regimes are defined (Elefteriadou et. al, 2016)
Regime 1
The queue ends within the deceleration lane and does not spill back into the mainline freeway (Figure C-
3 (a)). During undersaturated conditions, the deceleration lane serves as a transition zone between speeds
on the mainline (typically 55 – 75 mi/h) and advisory speeds posted along the off-ramp (typically 20 – 50
mi/h). When queues begin to form on the deceleration lane, the available deceleration distance is reduced
and speeds along the rightmost lane are affected.
Regime 2
The queue of vehicles extends upstream beyond the deceleration lane, but sufficient lateral clearance on
the right-hand shoulder allows for additional queue storage. In this case there is no transition zone within
the deceleration lane and drivers decelerate and join the back of the queue more abruptly, resulting in
turbulence and reduced speeds in the rightmost lane (Figure C-3 (b)). If no lateral clearance exists
immediately upstream of the deceleration lane, Regime 2 conditions are not possible. In some cases, this
regime does not occur even if storage is available; this depends on local driver behavior and is site-specific.
Regime 3
The queue extends to the rightmost lane of the freeway mainline (Figure C-3 (c)). This may occur either
when there is no shoulder available for additional queue storage, or when drivers choose to queue in the
rightmost lane once the deceleration lane is entirely occupied. Non-exiting vehicles on the rightmost lane
are delayed or change lanes, which causes increased turbulence and reduced speeds in both rightmost lanes.
Regime 4
The queue blocks the rightmost lane, and drivers occasionally or often use the adjacent freeway mainline
lane next to the rightmost freeway mainline lane to force their way into the queue, blocking thus an
additional lane (Figure C-3(d)). During this regime, speed and capacity are significantly reduced. The
effects of spillback vary from site to site and from time period to time period due to driver behavior and
site geometry. Data collection at locations around the US has shown that at some sites drivers block the
adjacent lane, while at other sites they do not, regardless of the queue spillback length at the site.
247

Figure C-3 –Off-ramp spillback regimes
4. Glossary of variable definitions

This glossary defines internal variables used in the methodology for off-ramp queue spillback evaluation.
The structure of the variables is similar to the one used in HCM Chapter 25 – Freeway Facilities
Supplemental.
Facility variables
• QIA(i, p): Length of the queue influence area (ft) for segment i during time period p, measured
from the back of the queue.
Segment variables
• KBBL(i,j): background density (pc/mi/ln) at the blocked lanes in segment i, when queue spillback
occurs at a downstream segment j
• KBUB(i,j): background density (pc/mi/ln) at the unblocked lanes in segment i, when queue
spillback occurs at a downstream segment j
• LCR(i,t,p): rate of lane change maneuvers in the queue influence area upstream of a queue from an
off-ramp, for segment i during time period p and time step t.
• LD(i,p): available deceleration lane length (ft) for segment i during time period p. This variable is
used to calculate performance measures for ramp segments (Chapter 14 - LD.)
• MQ1(i,t,p): mainline queue length of off-ramp unserved vehicles in the rightmost mainline lane,
for segment i during time period p in time period t.
• MQ2(i,t,p): mainline queue length of off-ramp unserved vehicles in the rightmost mainline lane,
for segment i during time period p in time period t. If Regime 4 is not expected to occur, this parameter
value is set to zero.
• NQ(i): number of blocked lanes if the off-ramp queue backs up into the freeway mainline. This
parameter is a function of the prevailing spillback regime at segment i as provided by the analyst. The
value for this parameter is an input and can be either 1 (Regime 3 - one blocked lane) or 2 (Regime 4 –
two blocked lanes);
• OFRFUP(i,t,p): flow that can exit at the closest off-ramp downstream of i during time step t in time
period p.
• OFRLQ(i,t,p): queue length of off-ramp unserved vehicles for diverge segment i during time period
p in time period t.
248

• OFRUV(i,t,p): number of off-ramp unserved vehicles for segment i during time period p in time
period t.
• SBKQ (i,t,p): spillback queue density for segment i during time period p in time period t.
• SBLC(i,t,p): number of lane change maneuvers within the Queue Influence Area at node i, during
time step t in time period p.
• SBLQ(i,t,p): queue length within segment i during time period p in time period t, caused by a
downstream off-ramp bottleneck.
• SBQS(i,p): total available off-ramp queue storage (ft) for a diverge segment i during time period p,
if the subject segment has an off-ramp bottleneck. It is calculated as a function of the available storage
lengths in the deceleration lane, shoulder and prevailing spillback regime.
• SCEQ(i,N,NQ): equivalent capacity of the unblocked portion of a segment i with N total lanes and
NQ blocked lanes.
• SL(i,p): available shoulder length (ft) for segment i during time period p. If the value of SL is
greater than zero, any off-ramp queues that exceed the deceleration lane will occupy the shoulder before
blocking mainline lanes.
• TIA(i,p): total influence area (ft) of a queue from an off-ramp bottleneck on segment i, during time
period p in time period t. It is calculated as the sum of parameters QIA(i,t,p) and MQ(i,t,p).
Node variables
• CAFBL(i,t,p): capacity adjustment when one or more lanes of segment i are entirely blocked during
time period p in time period t. This is used to calculate friction effects that cause through vehicles to
slow down due to the presence of a queue in the rightmost lanes.
• CAFUP(i,t,p): capacity adjustment factor of node i during time step t in time period. This capacity
adjustment factor affects approaching vehicles within the queue influence area (QIA) upstream of an
off-ramp queue. This factor accounts for the turbulence caused by intense lane changing within the
queue influence area as vehicles adjust their position when there is a downstream off-ramp queue.
• MFBL(i,t,p): mainline flow rate that can cross the blocked portion of node i during time step t in
time period p.
• MFUB(i,t,p): mainline flow rate that can cross the unblocked portion of node i during time step t
in time period p.
• MIBL(i,t,p): maximum flow desiring to enter the blocked portion of node i during time step t in
time period p.
• MIUB(i,t,p): maximum flow desiring to enter the unblocked portion of node i during time step t in
time period p.
• MO2BL(i,t,p): maximum number of passenger cars that can enter the blocked portion of segment
i, during time step t and time period p, due to the presence of a queue in the downstream ramp segment.
• MO2UB(i,t,p): maximum number of passenger cars that can enter the unblocked portion of segment
i, during time step t and time period p, due to the presence of a queue in the downstream ramp segment.
• NEXTOFR(i): index of the nearest downstream diverge segment relative to subject node i.
• OFRDIST(i): distance (ft) from node i to the start of the deceleration lane at the nearest downstream
off-ramp.
• OFRPCT(i,j): percent of the off-ramp demand at segment j over the mainline entering volume at
segment i.
Ramp variables
• RC(i,p): capacity of the ramp proper (pc/h) during time period p in time period t. Capacity values
for the ramp proper are provided in HCM Exhibit 14-12.
249

• RF(i,t,p,k): flow (pc/ts) that can enter the ramp proper at segment i during time period p in time
period t and level k.
• RI(i,t,p,k): maximum flow (pc/ts) desiring to enter the off-ramp on segment i during time period p
in time period t and level k, including queues accumulated from previous time periods.
• RKB(i,t,p,k): ramp proper queue density (pc/mi/ln) for segment i during time period p in time period
t and level k.
• RL(i): length of ramp proper (ft) for segment i.
• RN(i): number of ramp lanes for segment i.
• RNV(i,t,p,k): maximum number of passenger cars within the ramp of segment i at the end of time
step t during time period p and level k. The number of vehicles is initially based on the calculations of
Chapters 12, 13, and 14, but, as queues grow and dissipate, input–output analysis updates these values
during each time step.
• RSTG(i,t,p,k): maximum number of passenger cars that can enter the ramp level k of segment i,
during time step t and time period p, due to the presence of a queue in the downstream ramp segment.
• RUV(i,t,p,k): number of unserved vehicles at the entrance of the ramp proper of segment i at the
end of time step t during time period p and level k. Any values of RUV greater than zero indicate the
occurrence of queue spillback from an off-ramp.
Intersection (ramp terminal) variables
• ID (i,t,p,k): discharge capacity (pc/ts) for intersection movement k in segment i during time period
p in time period t.
• IF(i,t,p): flow (pc/ts) that can enter the intersection on segment i, level k, during time period p in
time period t.
• II(i,t,p,k): maximum flow (veh/ts) desiring to enter the intersection on segment i, level k, during
time period p in time period t, including queues accumulated from previous time periods.
• IL(i,k): storage length of movements at intersection of segment i, for level k (ft)
• INV(i,t,p,k): number of vehicles at the intersection of segment i, for level k at the end of time step
t during time period p
• IO(i,t,p): flow (pc/ts) that can be discharged from the intersection on segment i, level k, during
time period p in time period t.
• ISTG(i,k): total available storage length at intersection of segment i, for level k (ft)
• IUV (i,t,p,k): number of unserved vehicles at the entrance of the intersection of segment i, for level
k, at the end of time step t during time period p
5. Evaluation of operations on the freeway mainline: step-by-step methodology

description
The methodology for evaluating off-ramp queue spillback is integrated to the core methodology for
Freeway Facilities Oversaturated Segment Evaluation (HCM Chapter 25). Figure C-4 through Figure C-7
show the core methodology, highlighting additions and changes to address off-ramp queue spillback.
250

Source: adapted from HCM 6th Edition Exhibit 25-3

Figure C-4 – Freeway facilities oversaturated segment evaluation procedure, adapted for off-ramp
queue spillback evaluation
251


queue spillback evaluation - continued
252


253


254

Step 1 - Calculate background density for unblocked lanes on each segment in the case of queue
spillback
The first step in the Oversaturated Segment Evaluation procedure computes a background density (KB),
for each segment at the start of each time period, defined as the expected density when there is no queueing
on the segment. It is used as a reference to estimate how many vehicles occupy a given segment at
undersaturated conditions, creating an initial reference point for oversaturated analyses.
When Regime 3 or Regime 4 occur, there is blockage of one or more freeway lanes in the affected
segments, and the through vehicles aim to move to the unblocked lanes. The capacity of the unblocked
lanes must be calculated at the initialization step, to be used as a reference value.
For a segment i with N lanes, a subset NQ of lanes will be blocked when spillback occurs (NQ = 1 for
Regime 3 and NQ = 2 for Regime 4). Therefore, the capacity of the unblocked lanes will be equivalent to
a similar segment with (N - NQ) lanes, adjusted for the impact of the blockage using a capacity adjustment
factor CAFBL. The values of CAFBL are equal to the Incident Capacity Adjustment Factors of Chapter 11,
Freeway Reliability Analysis (Exhibit 11-23), as there are currently no data available to accurately assess
the impacts of blockage due to spillback. These values may be conservative, as during incidents capacities
may be further reduced due to the presence of police vehicles. Table C-1 presents the recommended values
for CAFBL.
Table C-1. Capacity adjustment factors for lane blockage (CAFBL) as a function of the number of
directional lanes and the number of blocked lanes
Directional Lanes 1 Blocked Lane 2 Blocked Lanes

2 0.70 N/A
3 0.74 0.51
4 0.77 0.50
5 0.81 0.67
6 0.85 0.75
7 0.88 0.8
8 0.89 0.84
The equivalent capacity SCEQ of segment i, with N lanes and NQ blocked lanes, is estimated as:
𝑆𝐶𝐸𝑄 𝑖, 𝑁, 𝑁𝑄 𝑆𝐶 𝑖, 𝑁 − 𝑁𝑄 𝐶𝐴𝐹 (Equation C- 1)
Figure C-8 presents an example of a basic 4-lane directional segment operating in Regime 4 (2 blocked
lanes). The capacity of the unblocked lanes will be equivalent to the capacity of a 2-lane basic segment with
a capacity adjustment factor CAFBL = 0.50 (4 directional lanes with 2 blocked lanes).
Figure C-8 – Equivalent segment capacity for unblocked lanes when lane blockage occurs
For the segment of Figure C-8, capacity at ideal conditions is:
255

𝑐 = 2,400 𝑝𝑐/ℎ/𝑙𝑛 (Capacity per lane) or

𝑆𝐶 = 9,600 𝑝𝑐/ℎ (Segment capacity)
When Regime 4 occurs (2 blocked lanes), the equivalent capacity SCEQ is obtained as the equivalent
capacity of a 2-lane segment multiplied by a corresponding CAFBL of 0.5 (Table C-1):
𝑆𝐶𝐸𝑄 = 2 𝑥 2,400 𝑥 0.5 = 2,400 𝑝𝑐/ℎ
Next, the unblocked background density KBUB is calculated. This parameter estimates the background
density of the uncongested portion of a given segment operating under a two-pipe regime due to a queue
spillback from a downstream off-ramp. To estimate this value, the method first determines the ratio of the
Expected Demand (ED) that will move to the uncongested side of the segment. When queue spillback
occurs in a diverge segment j, the parameter OFRPCT(i,j) is defined as the percent of the off-ramp demand
over the mainline entering volume vf:
𝑣 𝑗
𝑂𝐹𝑅𝑃𝐶𝑇 𝑖, 𝑗 = (Equation C-2)
𝑣 (𝑖)
For any segment i, upstream of segment j and affected by the off-ramp spillback from segment j, the
ratio of vehicles traveling towards the off-ramp at segment i is given by OFRPCT(j), while the ratio of
vehicles traveling through in the unblocked lanes is given by (1- OFRPCT(j)). Therefore, the unblocked
background density KBUB at any segment i upstream of an off-ramp spillback in a segment j is given by:
𝐾𝐵𝑈𝐵(𝑖, 𝑗) = 𝐾𝐵[𝐸𝐷(𝑖) × (1 − 𝑂𝐹𝑅𝑃𝐶𝑇(𝑖)), 𝑆𝐶𝐸𝑄(𝑗)] (Equation C-3)
Where:
KBUB(i,j)I = background density at the unblocked lanes in segment i, when queue spillback occurs at
the downstream segment
ED(i) = expected demand at segment i , as defined in HCM Chapter 25
OFRPCT(i) = rate of off-ramp flow and mainline flow at segment i
KB (v,c)I = density at a segment with demand flow rate v and capacity c, as provided by HCM
Chapters 12 (basic), 13 (weaving) and 14 (merge and diverge)

These calculations are performed at the start of the analysis, to prepare the flow calculations for the first
time step and specify return points, such as background density (KB), for later time steps. This subsection
presents the additional parameters required for queue spillback analysis.
Number of mainline blocked lanes
The number of mainline blocked lanes is stored in the parameter NQ(i) and is determined by the prevalent
queue spillback regime as provided by the analyst. If the back of an off-ramp queue is calculated to reach
the freeway mainline, two possible spillback regimes may occur:
• Regime 3: blockage of one lane in the freeway mainline → Set NQ(i) = 1
• Regime 4: blockage of two lanes in the freeway mainline → Set NQ(i) = 2
256

The analyst should select one of these two regimes based on prevailing driver behavior at the site and in
the vicinity of the site.
Shoulder length
The available shoulder length must be input by the analyst for queue spillback analysis, and is stored
under the parameter SL(i) for oversaturated calculations.
Deceleration lane length
The deceleration lane length is provided by the analyst for the analyses of diverge segments, and is stored
under the parameter LD(i) for oversaturated calculations.
Spillback queue storage length
The maximum storage length for off-ramp queues on segment i is computed as a function of the segment
length L(i), the deceleration lane length LD(i) and the number of queued lanes NQ(i). Figure C-9 provides
guidance on measuring each of the components required for Regimes 3 and 4.
Figure C-9 – Maximum off-ramp queue storage length at diverge segments with occurrence of (a)
Regime 3 queue spillback and (b) Regime 4 queue spillback, when no shoulder is available
Figure C-10 illustrates queue length measurements for special cases of queue spillback, when a shoulder
is present but its storage length is not sufficient to accommodate the unserved vehicles. Regime 3A (Figure
C-10a) occurs when there is blockage of one mainline lane in addition to the shoulder. Regime 4A (Figure
C-10b) occurs when there is blockage of two mainline lanes in addition to the shoulder.
Figure C-10 – Maximum off-ramp queue storage length at diverge segments with occurrence of (a)
Regime 3A queue spillback and (b) Regime 4A queue spillback, when shoulder is available
257

Step 2A - Model off-ramp geometry

The three-level node structure for the off-ramp shown in Figure C-1 must be modeled to reflect the
geometric characteristics of the site, as illustrated in Figure C-2. This is accomplished by setting a “branch”
structure, where a node can connect to multiple links downstream. If a node is connected to more than one
downstream link, the flow through the node will be constrained by the downstream link with the highest
queue storage ratio.
The ramp structure must be modeled from the downstream end towards the upstream end:
• For the most downstream location provide one node for each lane group or movement at the
approach;
• For the next upstream change in alignment provide one node for each ramp proper lane connecting
to a distinct lane group downstream.
The data structure used in the methodology computations should be adjusted according to this “branch”
structure. Most parameters in the Oversaturated Segment Evaluation methodology are computed as a 3-
dimensional array (i, t, p), where i is the segment index in the freeway facility and t refers to a specific time
step within a given time period p. In the case of two-lane ramps that need to be evaluated independently, a
new dimension k will be added to the ramp parameter arrays to account for the specific lane under analysis.
Lanes are numbered right from left; therefore, k=1 stands for the rightmost lane and k=2 for the leftmost
lane of the ramp.
Example 1 – In this example, there is only one lane connecting the freeway exit to the entry leg of the
downstream roundabout. Therefore, only one node is required at each location (single branch structure,
with k=1 in all nodes), as shown in Figure C-11.
Figure C-11 – Node structure for Example 1
Example 2 – A single-lane ramp connects with a stop-controlled T-intersection ramp terminal (Figure
C-12). The intersection node is comprised of two branches (k=2), while the ramp proper has only one lane
(k=1). Each movement of the intersection (LT and RT) is represented by a node, and when there is a queue
on either one of the movements, the one with the longest length will constrain the flow of vehicles from the
ramp proper.
258

Example 3 – A two-lane ramp connects with a signalized intersection ramp terminal (Figure C-13). Both
the intersection and the ramp proper nodes comprise of two branches each (k=2). At the downstream end,
one node is defined for each lane group at the intersection (LT and RT). According to the ramp geometry,
left-turning drivers will be positioned along ramp lane 2, while right-turning drivers will be located along
ramp lane 1. Therefore, two nodes are also defined at the upstream location. If the queue storage ratio for
any of the ramp lanes reaches 1, vehicle flow in the respective upstream node will be constrained, resulting
in queue spillback on the freeway mainline.
Step 2B - Determine spillback regime for each diverge segment

Field observations have shown that locations that experience recurring queue spillback always have the
same type of spillback regime when the queue extends beyond the deceleration lane (Regime 3 or 4).
Regime 4 occurs often at ramp junctions with a lane drop. At these locations, the exiting traffic can access
259

the off-ramp with a single lane change. Therefore, drivers are more likely to wait until they are closer to
the exit to change lanes, blocking the adjacent through lane. However, not all lane drop exits experience a
Regime 4 queue spillback. Regime 4 occurs more frequently in locations with more aggressive driver
behavior. Local information and driver behavior should be taken into consideration in determining the
prevailing regime at a given site.
For operational analyses of existing locations, it is recommended that the analyst provides the expected
spillback regime based on observed field conditions. For planning level purposes where no field data is
available, Table C-2 provides the expected queue spillback regime as a function of the number of exiting
lanes and driver aggressiveness.
Table C-2. Default spillback regimes as a function of ramp geometry and driver aggressiveness
Ramp Driver aggressiveness
geometry Low Medium High
Diverge Regime 3 Regime 3 Regime 3
Lane drop Regime 3 Regime 4 Regime 4

The Highway Capacity Manual (Chapter 14) provides the following definition for the ramp influence
area for off-ramps operating under steady conditions:
“For right-hand off-ramps, the ramp influence area includes the deceleration lane(s) and Lanes 1 and
2 of the freeway for a distance of 1,500 ft upstream of the diverge point.”
When there is queue spillback in one or more freeway lanes, drivers would react to the presence of the
queue further upstream resulting in increasing lane changes and additional turbulence upstream of the ramp
influence area (Figure C-14). In this step the methodology estimates the length of the Queue Influence Area
(QIA), measured upstream from the back of queue.
Figure C-14 – Queue Influence Area with increased turbulence
Field data (video observations and loop detector data) were used to estimate the length of the Queue
Influence Area. This measurement process is illustrated in Figure C-15. For a given off-ramp bottleneck,
the distance between the exit and the upstream loop detector is known and fixed. The back of queue length
Q(t) at time t was measured by video observations of congested diverge segments. Speed measurements
from the loop detector were obtained with resolutions ranging between 20s and 60s (depending on the
source) and analyzed to determine the onset of congestion. Oversaturated conditions were determined to
occur when a speed drop greater than 20% occurred in at least one lane, and sustained for at least 15 min.
260

Figure C-15 – Measurement of queue influence area length based on queue lengths
For the timestamp tbd when congestion begins in at least one lane, the back of queue length is also known
from video observations. The distance between the detector and the back of queue Q(tbd) at the congestion
initiation time is defined as the Queue Influence Area. The speed prior to congestion, sbd, was also measured
(Figure C-16), and used in further calculations.
Figure C-16 – Sample measurement of queue lengths and speeds at the time of breakdown
261

This process was performed for all data obtained. It was observed that different locations operate at
significantly different speeds prior to congestion, therefore the Queue Influence Area measurements were
normalized to estimate the reaction headway, defined as the travel time between detector location (where
breakdown occurred) and the back of the queue:
3600 × 𝑄𝐼𝐴
ℎ = (Equation C-4)
5280 × 𝑠
Where:
hR = reaction headway (s)
QIAbd = measured Queue Influence Area at time of breakdown (ft)
sbd = measured speed at the beginning of congestion at the upstream detector (mi/h)
After all queue spillback observations were analyzed, the measured values of the reaction headway can
be found in the histogram of Figure C-17, with a median value of 10.95 s.
Figure C-17 – Frequency distribution of measured headways
Using this median value of 10.95s, the length of the QIA is estimated as a function of the segment free-
flow speed (FFS), as shown in Table C-3. The exact location of the QIA varies as a function of the queue
length. The QIA values are shorter than the ramp influence distance of 1,500 ft. However, the two concepts
are very different and are used differently in analyzing ramp operations: the ramp influence area is used to
analyze undersaturated conditions, while the QIA is used to analyze oversaturated conditions. Since drivers
can only detect a downstream queue visually, they have shorter times to react when compared to the
presence of undersaturated off-ramps, where signing and navigation information is provided in advance
and allows drivers to adjust their position earlier.
Table C-3. Queue influence area as function of the segment FFS

Segment FFS Queue Influence
(mi/h) Area (ft)
50 810
55 900
60 980
65 1060
70 1140
75 1220
262

When Regimes 3 or 4 occur and lane blockage is present in the mainline, the estimated QIA is added to
the queue length to determine the extent of spillback effects. If an upstream node is located within the
combined length of the queue and QIA, capacity adjustment factors must be applied to account for the
spillback effects.
Step 2D - Determine ramp proper capacity and speed

The first off-ramp parameter to be determined is its capacity (RC), defined as function of the ramp free-
flow speed and is obtained from HCM Exhibit 14-12, replicated below in Figure 18.
Source: HCM 6th Edition Exhibit 14-12

Figure C-18 – Capacity of ramp proper for off- ramps
The RC is compared to the off-ramp demand, and if the demand-to-capacity ratio is greater than 1.0 then
spillback is expected to occur.
Determining the speed-flow relationship at the ramp proper is also critical for the analysis. Speed data
along off-ramps are scarce, but a few field observations at off-ramp speed-flow curves (Figure C-19) have
shown that speeds have little variation as a function of demand.
Figure C-19 – Sample speed-flow curves for: (a) I-694 EB to Silver Lake Rd. and (b) I-94 EB to
Brooklyn Blvd. Minneapolis/MN
Determining the speed-flow relationship at the ramp proper is also critical for the analysis. Ramp speeds
can be obtained through the following equation:
𝑣
𝑆 = 1 − 0.109 × ×𝑆 (Equation C-5)
1000
where
𝑆 = ramp speed (mi/h);
263


The speed-flow relationship for ramps is linear and speed decreases with higher ramp flows, as presented
in Figure C-20. The maximum allowed values of vR are bounded by ramp capacity, consistent with guidance
provided by Chapter 14 – Merge and Diverge segments (Exhibit 14-12).
Figure C-20 – Speed-flow curves for freeway ramps
The ramp density at capacity (RKC) is not necessarily equal to 45 pc/mi/ln as assumed for freeway
mainline lanes. This parameter is required to evaluate the queue density at the ramp proper when operating
in oversaturated conditions. The ramp density at capacity can be found by dividing the capacity by speed.
Table C-4 summarizes the values of RKC as a function of the Ramp FFS.
Table C-4. Ramp density at capacity, as a function of Ramp FFS
Ramp FFS (mi/h) Capacity (pc/h/ln) RKC (pc/mi/ln)

50 2200 44.0
45 2100 46.7
40 2100 52.5
35 2000 57.1
30 2000 66.7
25 1900 76.0
20 1900 95.0
15 1800 120.0
Step 2E - Determine intersection storage capacity

The storage capacity at the intersection, ISTG, is obtained as the sum of the available storage of every
lane group, multiplied by the number of lanes. If the off-ramp has multiple branches at the intersection (k
> 1), then the available storage capacity must be computed for each branch k individually. This distinction
is necessary to evaluate cases with unbalanced demands at the intersection, when the queues developed in
264

one oversaturated movement may extend upstream and block the throughput of all movements at the off-
ramp. ISTG is estimated as:
𝐼𝑆𝑇𝐺(𝑖, 𝑝, 𝑘) = 𝑁 𝑥𝐿 𝑥𝐿 (Equation C-6)
Where:
Nm = number of lanes serving movement m at the intersection
Lm = storage length for movement m at the intersection (ft)
N = number of movements at the approach
Lh = average vehicle spacing in stationary queue (ft/veh) (HCM Equation 31-155)

The computation of the number of vehicles in the facility at every time step is critical for deriving
performance measures of oversaturated freeway facilities. Similar to the Freeway Facilities Oversaturated
Segment Evaluation methodology, the estimation of the number of vehicles in the ramp during
oversaturated conditions requires a reference value for undersaturated conditions to be computed during
the initialization steps.
First, the initial number of vehicles on the ramp during undersaturated conditions is determined as an
initial reference point. Given the ramp speed-flow relationship from Figure C-20, the density at an off-ramp
segment can be obtained by dividing the off-ramp flow rate (vR) by its free-flow speed (SR). Then, the total
number of vehicles is obtained by multiplying the ramp density by the ramp length (RL) and number of
lanes (RN), as follows
𝑣 ,
𝑅𝑁𝑉(𝑖, 0,0, 𝑘) = 𝑥 𝑅𝐿(𝑖, 𝑘)𝑥 𝑅𝑁(𝑖, 𝑘) (Equation C-7)
𝑆
Where:
RNV(i,0,0,k)) = number of vehicles in the ramp proper at the initialization step
IN(i,k) = off-ramp demand at the first time period in the analysis (pc/h)
Qk = off-ramp free-flow speed (mi/h)
The initial number of vehicles in the intersection approach are also determined as an initial reference
point, as follows:
𝐼𝑁𝑉(𝑖, 0, 𝑝, 𝑘) = 𝐼𝑁(𝑖, 𝑘) 𝑥 𝑄 (Equation C-8)
Where:
INV(i,t,p,k) = number of vehicles at the intersection of segment i, for level k at the end of time
step t during time period p
IN(i,k) = number of lanes serving the subject approach k
Qk = back-of-queue length for the subject approach k (veh)
The back-of-queue length Qk is estimated using equations corresponding to the intersection type at the
ramp terminal (Table C-5).
Table C-5. Reference HCM equations for back-of-queue length estimation
Intersection type Reference Equation
265

Signalized 31-149
TWSC 20-68
AWSC 21-33
Roundabout 22-20
At signalized intersections, due to their cyclic nature, queues form and discharge at different times for
different movements. Therefore, a reference point within the cycle must be selected as a starting point in
the methodology. The methodology assumes pretimed signalization, or converts actuated control to the
equivalent pretimed pattern. Typical signalized intersections at ramp terminals have the off-ramp approach
as the minor movement, with a start of green on the right side of the barrier (Figure C-21). It is
recommended setting a reference point at the onset of green for phases 3 and 7, as the back-of-queue lengths
at this time can be easily estimated using the methodology of Section 4, HCM Chapter 31.
Figure C-21 – Selection of a cycle reference point to determine the initial number of vehicles within
the approach

The methodology to evaluate the capacity of the terminal is specific to each intersection type and relies
mostly on the respective HCM chapters (19 through 23).
For a signalized intersection approach, the capacity for each movement at each time step is a function of
the signal phase sequence and the capacities of the individual movements at the intersection. Figure C-22
illustrates a sample signalized intersection approach from an off-ramp, with two lane groups: left-turn
(Phase 3) and right turn (Phase 8).
266

Figure C-22 – Sample signalized intersection approach from an off-ramp
Input Parameters
The required parameters to evaluate the capacity of a ramp terminal capacity are generally the same
required for standard signalized intersection analyses, as listed in Exhibit 19-11.
Arrival type: Chapter 19 of the HCM (Exhibit 19-14) provides guidelines for selecting the appropriate
Arrival Types based on the characteristics of arterial operations, such as quality of progression and
coordination. For an off-ramp approach to the intersection, vehicles arrivals can be considered random.
Therefore, Arrival Type 3 (random arrivals) is recommended to analyze the off-ramp approach at a
signalized ramp terminal.
Phase duration and effective green time: The duration of each phase at the signal can be fixed (pre-timed
control), or variable (semi-actuated or actuated control). For the former case, phase duration is known. For
the latter, an average phase duration is estimated as described in Section 2 of HCM Chapter 31 – Signalized
Intersections Supplemental. The effective green time g for each phase can then be computed according to
HCM Equation 19-3:
𝑔 =𝐷 −𝑙 −𝑙 (Equation C-9)
Where:
g = effective green time (s)
Dp = phase duration (s)
l1 = start-up lost time = 2.0 (s)
l2 = clearance lost time = Y + Rc – e (s)
Y = yellow clearance interval
Rc = red clearance interval
e = extension of effective green = 2.0 (s)
Converting approach capacity from time periods to time steps
The standard signalized intersection analysis is performed in 15-min periods, while the queue spillback
evaluation requires a 15-second approach compatible with the Freeway Facilities oversaturated
267

methodology. Therefore, an adjustment is necessary to calculate the capacities of each movement in 15-
second intervals.
The cycle length C can be divided into n time steps, with a duration of 15 s each (Figure 23). If an integer
number of time steps is not obtained, the difference is included in the first time step of the next cycle. Then,
green times for each time step from 1 to n are computed. This procedure must be repeated for every time
step within the 15 minutes time period, resulting in a total of 900/15 = 60 time steps.
Figure C-23 –Conversion of green times to time steps
The capacity ID for each approach and for each time step, is then obtained by multiplying its respective
green time by its capacity, as shown:
𝐼𝐷(𝑖, 𝑡, 𝑝, 𝑘) = 𝑁 𝑠 𝐺𝑇(𝑖, 𝑡, 𝑝, 𝑚) × 𝑓 (Equation C-10)

Where:
Nk = number of lanes serving movement k
sk = saturation flow rate for movement k (veh/h/ln)
GT(i,t,p,m)= green time for each movement m (s)
The green time parameter GT(i,t,p,m) measures the available green time for a given intersection
movement m, downstream of a freeway segment i, in time step t and time period p. It can range from 0
(when the movement has red through the entire time step length) to 15 (movement has green through the
entire time step length).
The heavy vehicle factor fHV needs to be applied to the equation for intersection discharge to make the
units used in intersection capacity (veh/h) consistent with the flow rates used in uninterrupted flow methods
(pc/h).
268

Merge segments (freeway-to-freeway connectors)
When two freeway facilities are connected through a ramp junction, the merge segment at the
downstream facility becomes the ramp terminal. In this case, the capacity of the ramp terminal is equal to
the merge capacity at the downstream freeway.
If the downstream segment operates at undersaturated conditions, there is no data available in the
literature to estimate the capacity of the merge segment. In this case, the merge capacity is considered
unrestricted (for a computational engine, a very high capacity value such as 9999 pc/h can be assumed) and
the only constraint at the freeway-to-freeway interaction will be the capacity of the ramp roadway, provided
by HCM Exhibit 14-12.
If the downstream segment operates at oversaturated conditions, the merge capacity is constrained by the
congested conditions in the mainline. The Freeway Facility Oversaturated Segment Evaluation procedure
computes, for every time step, the parameter ONRO as the maximum number of vehicles that can merge
into the freeway in a given time period. Therefore, in these conditions the merge capacity can be obtained
by analyzing the downstream freeway facility and aggregating the yielded values of ONRO to an hourly
flow rate.
Step 2H - Determine reference index for next downstream off-ramp

This step is essential for building the computational engine for this procedure, but it is not important for
understanding the overall methodology. The Freeway Systems methodology uses the parameter
OFRF(i,t,p) to store the off-ramp flow rate at diverge segment i. When a segment upstream of an off-ramp
is evaluated for queue spillback, the off-ramp flow rate must be referenced in order to estimate the incoming
flows for the blocked and non-blocked lanes. Therefore, a new variable NEXTOFR(i), is introduced to
reference the index of the closest diverge segment downstream of segment i. This is illustrated in Figure C-
24, where the node (i+2) represents a diverge segment with an off-ramp flow vR. When the queue extends
upstream to node i, the approaching flow vf is segregated into two groups: the exiting vehicles that will join
the back of the queue, and the through vehicles that will use the non-blocked lanes.
Figure C-24 – Illustration of mainline flow rate split into blocked and unblocked lanes
For nodes i and i+1, the closest downstream off-ramp is located at node (i+2), therefore the following
parameter is computed:
𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖) = 𝑖 2
The use of the parameter NEXTOFR facilitates referencing diverge segments downstream of a given
segment i and will be used for the spillback analysis procedure described over the next section.
269


This is a new step in the Freeway Facilities Analysis method (Figure C-4). In this step, spillback effects
in a diverge segment are determined after the off-ramp flow OFRF is determined (steps 7/8).
Determine ramp input, RI
The ramp input, RI, represents demand, and it is the number of vehicles that wish to travel through the
ramp proper node during a given time step. It takes into account the off-ramp demand, OFRF (as defined
in the Freeway Facilities Oversaturated methodology) and the number of off-ramp unserved vehicles from
the previous time step, RUV. The OFRF parameter already takes into consideration any bottleneck segments
upstream of the diverge that may meter the off-ramp demand (HCM Equations 25-23 through 25-25). The
RI is calculated as:
𝑅𝐼(𝑖, 𝑡, 𝑝) = 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) + 𝑅𝑈𝑉(𝑖, 𝑡 − 1, 𝑝) (Equation C-11)

Where:
OFRF(i,t,p) = flow that can exit at the off-ramp i during time step t in time period p
RUV(i,t,p,k) = number of unserved vehicles at the off-ramp exit at segment i, during time step t
in time period p
Calculate flow to the off-ramp and number of unserved vehicles
The ramp maximum flow RF represents capacity, i.e., the number of vehicles that are able to enter the
ramp proper by crossing the boundary node between the diverge segment and the ramp proper. It is
calculated as the minimum of three variables: RI, RC and RSTG.
𝑅𝐹(𝑖, 𝑡, 𝑝) = min(𝑅𝐼(𝑖, 𝑡, 𝑝, 𝑘), 𝑅𝐶(𝑖, 𝑘), 𝑅𝑆𝑇𝐺(𝑖, 𝑡, 𝑝, 𝑘)) (Equation C-12)
The parameters RI and RC have been previously defined. The parameter RSTG represents the maximum
number of vehicles that can enter the ramp due to a queue inside the ramp proper. The calculations follow
the same approach taken by the Mainline Output 2 (MO2) parameter (Equation 25-11). It starts by
calculating the maximum number of vehicles allowed on the ramp at a given ramp queue density RKQ:
𝑅𝐾𝑄(𝑖, 𝑡, 𝑝, 𝑘) = 𝐾𝐽– [(𝐾𝐽 – 𝑅𝐾𝐶) 𝑥 𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)] / 𝑅𝐶(𝑖, 𝑡, 𝑝) (Equation C-13)
The calculation of RKQ takes an approach similar to the calculation of the mainline queue density KQ
(Equation 25-10), with the following remarks on the inputs:
• The jam density parameter KJ uses the same value adopted for the mainline calculations
• The ramp density at capacity RKC is determined based on the ramp FFS (Table C-4)
• The parameters SF (segment flow) and SC (segment capacity) from Equation 25-10 are replaced
with RF (ramp flow, previously defined) and RC (ramp capacity, previously defined)
The maximum ramp storage constraint RSTG is then calculated using an approach similar to the Mainline
Output 2 (MO2) parameter from the Oversaturated segment evaluation procedure. This constraint limits the
number of vehicles able to enter the off-ramp due to the presence of a queue within the ramp proper. RSTG
is calculated as:
270

𝑅𝑆𝑇𝐺(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝑅𝐾𝑄(𝑖, 𝑡, 𝑝, 𝑘)𝑥[𝑅𝐿(𝑘) 𝑥 𝑅𝑁(𝑘)]– 𝑅𝑁𝑉(𝑖, 𝑡 −

(Equation C-14)
1, 𝑝, 𝑘)
Next, the number of unserved vehicles at the ramp entrance RUV is calculated. For each time step, the
number of unserved vehicles is computed as the value from the previous time step, plus the difference
between demand (RI) and throughput (RF) at the ramp node. RUV is calculated as:
𝑅𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝑈𝑉(𝑖, 𝑡 − 1, 𝑝 , 𝑘) + 𝑅𝐼(𝑖, 𝑡, 𝑝, 𝑘) − 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) (Equation C-15)
Where:
K = number of different branches at the intersection
If there are multiple branches k at the ramp proper (two lane ramps), RI and RF are compared for each
branch k to obtain RUV for each branch k. The total number of unserved vehicles at the ramp RUV(i,t,p) is
then obtained as the sum of RUV for each lane:
𝑅𝑈𝑉(𝑖, 𝑡, 𝑝) = 𝑅𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) (Equation C-16)
Calculate approach input, II
The intersection approach input II is the number of vehicles that wish to travel through the intersection
node during a given time step, i.e., its demand. It takes into account the off-ramp flow RF and the number
of unserved vehicles on the approach from the previous time step IUV. II is calculated as:
𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) + 𝐼𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) (Equation C-17)
Calculate maximum ramp output
The maximum allowable ramp output (RO) is calculated as a function of the available storage space
within the intersection approach, minus the number of vehicles present at the previous time step and the
number of vehicles discharged (IDC) in the present time period. RO is estimated as:
𝑅𝑂(𝑖, 𝑡, 𝑝, 𝑘) = 𝐼𝑆𝑇𝐺(𝑖, 𝑘) − 𝐼𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝐼𝐷𝐶(𝑖, 𝑡, 𝑝, 𝑘) (Equation C-18)
Calculate intersection approach flow and number of unserved vehicles
The intersection flow IF represents the number of vehicles that are able to cross the boundary node
between the ramp proper and the intersection (i.e., its capacity). It is computed as the minimum value
between the number of vehicles that wish to enter the intersection and the maximum number of vehicles
allowed to enter the intersection due to the available queue storage in the intersection:
𝐼𝐹(𝑖, 𝑡, 𝑝, 𝑘) = min(𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘), 𝑅𝑂(𝑖, 𝑡, 𝑝, 𝑘)) (Equation C-19)
If the number of vehicles trying to enter the intersection exceeds the amount of vehicles allowed to enter
the intersection, then the number of total unserved vehicles must be computed and considered in the
intersection input II during the next time period:
271

𝐼𝑈𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 𝐼𝑈𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘) − 𝑅𝑂(𝑖, 𝑡, 𝑝, 𝑘) (Equation C- 20)
Update number of vehicles at the ramp terminal intersection
The number of vehicles at the intersection, INV, is updated every time step based on the NV from the
previous time step, plus the number of vehicles that enter the intersection approach minus the number of
vehicles that are discharged. The maximum allowable total number of vehicles is function of the available
storage at the intersection, ISTG. NV is calculated as:
𝐼𝑁𝑉(𝑖, 𝑡, 𝑝) = 𝐼𝑁𝑉(𝑖, 𝑡 − 1, 𝑝) + 𝐼𝐹(𝑖, 𝑡, 𝑝, 𝑘) − 𝐼𝐷𝐶(𝑖, 𝑡, 𝑝, 𝑘) (Equation C- 21)
Calculate number of unserved vehicles at the off-ramp
The number of unserved vehicles, OFRUV, at the entrance of the ramp proper is updated every time step
as the difference between the number of vehicles that wish to enter the ramp proper (RI) and the flow
through the ramp node (RF):
𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡, 𝑝) = 𝑅𝐼(𝑖, 𝑡, 𝑝) − 𝑅𝐹(𝑖, 𝑡, 𝑝) (Equation C- 22)
Calculate intersection approach output
The intersection flow, IO, represents the actual number of vehicles discharging from the intersection
approach. It is computed as the minimum value between the intersection discharge capacity and the sum of
number of vehicles present in the intersection and the intersection input demand:
𝐼𝑂(𝑖, 𝑡, 𝑝, 𝑘) = min(𝐼𝐷𝐶(𝑖, 𝑡, 𝑝, 𝑘), 𝐼𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝐼𝐼(𝑖, 𝑡, 𝑝, 𝑘)) (Equation C- 23)
Update number of vehicles at the ramp roadway
The number of vehicles at the ramp proper, RNV, at the end of each time step is calculated based on the
number of vehicles from the previous time step plus the number of vehicles that entered the ramp minus
the number of vehicles that left the ramp:
𝑅𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝑁𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) − 𝐼𝐹(𝑖, 𝑡, 𝑝, 𝑘) (Equation C- 24)
Determine the back-of-queue length and spillback regime
Field observations have shown that off-ramp queues blocking mainline lanes are typically not stationary.
These queues usually consist of a platoon of closely-spaced vehicles moving at very low speeds (< 15mph).
The spacing between vehicles is also longer than the average vehicle spacing in stationary queues,
represented in the HCM by Lh (Equation 31-155). Therefore, the density of the spillback queue follows the
queue density at the ramp (RKQ, as previously defined), which allows the estimation of the queue length
OFRLQ. This parameter estimates the total queue length upstream of the off-ramp if all unserved vehicles
formed a single queue:
𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡, 𝑝)
𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) = (Equation C- 25)
272

Next, the mainline queue length, SBLQ, is compared to the available spillback queue storage for the
prevalent spillback regime for the given time step, as follows:
If OFRLQ = 0 → Regime 0
If 0 < OFRLQ ≤ LD → Regime 1
If SBLQ > LD :
If SL(i,p) > 0:
If OFRLQ < (LD + SL) → Regime 2
Else: Regime 3 / 4
Finally, the queue length in the mainline lanes MQ1 (lane 1) and MQ2 (lane 2) are obtained as a function
of the expected spillback regime. The total queue length OFRLQ minus the available storage lengths at the
deceleration lane and shoulder computes the queue length that the associated blockage.
𝑀𝑄1(𝑖, 𝑡, 𝑝, 𝑘) = 𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝, 𝑘) − 𝐿𝐷(𝑖)– 𝑆𝐿(𝑖)

𝑀𝑄2(𝑖, 𝑡, 𝑝, 𝑘) = 0 (Equation C- 26)

𝑀𝑄1(𝑖, 𝑡, 𝑝) = 𝑀𝑄2(𝑖, 𝑡, 𝑝) = [𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) − 𝐿𝐷(𝑖)– 𝑆𝐿(𝑖) ] / 2
(Equation C- 27)
Check for impacts on upstream nodes
The freeway nodes upstream of a congested off-ramp may be affected by spillback as queues grow.
When this occurs, the methodology calculates the length of the queue in the upstream segment. The length
of the queue within the subject segment will then be used to evaluate whether the capacity of any upstream
node is affected by the queue.
For upstream segments that may be affected by spillback, the queue length within the segment (measured
from its downstream end) must be computed and stored in the parameter SBLQ. This check is performed
for every node upstream of a congested off-ramp (Figure C-25).
273

Figure C-25 – Procedure for evaluating the impact of queue spillback on upstream nodes and
determination of the queue length within upstream segments
When queue spillback occurs in a downstream off-ramp, the length of the mainline queue measured from
the start of the deceleration lane is known from the previous step. If a given segment has any queues
blocking one or more lanes, three possible scenarios may occur at the node (Figure C-26):
(a) Lane blockage: Queues extend through the entire segment and reach the upstream node, causing the
subject node to operate in a two-pipe regime. The blocked lanes operate in a congested regime, with
their capacity constrained by the off-ramp capacity. The unblocked lanes, on the other hand, operate
at uncongested conditions with a small reduction in capacity due to the friction of through vehicles
passing along congested lanes. For the through lanes, an adjustment factor CAFBL is applied. This
condition occurs when the Spillback Queue length SBLQ(i) is equal or greater than the Segment
Length L(i).
(b) Increased turbulence: Queues extend partially through the segment and the upstream node is located
within the Queue Influence Area (QIA). This region is characterized by intense turbulence as vehicles
quickly perform lane changes to adjust their position reacting to the queue ahead, and all lanes in
node i have their capacity reduced by an adjustment factor CAFUP. This condition occurs when the
sum of the Spillback Queue length SBLQ(i) and the Queue Influence Area QIA(i) is equal or greater
than the segment length L(i).
(c) No effect: Queues extend partially through the segment but the upstream node is located within the
Queue Influence Area (QIA). For this condition, no capacity adjustment factors are applied to the
node i. This condition occurs when the sum of the Spillback Queue length SBLQ(i) and the Queue
Influence Area QIA(i) is smaller than the segment length L(i).
274

Figure C-26 – Illustration of different impacts of an off-ramp queue at node i: (a) lane blockage, (b)
increased turbulence and (c) no effect
Calculate capacity adjustment factors
Based on how upstream nodes are affected as described under Step 6B (Lane Blockage, Increased
Turbulence or No Effect), the corresponding impacts on capacity are computed in this step. This section
describes the calculations of capacity adjustments depending on how upstream nodes are affected.
Lane blockage adjustment factor
When one or more lanes are blocked, the subject node is analyzed as a two-pipe operation, with a
congested flow in one or more lanes of the ramp side and uncongested flow in the remaining lanes.
The capacity of these lanes is equal to the number of queued vehicles discharged at the downstream
segment. The flow rate attempting to cross the node through the congested lanes is equal to the off-ramp
flow rate (OFRF) at the closest downstream off-ramp
Increased turbulence adjustment factor
When a node falls under the Increased Turbulence case (Figure C-26b), all lanes are affected by the
turbulence caused by the intense lane changing. In this case, an adjustment factor CAFUP is applied
uniformly to the node capacity:
𝐶𝐴𝐹𝑈𝑃(𝑖, 𝑡, 𝑝) = 1 − 𝛼 × 𝐿𝐶𝑅(𝑖, 𝑡, 𝑝) (Equation C- 28)
The calibration adjustments α and β were calibrated to match field conditions. Based on observed field
data, the recommended values for the parameters are α = 0.52 and β = 0.81.
The parameter LCR estimates the rate of lane change maneuvers performed by vehicles within the Queue
Influence Area trying to adjust their position when spillback occurs. Vehicles traveling towards the exit
ramp will move to the shoulder lane attempting to join the back of the queue, while vehicles traveling
through will move to the median lanes in order to avoid the queue. Therefore, the lane change rate LCR is
computed as:
275

𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝)
𝐿𝐶𝑅(𝑖, 𝑡, 𝑝) = (Equation C- 29)
𝑆𝐹(𝑖, 𝑡, 𝑝)
The parameter SBLC represents the number of lane change maneuvers performed in the queue influence
area. In order to compute SBLC for a given node, the number of vehicles driving toward the off-ramp must
be estimated for each freeway lane. For each lane i, the parameter pi represents the percent of the off-ramp
demand vR traveling on the subject lane. In order to estimate the values of pi as a function of the distance
from the off-ramp to the subject node, the following steps and assumptions are used:
a) Within the influence area (1,500 ft from the exit point), the off-ramp demand flow rate vR
is entirely positioned in the two rightmost lanes, according to the guidance provided in
HCM Chapter 14. Therefore, the sum of the off-ramp flow rate percentages in the ramp
influence area p1,R and p2,R is equal to 1. The methodology to estimate lane-by-lane flow
distribution in freeway segments allows the estimation of the Lane Flow Ratio (LFR) for
lanes 1 and 2. The proportion between p1,R and p2,R can then be estimated as follows:
𝑝 , = , 𝑝 , = (Equation C- 30)
b) According to the guidance provided in HCM Chapter 14, the influence of ramps rarely
extend beyond 8,000 ft. Therefore, for any nodes located beyond 8,000 from the off-ramp,
the distribution of pi is taken as equal among all N freeway lanes:
1
𝑝 = (Equation C- 31)
𝑁
c) At intermediate distances from the off-ramp dOFR ranging between 1,500 ft and 8,000 ft,
the distribution values of pi can be obtained through linear interpolation between the cases
previously described.
Figure C-27 – Distribution of pi as function of distance from the off-ramp exit, for a 3-lane segment
The value of pi as function of the distance from off-ramp exit dOFR can then be obtained through the
following equation:
276

1
− 𝑝 , 𝑅 × (𝑑 − 1,500)
𝑝 =𝑝, + 𝑁 (Equation C- 32)
6500
As the lane-by-lane distribution of the off-ramp flow is known, the number of lane change maneuvers,
SBLC, can then be estimated. For Regime 3 cases (one blocked lane), the number of lane changes is
𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝) = (𝑆𝐹1(𝑖, 𝑡, 𝑝) − 𝑣 , )+ (𝑖 − 1) × 𝑣 , (Equation C- 33)
The equation adds the number of through vehicles in lane 1 that move to lane 2 to avoid the queue and
the number of exiting vehicles in the remaining lanes that adjust their position to join the back of the queue,
multiplied by the necessary number of lane changes. Figure C-28 illustrates an example of the proposed
equation applied to a 4-lane segment.
Figure C-28 – Illustration of lane change maneuvers within the queue influence area in a 4-lane
segment with Regime 3
For Regime 4 cases, the following equation is applied to obtain SBLC:
𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝) = 2 × (𝑆𝐹1(𝑖, 𝑡, 𝑝) − 𝑣 , ) + 𝑆𝐹2(𝑖, 𝑡, 𝑝) − 𝑣 ,

(Equation C- 34)
+ (𝑖 − 2) × 𝑣 ,
Figure C-29 illustrates an example of the proposed equation applied to a 4-lane segment.
Figure C-29 – Illustration of lane change maneuvers within the Queue Influence Area in a 4-lane
segment with Regime 4
Step 9 - Calculate mainline input
277

The Oversaturated Segment Evaluation procedure computes the Mainline Input (MI) for each node, in
every time step. It is defined as the maximum flow desiring to enter the subject node during the current
time step.
An adjustment is necessary when the subject node is operating in a two-pipe regime, as the blocked and
unblocked portions will be subject to different input demands. Since exiting and through drivers segregate
when approaching a queue, the mainline input demand in the blocked side consists of the off-ramp demand,
while the remaining demand will move to the unblocked portion.
When node i operates in a two-pipe regime, the Mainline Input (MI) parameter is split into two
components: MIUB, representing the mainline input in the unblocked lanes, and MIBL, representing the
mainline input joining the back of the queue. These parameters are computed as follows:
𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑂𝐹𝑅𝐹(𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖), 𝑡, 𝑝) (Equation C- 35)
𝑀𝐼𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝐼(𝑖, 𝑡, 𝑝) − 𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝) (Equation C- 36)
Step 12 - Calculate on-ramp maximum output

If there is a merge segment upstream of an off-ramp bottleneck, the capacity of on-ramp output may be
affected due to the blockage caused by the spillback queue. The Oversaturated Segment evaluation
procedure calculates the on-ramp maximum output through HCM Equation 25-18, based on a series of
potential constraints that include ramp metering, the on-ramp capacity, the capacity of the merge, or the
presence of downstream queues. At high demands on both the freeway and the on-ramp, zipper merge (one-
to-one) is expected to occur. Therefore, a new capacity constraint is added to Equation 25-18, included in
the equation below in bold font and illustrated in Figure C-30:
𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝)
𝑅𝑀(𝑖, 𝑡, 𝑝)
⎧ 𝑂𝑁𝑅𝐶(𝑖, 𝑡, 𝑝)
⎪
𝑀𝐹(𝑖 + 1, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪ ⎧𝑚𝑖𝑛 − 𝑀𝐼(𝑖, 𝑡, 𝑝)
⎪ 𝑀𝑂3(𝑖, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪
= 𝑚𝑖𝑛( ⎪ 𝑆𝐶(𝑖, 𝑡, 𝑝) (Equation C- 37)
⎨𝑚𝑎𝑥( 𝑚𝑖𝑛 𝑀𝐹(𝑖 + 1, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝) /2𝑁(𝑖, 𝑝)
⎪ ⎨ 𝑀𝑂3(𝑖, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)
⎪ ⎪
⎪ ⎪ 𝑹𝑭(𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊), 𝒕, 𝒑))
⎩ ⎩ 𝟐 × 𝑵𝑸(𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊))
278

Figure C-30 – Impact of a queue spillback on the discharge capacity of an upstream on-ramp
If one or more lanes are blocked due to a downstream off-ramp bottleneck, the throughput in Lane 1 will
be equal to the maximum exit throughput in the congested off-ramp if the site operates in Regime 3, or 50%
of the maximum exit throughput in the off-ramp, if it operates in Regime 4. It is assumed that the on-ramp
and the flow arriving from the upstream on Lane 1 contribute equally to the downstream Lane 1 flow, and
thus the on-ramp maximum output, in this case, is assumed to be half of the downstream throughput in
Lane 1.
Step 21 - Calculate mainline output (2)

The Oversaturated Segment Evaluation methodology calculates the maximum number of vehicles, MO,
that can exit a node, constrained by a downstream bottleneck or by merging on-ramp traffic. Among the
potential constraints to calculate MO, the Mainline Output 2 accounts for the growth of queues on a
downstream segments, eventually limiting the maximum number of vehicles that can enter it.
When there is a queue in a downstream segment caused by a downstream off-ramp bottleneck, the
segment is expected to operate under two distinct densities (Figure C-31). Therefore, the total number of
vehicles in the downstream segment takes into account two different density values: the ramp queue density
(RKB), prevailing at the queued area in red, and the background density (KB), prevailing in the remaining
area of the segment (blue).
Figure C-31 – Illustration of different density values within one diverge segment
If there are no spillback effects, the segment operates with a uniform density. In this case, the constraints
for the unblocked and blocked portions (MO2UB and MO2BL, respectively) are calculated proportionately
to the number of unblocked and blocked lanes:
279

(1 − 𝑁𝑄(𝑖))
𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) × (Equation C- 38)
𝑁(𝑖)
𝑁𝑄(𝑖)
𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) × (Equation C- 39)
𝑁(𝑖)
If node i operates under Increased Turbulence (node is in the Queue Influence Area), the unblocked
portion of segment i will operate similar to a regular segment. Therefore, the component MO2UB is equal
to MO2 but proportional to the number of lanes in the unblocked portion:
(1 − 𝑁𝑄(𝑖))
𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) × (Equation C- 40)
𝑁(𝑖)
For the blocked portion of segment i, the parameter is calculated as equal to MO2 proportional to the
number of lanes in the blocked portion plus an additional number of vehicles due to the presence of a partial
queue. This additional number of vehicles is obtained by the bold terms in the following equation, which
takes into account the difference between the queue spillback density (RKQ) and the segment queue density
(KQ), multiplied by the queue length:
𝑁𝑄(𝑖) 𝑺𝑩𝑳𝑸(𝒊, 𝒕 − 𝟏, 𝒑)
𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡, 𝑝) × + × 𝑵𝑸(𝒊, 𝒕 − 𝟏, 𝒑)
𝑁(𝑖) 𝟓𝟐𝟖𝟎 (Equation C- 41)
× [𝑹𝑲𝑸(𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊), 𝒕 − 𝟏, 𝒑) − 𝑲𝑸(𝒊 − 𝟏, 𝒕 − 𝟏, 𝒑)]
If node i experiences lane blockage, the values of queue density must be computed for both the unblocked
(KQUB) and blocked (KQBL) portions of segment i. For the unblocked portion, the queue density KQUB
is calculated similarly to Equation 25-10, but the inputs for segment flow (SF) and segment capacity (SC)
are replaced by their equivalent parameters SFUB and SCEQ:
𝐾𝑄𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝐾𝐽 − [(𝐾𝐽 − 𝐾𝐶)] × 𝑆𝐹𝑈𝐵(𝑖, 𝑡 − 1, 𝑝)]/𝑆𝐶𝐸𝑄(𝑖, 𝑝) (Equation C- 42)
The queue density for the blocked portion is computed as equal to the ramp queue density:
𝐾𝑄𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑅𝐾𝑄(𝑂𝐹𝑅𝑁𝐸𝑋𝑇(𝑖), 𝑡 − 1, 𝑝) (Equation C- 43)
With the queue density values for both the blocked and unblocked portions known, the MO2 components
MO2BL and MO2UB can be computed:
𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝) = 𝑀𝐹𝑈𝐵(𝑖, 𝑡 − 1, 𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) + [𝐾𝑄𝑈𝐵(𝑖, 𝑡, 𝑝) × 𝐿(𝑖) ×

(Equation C- 44)
(𝑁(𝑖, 𝑝) − 𝑁𝑄(𝑖, 𝑝))] − 𝑁𝑉𝑈𝐵(𝑖, 𝑡 − 1, 𝑝)
𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑀𝐹𝐵𝐿(𝑖, 𝑡 − 1, 𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) + [𝐾𝑄𝐵𝐿(𝑖, 𝑡, 𝑝) × 𝐿(𝑖) ×

(Equation C- 45)
𝑁𝑄(𝑖, 𝑝)] − 𝑁𝑉𝐵𝐿(𝑖, 𝑡 − 1, 𝑝)
280

Step 22 - Calculate mainline flow

The Oversaturated Segment Evaluation procedure computes the Mainline Flow through a subject node
as the minimum of several variables, as presented in HCM Equation 25-16. If the node experiences
spillback, the calculation of Mainline Flow must consider the flow through both the blocked and the
unblocked portions of the node. Therefore, the Mainline Flow (MF) parameter is split into two components
in an approach similar to the Mainline Input: the component MFUB represents flow across the node in the
unblocked lanes, while the component MFBL represents the flow across the node in the blocked lanes. For
both components, the resulting flow is computed as the minimum value between input and the maximum
allowed flow.
For MFUB, the maximum allowed flow is equal to the capacity of unblocked lanes in the downstream
segment, represented by the parameter SCEQ as computed in the initialization step:
𝑀𝐹𝑈𝐵(𝑖) = min(𝑀𝐼𝑈𝐵(𝑖, 𝑡, 𝑝), 𝑆𝐶𝐸𝑄(𝑖, 𝑡, 𝑝), 𝑀𝑂2𝑈𝐵(𝑖, 𝑡, 𝑝)) (Equation C- 46)
For MFBL, the maximum allowed flow is equal to the flow allowed to enter the nearest downstream off-
ramp RF, as presented in the following equation:
𝑀𝐹𝐵𝐿(𝑖) = 𝑚𝑖𝑛(𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝), 𝑅𝐹(𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖, 𝑡, 𝑝), 𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝)) (Equation C- 47)

Next, the Mainline Flow MF through node i is computed as the sum of the blocked and unblocked
portions, as follows:
𝑀𝐹(𝑖, 𝑡, 𝑝) = 𝑀𝐹𝑈𝐵(𝑖, 𝑡, 𝑝) + 𝑀𝐹𝐵𝐿(𝑖, 𝑡, 𝑝) (Equation C- 48)
Step 23 - Update number of vehicles in the blocked portion of the segment

The number of vehicles in the blocked portion NVBL during increased turbulence is updated based on
the number of vehicles in the previous time step and considers the number of vehicles that are able to leave
the current and upstream segment :
𝑁𝑉𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑁𝑉𝐵𝐿(𝑖, 𝑡 − 1, 𝑝) + 𝑀𝐹𝐵𝐿(𝑖 − 1, 𝑡, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝) (Equation C- 49)

− 𝑀𝐹𝐵𝐿(𝑖, 𝑡, 𝑝) − 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝)
Step 24 - Additional number of vehicles ΔNV due to the off-ramp queue

The additional number of vehicles in the segment due to an off-ramp queue is obtained by the following
equation:
𝑅𝐾𝑄(𝑖, 𝑡, 𝑝) − 𝐾𝐵(𝑖, 𝑝) (Equation C- 50)

∆𝑁𝑉(𝑖, 𝑡, 𝑝) = 𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) ×
5280

The aggregated segment flow for a 15-min time period is obtained as the sum of flows for every time
step (HCM Equation 25-30):
𝑇
𝑆𝐹(𝑖, 𝑝) = 𝑆𝐹(𝑖, 𝑡, 𝑝) (Equation C- 51)
𝑆
281

Similarly, the aggregated off-ramp ramp is aggregated at a 15-min time period:

𝑇
𝑂𝐹𝑅𝐹(𝑖, 𝑝) = 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) (Equation C- 52)
𝑆
The additional density in the queued lanes is obtained by aggregating the additional number of
vehicles ΔNV(i,t,p) in the off-ramp queue:
1
∆𝐾(𝑖, 𝑝) = ∆𝑁𝑉(𝑖, 𝑡, 𝑝) (Equation C- 53)
𝑆×𝑁
Similar to the mainline, the flow in the ramp roadway is also aggregated:
𝑇
𝑅𝐹(𝑖, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) (Equation C- 54)
𝑆
The aggregated density at the ramp is calculated as the average of the number of vehicles inside the
ramp along the time period:
1
𝑅𝐾(𝑖, 𝑝, 𝑘) = 𝑅𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘) (Equation C- 55)
𝑆
Finally, the speed at the ramp for a time period p is obtained by dividing the total ramp flow in the
time period by its average density:
𝑅𝐹(𝑖, 𝑝, 𝑘)
𝑆𝑅(𝑖, 𝑝, 𝑘) = (Equation C- 56)
𝑅𝐾(𝑖, 𝑝, 𝑘)
282

Case Study: Evaluating Queue Spillback on a Freeway-to-Freeway

connector
This case study illustrates the application of the off-ramp spillback methodology to evaluate a network
comprised of two freeway facilities (I-75 SB to SR-826 SB, Miami, Florida), as shown in Figure C-32. Due
to congested conditions at the downstream merge segment (SR-826), spillback is expected to affect the
operations of the upstream freeway facility (I-75). Vehicles traveling from node A to D are likely to have
their travel time severely affected if spillback occurs.
Figure C-32 – Study site for freeway-to-freeway queue spillback check, Miami, FL
This freeway-to-freeway connector is modeled as two separate freeway facilities. The upstream freeway
(Facility 1: I-75) is modeled as a diverge section that is connected to the downstream freeway (Facility 2:
SR-826). The system’s detailed geometry is shown in Figure C-33.
283

Figure C-33 – Individual freeway facilities: (a) I-75 SB and (b) SR-826 SB
Input data
Traffic demands for the freeway facilities and ramps are provided in Table C-6 in 15-minute time periods.
Table C-6. Traffic Demands for the Subject Freeway Facilities

Freeway Facility 1 (I-75 SB) Freeway Facility 2 (SR-826 SB)
Time Mainline Diverge Mainline
Period Merge demand
demand flow demand flow demand flow
(veh/h)
rate (veh/h) rate (veh/h) rate (veh/h)
1 5400 1400 4000 1400
2 6200 3000 5700 3000
3 6000 3400 5600 3400
4 4500 800 4500 800
Additional input parameters are as follows:

• Urban area with level terrain;
• Grade: 0%;
• Regime 4 is expected;
• Base FFS: 65 mi/h (I-75) and 67.1 mi/h (SR-826);
• Ramp side: right for both facilities;
• Traffic composition: 12% trucks on both freeway and ramps;
• Ramp length: 3588 ft;
• Acceleration lane length: 1500 ft;
• No shoulder available;
284

• Deceleration lane length: 700 ft;

• Number of ramp lanes: 2; and
Performance measures - individual facilities

The performance measures for both freeway facilities, if analyzed independently, are presented in Table
C-7 and Table C-8. Facility 1 (I-75) is undersaturated, while Facility 2 (SR-826) experiences congestion in
time periods 2 and 3. Ignoring the interactions between these two facilities would lead to inaccurate
estimations of performance for the upstream facility. The merge segment (segment 2) in the SR-826 facility
operates at LOS F, and the on-ramp capacity may be affected leading to queue formation and potential
spillback.
Table C-7. Performance measures for I-75 (Freeway facility 1)
Time Segment 1 Segment 2 Segment 3 Segment 4

period Basic Basic Diverge Basic
1 C C B B
2 C C C A
3 C C C A
4 B B A B
Table C-8. Performance measures for SR-826 (Freeway facility 2)
Segment 1 Segment 2 Segment 3 Segment 4 Segment 5

Time period
Basic Merge Basic Diverge Basic
1 B C C B C
2 C F E F E
3 C F F F E
4 C C C C C
Spillback check
The analysis of SR-826 using the Freeway Facilities Oversaturated Segment Evaluation provides the
expected on-ramp queue for every time period. The first check compares the off-ramp demand to the ramp
roadway capacity, as shown in Table C-9. The ramp queue starts to develop during time period 2. At the
end of this time period, a ramp queue length of 1188 ft is expected, yielding a queue storage ratio of 0.33.
Therefore, spillback is not expected during time period 2. During time period 3 a ramp queue length of
5160 ft is expected with a queue storage ratio of 1.41. Therefore, spillback will occur during time period 3.
285

Table C-9. Estimation of queue length and storage ratio at the SR-826 on-ramp
Number of
Total number Average Queue Ramp Queue
queued
of queued vehicle length length storage
Time vehicles in Spillback
vehicles spacing (ft) (ft) (ft) ratio
period each lane occurs?
[D] = [F] =
[A] [B] = [A]/2 [C] [E]
[B]*[C] [D]/[E]
1 0 0 - 0 0.00 No
2 38.3 19.15 62 1188 0.33 No
3588
3 159.1 79.55 65 5160 1.44 Yes
4 0 0 - 0 0.00 Yes
Spillback analysis
Since spillback is expected to occur, the methodology of this chapter (Figure C-4 through Figure C-7) is
applied to evaluate its impacts on I-75 SB. The application of the methodology for each time period is
presented below.
Time period 1
No oversaturated conditions occur, therefore no additional calculations are needed for this time period.
Time period 2
During time period 2, the downstream merge segment operates at LOS F and the on-ramp capacity is
expected to be reduced.
Step 1 - Calculate background density for unblocked lanes on each segment in the case of queue
spillback
The diverge segment at I-75 has 5 lanes and Regime 4 (two blocked lanes) is expected. Therefore, when
queue spillback occurs this segment operates with two blocked lanes (lanes 1 and 2) and three unblocked
lanes (lanes 3 through 5).
The capacity per lane at the diverge segment SC(3) is 2,350 pc/h/ln or 11750 pc/h. For the time step level
analysis, the capacity is converted to 48.95 passenger cars per time step (ts), Therefore, the capacity for the
unblocked portion of the segment is given by (Equation C- 1):
𝑆𝐶𝐸𝑄(𝑖, 𝑁, 𝑁𝑄) = 𝑆𝐶(𝑖, 𝑁 − 𝑁𝑄) × 𝐶𝐴𝐹
The capacity adjustment factor CAFBL is obtained from Table C-1. For a segment with 5 directional lanes
and 2 blocked lanes, an adjustment factor CAFBL = 0.67 is applied. Therefore, the equivalent capacity of
the unblocked portion is given by:
𝑆𝐶𝐸𝑄(3, 5, 3) = 48.95 × 0.67 = 38.8 pc/ts or 7872 pc/h
286

The unblocked background density KBUB is calculated next. For time period 2, an expected demand of
4165.8 pc/h for the mainline is used in the calculations. The KBUB parameter of the unblocked lanes is
computed as the density of a 3-lane basic segment with a capacity SCEQ = 7872 pc/h:
𝐾𝐵𝑈𝐵(3, 5, 3) = 30.4 pc/h/mi

When spillback occurs, the subject freeway facility is analyzed as a link-node structure similar to the
oversaturated procedure for freeway facilities. The facility structure is also expanded to consider the ramp
segments. Figure C-34 illustrates the structure for the current analysis. Node 4.1 represents the interface
between the diverge segment and the ramp roadway, while node 4.2 represents the interface between the
ramp roadway and the merge at the downstream facility.
Figure C-34 – Link-node structure for spillback analysis – I-75 SB

The queue influence area is obtained as function of the segment FFS, as shown in Table C-3. Therefore,
for a FFS = 65mi/h, the QIA length is equal to 1060 ft.

The ramp speed at the expected demand is obtained as:
𝑣
𝑆 = 1 − 0.109 × ×𝑆
1000
1679
𝑆 = 1 − 0.109 × × 55 = 44.9 mi/h
1000
Next, the ramp background density is obtained:

𝑣 1679
𝑅𝐾𝐵 = = = 37.4 𝑝𝑐/𝑚𝑖/𝑙𝑛
𝑆 44.9
The initial number of vehicles in the ramp is then computed as:
287

3588
𝑅𝑁𝑉(3,0,2,1) = 37.4 × × 2 = 50.8 𝑝𝑐
5280

The capacity of the merge is obtained by analyzing the downstream freeway facility using the
oversaturated segment evaluation procedure and aggregating the parameter ONRO for an hourly flow rate.
During this time period, the merge capacity is constant at 13.4 pc/ts or 3217 pc/h, while the ramp demand
is 14 pc/ts or 3369 pc/h.
Given the demand and capacity at the merge, the queue in the ramp roadway increases by 0.6 pc for
every time step. Figure C-35 illustrates the ramp queue and the total number of vehicles in the ramp,
considering an initial number of 50.8 pc in the ramp at the start of the time period as previously computed.
Figure C-35 – Queued vehicles and total number of vehicles in the ramp – time period 2

The flow RF that can travel across the ramp node 4.1 and enter the ramp roadway is obtained as the
minimum of demand (RI), the ramp roadway capacity (RC) and the constrained capacity due to a
downstream queue in the ramp (RSTG), as shown in (Equation C-12):
𝑅𝐹(𝑖, 𝑡, 𝑝) = min(𝑅𝐼(𝑖, 𝑡, 𝑝, 𝑘), 𝑅𝐶(𝑖, 𝑘), 𝑅𝑆𝑇𝐺(𝑖, 𝑡, 𝑝, 𝑘))
The capacity of the ramp roadway for a 2-lane ramp with FFS = 55mph, is equal to 4,400 pc/h or 18.3
pc/ts. Therefore, the capacity of the ramp roadway is not a constraint to ramp flow. The other potential
capacity constraint RSTG is calculated through (Equation C-14):
𝑅𝑆𝑇𝐺(𝑖, 𝑡, 𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡 − 1, 𝑝, 𝑘) + 𝑅𝐾𝑄(𝑖, 𝑡, 𝑝, 𝑘)𝑥[𝑅𝐿(𝑘) 𝑥 𝑅𝑁(𝑘)]– 𝑅𝑁𝑉(𝑖, 𝑡 − 1, 𝑝, 𝑘)
The constraint RSTG is dependent on the number of vehicles in the ramp RNV, which increases
progressively as the queue grows along the ramp. Figure C-36 compares the decreasing value of RSTG with
the ramp input RI during time period 2. At the end of the time period, the capacity is still greater than
demand, therefore no spillback occurs at the end of this time period as predicted by the queue spillback
check previously described.
288

Figure C-36 – Ramp capacity and ramp inputs – time period 2
Since spillback does not occur, no additional calculations for the mainline are required.

Since spillback does not occur during this time period, the performance measures for the mainline do not
need to be recalculated.
Since the ramp experiences queueing, the ramp speed in this time period is calculated using (Equation
C- 54) through (Equation C- 56):
𝑅𝐹(𝑖, 𝑝, 𝑘) = 4 × 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) = 1679.5 pc/h/ln
1
𝑅𝐾(𝑖, 𝑝, 𝑘) = × 𝑅𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 71.6 pc/mi/ln
60
𝑅𝐹(𝑖, 𝑝, 𝑘) 1679.5
𝑆𝑅(𝑖, 𝑝, 𝑘) = = = 31.9mi/h
𝑅𝐾(𝑖, 𝑝, 𝑘) 71.6
Time period 3
The same steps are repeated for time period 3. The ramp analysis is summarized in Figure C-37. For this
time period, the ramp demand is 15.4 pc/ts, while the merge capacity is 13.9 pc/ts. Since demand is greater
than capacity, the number of vehicles increases gradually, causing the capacity constraint RSTG to decrease
each time step. At time step 14, the value of RSTG becomes equal to the merge capacity (13.9 pc/ts), which
implies that the ramp has reached jam density and the maximum flow that can enter the ramp is equal to
the flow that departs the ramp. Therefore, queue spillback into the mainline starts at time step 15.
289

Figure C-37 – Ramp capacities and ramp inputs – time period 3
After the onset of queue spillback, the number of unserved vehicles at the exit is computed every time
step through the parameter OFRUV(i,t,p). Then, the expected length of the mainline queue OFRLQ(i,t,p)
is computed based on the number of unserved vehicles and the ramp queue density RKQ, as shown in
(Equation C- 25):
𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡, 𝑝)
𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) =
The ramp queue density RKQ is obtained using (Equation C-13):

RKQ(i, t, p, k) = KJ– [(KJ – RKC) x RF(i, t − 1, p)] / RC(i, t, p)
𝑅𝐾𝑄(𝑖, 𝑡, 𝑝, 𝑘) = 190– [(190 – 46.5) × 13.87)] / 18.33 = 81.4 pc/mi/ln
Figure C-38 illustrates the expected spillback queue length during time period 3.
Figure C-38 – Spillback queue length – segment 3 (diverge) – I-75 SB
290

The parameter OFRLQ represents the length of the queue if all unserved vehicles were queued in a single
line. Given the segment geometry (Figure C-39), the operating regimes and flow modes can be obtained as
a function of OFRLQ:
• 0 < OFRLQ ≤ 1,400 ft: Regime 1
• 1400 ft < OFRLQ ≤ 3000 ft: Regime 4, with increased turbulence
• 3000 ft < OFRLQ: Regime 4, with lane blockage (queue extends upstream beyond the diverge)
Figure C-39 – Available queue storage – segment 3 (diverge) – I-75 SB
As previously shown in Figure C-38, the maximum queue length OFRLQ at time period 3
is equal to 4696 ft. Since queues develop along lanes 1 and 2, at the end of time period 3 the
back of queue will be located 848ft upstream of the boundary of segments 2 and 3. The length
of the queue influence area (QIA) is 1060 ft, and when it is added to the back of the queue it
does not reach the upstream node of segment 2. Therefore, segment 2 capacity is not affected by
the turbulence area upstream of the queue.
Figure C-40 – Back of queue length, including QIA, at the end of time period 3

The ramp speed is computed similarly to time period 2:
𝑅𝐹(𝑖, 𝑝, 𝑘) = 4 × 𝑅𝐹(𝑖, 𝑡, 𝑝, 𝑘) = 1707 pc/h/ln
291

1
𝑅𝐾(𝑖, 𝑝, 𝑘) = × 𝑅𝑁𝑉(𝑖, 𝑡, 𝑝, 𝑘) = 108.4 pc/mi/ln
60
𝑅𝐹(𝑖, 𝑝, 𝑘) 1707
𝑆𝑅(𝑖, 𝑝, 𝑘) = = = 21.5 mi/h
𝑅𝐾(𝑖, 𝑝, 𝑘) 108.4
For the freeway facility, performance measures are computed for the blocked and unblocked portions of
each segment.
Segment 3 (diverge) – blocked portion
Similar to the ramp, the flow through the blocked portion is aggregated for this time period:
𝑆𝐹𝐵𝐿(𝑖, 𝑝) = 4 × 𝑡𝑖𝑚𝑒𝑠 𝑆𝐹𝐵𝐿(𝑖, 𝑡, 𝑝) = 3030 pc/h
The average density is obtained as the sum of two separate components. The average number of vehicles
in the blocked portion of the segment is computed as:
1
𝐾𝐵𝐿(𝑖, 𝑝) = × 𝑁𝑉(𝑖, 𝑡, 𝑝) = 51 pc/mi/ln
60
The increase in density due to the lane blockage ΔK is obtained as:

1
∆𝐾(𝑖, 𝑝) = ∆𝑁𝑉(𝑖, 𝑡, 𝑝) = 20.1 pc/mi/ln
𝑆×𝑁
The total density is then computed as:

𝐾(𝑖, 𝑝) = 𝐾𝐵𝐿(𝑖, 𝑝) + ∆𝐾(𝑖, 𝑝) = 70.1 pc/mi/ln
Finally, the speed in the blocked lanes is obtained through the fundamental equation:
𝑆𝐹𝐵𝐿(𝑖, 𝑝) 3030
𝑆𝐵𝐿(𝑖, 𝑝) = = = 21.2 𝑚𝑖/ℎ
𝑁(𝑖, 𝑝) × 𝐾(𝑖, 𝑝) 2 × 70.1
The same process is repeated for the unblocked portion of the segment, except the ΔK component is
omitted as no queues occur in these lanes:
𝑆𝑈𝐵(𝑖, 𝑝) = 56.1 𝑚𝑖/ℎ
Time period 4
During time period 4, the congestion at the downstream facility (SR-826) dissipates, which allows the
ramp to discharge at the ramp roadway capacity (4,400 pc/h, or 18.33 pc/ts). Given the low ramp demand
during this time period, the queue can be cleared quickly (9 time steps, or 135s). After the 10th time step,
the freeway facility returns to undersaturated conditions.
292

APPENDIX D
On-Ramp Queue Spillback Check
Queue spillback into an arterial intersection may occur when the freeway merge segment has insufficient
capacity to process the ramp’s demand. Spillback may also occur in cases of ramp metering. This Appendix
presents the methodology for determining whether spillback will occur from an on-ramp into the upstream
intersection.
The methodology considers signalized intersections, two-way stop controlled intersections, all-way stop
controlled intersections, and roundabouts. The first step of the proposed procedure estimates the demand
approaching the on-ramp (determined based on the upstream intersection’s configuration), while the second
step estimates the capacity of the off-ramp. The existing methodology for oversaturated conditions along
freeway facilities (HCM Chapter 10) can estimate the resulting queue length, however, the user must input
the on-ramp demand flow rate.
The methodology framework for conducting this spillback check is presented in Figure D-1 and described
in more detail in the remainder of this appendix.
293

Figure D-1. Procedure for detecting spillback occurrence at an on-ramp
294

Step 1 – Demand Estimation

The first step in the methodology calculates the entering demand flow rate at the onramp (vR), as a
function of the upstream intersection configuration and operations. Under low demand conditions, the on-
ramp demand flow rate is calculated as the sum of the demands on each of the intersection approaches that
discharge into the ramp. However, if any of these movements is operating over capacity, the total
throughput to the ramp will be constrained by the capacity of these oversaturated movements. Hence, this
check ensures that the on-ramp demand is not overestimated. The analysis approach for each of four
intersection types is presented next.
Case A – Signalized intersections

The throughputs of a signalized intersection are highly dependent on several parameters such as phasing
sequences, actuation, cycle lengths, and permitted-protected phasing, among others. The methodology
developed identifies the movements that discharge to the on-ramp and their operational characteristics
(permitted or protected). Typical diamond interchanges will include a left-turn movement, a right-turn
movement and a through movement (which will typically have negligible flow).
Protected movements are analyzed on an individual cycle basis using the Queue Accumulation Polygon
(QAP) described in HCM Chapter 31 (Signalized Intersection Supplemental). A typical QAP for a protected
movement is illustrated in Figure D-2 and can be divided into three discharging patterns:
Effective red time (r). During this period, no vehicles are discharged and queue is building at a rate qr
(arrival flow rate during the effective red time).
1. Queue service time (gs). During this period, the queue previously built discharges at the saturation
flow rate (sadj). Therefore, the total number of discharged vehicles for movement i during the queue
service time is given by:
𝑁 ,, = 𝑠 𝑥𝑔 (Equation D-1)
Where:
NR,i,gs = total number of vehicles discharged for movement i during the queue service time
si = saturation flow rate (veh/h/ln), as defined in HCM Equation 19-8, of movement i
gs = green service time (s) = Qr/(s – qg)
2. Extension green time (ge). Corresponds to the remaining portion of the effective green when the
queue has been completely discharged. During that time vehicles are discharged at the same rate they
arrive at the intersection. The extension green time calculation is only applicable to undersaturated
approaches, as its duration will be zero when the effective green time is insufficient to clear the
queue.
The total number of discharged vehicles for movement i during the extension green time is given by:
𝑁 ,, = 𝑞 𝑥𝑔 (Equation D-2)
Where:
NR,i,ge = total number of vehicles discharged for movementi during the green extension time
qg = arrival flow rate during the effective green time = P q C/g (veh/s)
ge = green extension time (s) = g - gs
The total number of vehicles discharged for a protected movement i during a cycle is then given by:
295

𝑁 , = 𝑁 ,, 𝑁 ,, (Equation D-3)
Figure D-2. Discharging patterns for a typically protected movement using a queue accumulation
polygon (QAP)
The next step is to estimate the permitted movements’ flow into the ramp. Right-turning movements
often operate as permitted (RTOR), however their effect is not addressed in the HCM Chapter 31
(Signalized Intersections Supplemental). Calculations to account for permitted movement flow are
increasingly more complex, given that each phasing combination requires the development of a specific
queue polygon.
Finally, the total on-ramp demand during a single cycle can be calculated as:
𝑁 , = ∑ 𝑁 , ∑ 𝑁 , (Equation D-4)
Where:
NR,i = total number of vehicles discharged from each protected movement i
NR,k = total number of vehicles discharged from each permitted movement
The last step is to convert the total demand to the on-ramp into an hourly flow rate. For a pre-timed
signal, the aggregated on-ramp flow can be estimated by Equation D-5:
𝟑𝟔𝟎𝟎
𝒗𝑹 = 𝑵𝑹,𝒕𝒐𝒕𝒂𝒍 𝒙 (Equation D-5)
𝑪
In the case of a semi-actuated or fully actuated intersection with unknown cycle length, the procedure
described in section 2 of HCM Chapter 31 can be applied to estimate phase durations and cycle lengths.
These can then be aggregated into an hourly flow rate using the same procedure.
Case B – Two-Way Stop Controlled (TWSC) intersections.

The current HCM methods for TWSC intersection analysis are based on the calculation of the potential
capacities of each movement, based on factors such as priority order, conflicting flow, and critical gap.
296

With very few adjustments, estimating the on-ramp throughput from this intersection type is a relatively
straightforward task.
The first step is to identify the movements that discharge to the on-ramp and their respective ranks
(priority orders). The proposed methodology on freeway-arterial interactions assumes that, for TWSC
interchanges, the arterial will always be the major street. Figure D-3 illustrates a typical TWSC interchange,
where movements discharging into the on-ramp are numbered according to their ranks, using the default
numbering of the HCM methodology (Chapter 20, Exhibit 20-1).
Figure D-3. Schematic of movements turning to an on-ramp from a TWSC intersection
Similarly to signalized intersections, there are three movements turning into the ramp, and their
respective flows are discussed below:
1. Rank 1 movement (right turn from the major street). This movement is considered unimpeded,
experiencing zero delay. The only physical constraint able to limit the throughput of this movement
is its saturation flow rate if demand is very high. Therefore, the maximum throughput λRT (veh/h) for
this right-turn movement is given by:
𝜆 = min 𝑣 , 𝑠 ) (Equation D-6)
Where:
λRT = departure rate from major street right turn into the on-ramp (veh/h)
vRT = demand flow rate for the major street right turn
sRT = saturation flow rate for a right-turn movement (veh/h)
2. Rank 2 movement (left turn from the major street). The maximum throughput for this movement
is limited by its potential capacity (cp,j), as defined in HCM Equation 20-36. Therefore, the maximum
throughput λLT (veh/h) for this left-turn movement is given by:
𝜆 = min 𝑣 , 𝑐 , ) (Equation D-7)
297

Where:
λLT = departure rate from major street left turn into the on-ramp (veh/h)
vLT = demand flow rate for the major street left turn
cp,j = potential capacity for the major street left turn (veh/h)
3. Rank 3 movement (through from the minor street). Similar to rank 2 movements, the maximum
throughput for this movement is limited by its potential capacity (cm,k), as defined in HCM Equation
20-47. Therefore, the maximum throughput λTh (veh/h) for this through movement is given by:
𝜆 = min 𝑣 , 𝑐 , ) (Equation D-8)
Where:
λTh = departure rate from the minor street through into the on-ramp (veh/h)
vTh = demand flow rate for the minor street through
cm,k = potential capacity for the minor street through (veh/h)
Finally, the total on-ramp demand flow rate vR can be estimated as follows:
𝑣 =𝜆 𝜆 𝜆 (Equation D-9)
Case C – All-Way Stop Controlled (AWSC) intersections

The current AWSC methodology already addresses departure headways (hd) for each approach, making
the calculation of the on-ramp flow straightforward. Figure D-4 illustrates the movements discharging into
an on-ramp from an AWSC intersection.
Figure D-4. Schematic of movements turning to an on-ramp from an AWSC intersection
The onramp demand flow rate can be obtained directly from the departure headways of the three
movements combined:
298

𝑣 = + + (Equation D-10)
, , ,
Where:
vR = on-ramp flow rate (veh/h)
hd,RT = departure headway for the major street right turn (s)
hd,LT = departure headway for the major street left turn (s)
hd,Th = departure headway for the minor street through(s)
Case D – Roundabouts
The current HCM methodology for roundabouts is based on the calculation of the potential capacities of
each approach, based on three main variables: the critical and the follow-up headways, and the circulating
flow (Equation 22-21 through Equation 22-23). Both critical and follow-up headway values can be obtained
from HCM Chapter 33.
The procedure to evaluate the occurrence of queue spillback into roundabouts is highly integrated to the
evaluation of the impacts of queue spillback, given the interdependence of entering flows and the capacities
at the roundabout. Therefore, the methodology for this case is discussed in Appendix E - On-Ramp Queue
Spillback Analysis.
299

Step 2 – Capacity Estimation

As shown in Figure D-1, capacity at the on-ramp must be estimated in order to predict the occurrence of
queue spillback. Three cases may occur:
Case 1 – Ramp metering is active

In this case, the metering rate is a required user input (veh/h), and it is used as the ramp capacity.
Regarding merging operations, there is a modification required for the Freeway Facilities Oversaturated
methodology where the maximum output flow rate value (ONRO) is set to be equal to the ramp metering
rate.
Case 2 – No ramp metering, oversaturated merge segment

In this case the ramp capacity can be obtained from the Freeway Facilities Oversaturated methodology
(HCM Chapter 25, parameter ONRQ). If a merge segment operates above capacity, the current methodology
is able to estimate the resulting queue across the on-ramp for every 15s time step.
Case 3 – No ramp metering, undersaturated merge segment

This case does not require any adjustments to the existing methodology.
300

Example Problem – Signalized intersection with ramp metering
This example is based on the configuration used in the HCM Chapter 34 (Ramp Terminals and
Alternative Intersections Supplemental), as shown in Figure D-5.
Figure D-5. Schematic of the study interchange for the example problem
The diamond interchange has two closely-spaced signalized intersections, spaced 500 ft from each other.
The on-ramp connecting Intersection 2 to the freeway is metered at a rate of 650 veh/h and is being
evaluated for queue spillback. The signal controller is set to pre-timed operation, and the phasing sequence
and timings are presented in Figure D-6.
Figure D-6. Phasing sequences and timing for the study interchange
301

There are two movements that discharge directly to the on-ramp: WBR (Φ16 – Phase I) and EBL (Φ5 –
Phase III). The WBR movement is a protected-only movement. Additional parameters used in the analysis
are presented in Table D-1.
Table D-1 - Input parameters for the two movements discharging to the on-ramp
Phase I Phase III

(WB R) (EB L)
Green (G) 63 39
Y+R 5 5
Demand flow rate (veh/h) 520 450
Effective green (g) 64 40
Effective red (r) 96 120
Platoon Ratio (Rp) 1.00 1.33
Prop veh arriving on green (P) 0.4 0.3325
Available queue storage (veh) 24 20
Sat flow rate (veh/h) 1818.5 1703
Sat flow rate (veh/s) 0.505 0.473
Table D-2 - Additional input parameters for the example problem
Ramp metering rate (veh/h) 650

Ramp metering rate (veh/s) 0.181
Average length of vehicle (ft) 25
Ramp length (ft) 1200
Cycle length (s) 160
Number of cycles per 15-min 5.625
For the spillback check procedures, a 15-minute aggregation is recommended. Though the intersection
throughput volumes are calculated for every individual movement and on a cycle-by-cycle basis, they must
be aggregated to a 15-minute time period. Given a cycle length of 160s, the analysis can consider 900/160
= 5.6 cycles.
The calculations to estimate on-ramp throughput for the WBR movement are presented in
Table D-3. For each cycle, 24 vehicles are discharged considering the sum of queue serving time and
green extension. Therefore, for a 15-minute period it is expected that a total of 24 x 5 = 120 vehicles enter
the onramp from the WBR movement:
302

Table D-3 – On-ramp throughput for WBR movement

Movement WBR Vehicles Vehicles
WBR Total
demand Qr discharged - discharged
arrival qr qg vehicle
flow (veh/ gs (s) ge (s) queue - green
rate (veh/s) (veh/s) discharge
rate cycle) serving time extension
(veh/s) (veh)
(veh/h) (veh) (veh)
WBR 520 0.144 0.144 0.144 13.87 38.44 25.56 109 21 135
EBL 520 0.144 0.144 0.144 13.87 38.44 25.56 116 0 118
Finally, the on-ramp demand (sum of the two contributing movements) is compared to the freeway
discharge capacity (given by the ramp metering rate), and any unserved vehicles in the cycle are stored for
the start of the next cycle. As shown in Table D-4, during the fourth cycle the ramp storage ratio exceeds
one, indicating that spillback into the intersection is expected to occur at that time.
Table D-4 – Queue storage analysis for the onramp
Hourly Total Freeway

Ramp
demand to demand to discharge Ramp queue Ramp storage Spillback
Cycle # queue
ramp - vR onramp capacity (ft) ratio (RQ) expected?
(veh)
(veh/h) (veh) (veh)
1 1012.5 45 29 16 400 0.33 No
2 1012.5 45 29 32 800 0.67 No
3 1012.5 45 29 48 1200 1.00 No
4 1012.5 45 29 64 1600 1.33 Yes
5 1012.5 45 29 80 2000 1.67 Yes
303

APPENDIX E
On-Ramp Queue Spillback Analysis
This document describes the methodological modifications required to address the occurrence
of queue spillback from an on-ramp. The occurrence of queue spillback affects each type of
intersection differently. The methods outlined here address signalized intersections, two-way
stop-controlled (TWSC) intersections, all-way stop-controlled (AWSC) intersections, and
roundabouts.
Figure E-1 presents the methodology for evaluating the performance of signalized intersections,
with proposed modifications to address impacts from an on-ramp queue spillback. New steps and
modified steps to the methodology are described in the following paragraphs.
304


Figure E-1.Signalized intersections methodology with adjustments to address on-ramp
queue spillback
305

The volume of vehicles that enters a freeway on-ramp is a function of the demands and
capacities of each individual intersection movements that discharge into the ramp. A typical
signalized intersection within a diamond interchange is shown in Figure E-2, with three
movements discharging into the on-ramp (SBL, EBT and NBR).
Figure E-2. Typical signalized intersection ramp terminal in a diamond interchange
The total throughput from the intersection into the on-ramp λONR is the sum of the throughput
from each of the contributing movements:
𝜆 𝜆 𝜆 𝜆 (Equation E-1)
The throughput for each movement i is the minimum value of its demand and capacity:
𝜆 𝑚𝑖𝑛 𝑣 , 𝑐 (Equation E-2)

Where:
vi = demand flow rate for intersection movement i (veh/h)
ci = capacity for intersection movement i (veh/h), as provided by HCM Equation 19-16
Unsignalized movements, which are common for right-turn movements to the on-ramp, are
unrestricted. The capacity of these movements can be estimated as the saturation flow rate (HCM
Equation 19-8), with an adjustment factor for right turns fRT (Equation 19-13).
If all movements at the intersection are undersaturated (vi ≤ ci for every i), then Equation E-1
is simplified and the total on-ramp demand throughput λONR is:
𝜆 𝑣𝑖 (Equation E- 3)
𝑖
Step 7B. Obtain merging capacity using freeway facilities methodology

This step computes the merging capacity into the freeway cmerge. Three potential bottlenecks
can limit the on-ramp discharge into the freeway:
306

• Capacity of the on-ramp (Exhibit 14-12)

• Capacity at the merge segment, when oversaturated conditions occur at the freeway
facility
• An active ramp metering RM
The procedure to obtain cmerge is presented in Figure E-3. The freeway facility must be analyzed
using the Freeway Facilities methodology (HCM Chapter 10) to evaluate whether the merging
capacity is constrained by oversaturated conditions in the mainline. If the freeway facility is
undersaturated (LOS A-E), the merging capacity cmerge takes the minimum value between the on-
ramp capacity and the ramp metering rate, if present.
If the freeway facility is oversaturated (LOS F), the Oversaturated Segment Evaluation
procedure described in Chapter 25 can provide the maximum on-ramp output ONRO, computed
at a time-step level (15 seconds). The merging capacity cmerge can then be computed by
aggregating the parameter ONRO to an hourly flow rate:
𝑇 (Equation E- 4)
𝑐 = 𝑂𝑁𝑅𝑂 𝑖, 𝑡, 𝑝
𝑆
Where:
ONRO (i,t,p) = maximum output flow rate that can enter the merge point from on-ramp i during
time step t in time interval p
T = number of time steps in 1 h (integer). T is set as a constant of 240 in the
computational engine, or equal to four times the value of S
S = number of computational time steps in an analysis period (integer). S is set as a
constant of 60 in the computational engine, corresponding to a 15-s interval and
allowing a minimum segment length of 300 ft.
t = time step index
307

Figure E-3. Step 7B – Estimation of merging capacity in a freeway ramp
Step 7C. Plot queue accumulation polygon for the on-ramp

In this step, a Queue Accumulation Polygon (QAP) must be built for the on-ramp, considering
the throughput from all contributing movements within the cycle. Figure E-4 illustrates a sample
intersection which will be used to describe this step.
The application of this methodology requires that the first analyzed time period is
undersaturated. Based on this requirement, the QAP starts with zero vehicles inside the on-ramp.
The on-ramp QAP for this example is provided in Figure E-5. The cycle starts with the SBL green
discharging into the on-ramp at a throughput rate λSBL, while the on-ramp discharges to the
freeway merge at a rate cmerge. Therefore, the number of vehicles within the on-ramp grows at a
rate equal to (λSBL - cmerge). When the number of vehicles along the on-ramp reaches the maximum
ramp storage length LONR, vehicles from the intersection can only be discharged to the on-ramp
at the same the rate they are discharged from the on-ramp into the freeway. The number of
vehicles within the on-ramp is then maintained and it is equal to LONR until the end of the green
308

for the SBL movement. At the end of the SBL green, the vertical difference between the projected
number of vehicles (dashed line) and the actual number of vehicles inside the on-ramp represent
the number of unserved vehicles for the SBL approach. This additional queue can be considered
in a multiperiod analysis for the signalized intersection or interchange, using the methods
provided in Chapter 23 – Ramp Terminals and Alternative Intersections.
Figure E-4. Sample intersection for calculation of a QAP for the on-ramp
The slope of the red line connecting the number of vehicles in the end and start of the green
represent the reduced capacity of the SBL movement due to queue spillback. For the remainder
of the cycle, the NBR movement discharges at a constant rate into the on-ramp, as this is an
unsignalized movement. Given that the discharge capacity cmerge is greater than the on-ramp
demand λNBR, the vehicles along the on-ramp are discharged to the freeway until the on-ramp is
cleared. Therefore, the NBR movement does not have its capacity affected by queue spillback.
This procedure can be applied for both pretimed and actuated control types, since the core
methodology can address both controller types. If the signal is actuated, the average phase
duration lengths are applied, as obtained in Step 6.
Step 7D. Calculate adjusted capacities for the affected movements

Based on the on-ramp QAP developed in the previous step, the adjusted capacity cSP must be
calculated for every movement affected by the queue spillback. For the example of Figure E-5,
the adjusted capacity for the SBL movement cSBL,SP can be obtained from the QAP as the slope
of the red line (cSBL,SP - cmerge) as follows:
𝑁 𝑔 −𝑁 0
𝑐 , −𝑐 − (Equation E-5)
𝑔
309

Where:
N(g1) = number of queued vehicles along the on-ramp at t = g1 (end of green for phase 1);
N(0) = number of queued vehicles along the on-ramp at t = 0 (start of the cycle);
g1 = effective green time for phase 1
Figure E-5. On-ramp queue accumulation polygon during queue spillback
The adjusted capacity of the SBL movement cSBL,SP is then computed as:
𝑁 𝑔 −𝑁 0
𝑐 , =𝑐 (Equation E-6)
𝑔
If the queue develops and fully discharges during every cycle, then subsequent cycles will have
the same discharge. However, if there are residual queues at the on-ramp by the end of the cycle,
the QAP must then be plotted again for the following cycle with an initial queue equal to the
number of queued vehicles in the end of the present cycle. This process must be then repeated for
a number of cycles N= 900/C, sufficient to analyze the entire 15-minute period. The adjusted
capacity for each movement is estimated as the average of the discharge rates during each cycle.
Step 8. Determine delay

The calculations for obtaining delay at the intersection approaches do not need to be modified.
The only change required is replacing the input value of the demand-to-capacity ratio X (Equation
19-17) for the adjusted value Xsp, estimated using the adjusted capacity due to spillback:
𝑣
𝑋 = (Equation E-7)
𝑐
Two-Way Stop-Controlled (TWSC) Intersections

The operation of TWSC intersections is based on determining the priorities of movements
arriving at the intersection. Minor street movements have lower priority and must stop before
entering the intersection. Left-turning drivers from the major street must yield to oncoming major-
310

street through or right turning traffic, but they are not required to stop in the absence of oncoming
traffic.
The methodologies for evaluating the operations of TWSC intersections are based on gap
acceptance theory. Drivers from lower priority movements must select a suitable gap in order to
proceed through the intersection. According to previous research (Aakre & Aakre, 2017), during
oversaturated conditions and when queue spillback occurs drivers show cooperative behavior,
with higher priority vehicles often yielding to those with lower priority. The microsimulation
package AIMSUN, which was used to simulate the study sites for this project, includes the feature
Turn Cooperation Model to simulate this behavior, as illustrated in Figure E-6. In such cases, the
gap acceptance model is no longer valid and a new approach must be used to evaluate the
intersection performance.
Figure E-6. Illustration of cooperative behavior in unsignalized intersections with queue

spillback
When queue spillback occurs at a TWSC intersection the maximum throughput to the on-ramp
(exit capacity) is constrained by the discharge capacity of the freeway merge. It is assumed that
during oversaturated conditions the intersection movements that discharge to the on-ramp share
the exit capacity proportionately to their demands.
Figure E-7 presents the methodology for evaluating the performance of TWSC intersections,
with proposed modifications to address impacts from an on-ramp queue spillback. New steps and
modified steps to the methodology are described in the following paragraphs.
311

Source: Adapted from HCM 6th Ed. Exhibit 20-6

Figure E-7. TWSC intersections core methodology with adjustments to address on-ramp
queue spillback

The throughput to the on-ramp is calculated using the approach described in Step 7A of the
queue spillback analysis for signalized intersections (Figure E-1). The total throughput from the
312

intersection into the on-ramp λONR is the sum of the throughput from each of the contributing
movements. For each movement i discharging into the on-ramp, the throughput is the minimum
value of its demand and its movement capacity:
𝜆 = 𝑚𝑖𝑛 𝑣 , 𝑐 , (Equation E-8)
Where:
vi = demand flow rate for movement i
This step computes the merging capacity into the freeway cmerge. The procedure described in
Step 7B of the queue spillback analysis for signalized intersections (Figure E-1) is applied.

While signalized intersections operate in a cyclical pattern, stop-controlled intersections have
relatively uniform patterns of demand and capacity within a time period. Therefore, the 15-minute
aggregated demand and capacity values are assumed to be constant, and the growth and discharge
of queues are assumed to be linear.
The queue accumulation polygon is used to illustrate the development of queues along the on-
ramp (Figure E-8). For a given time period of T minutes (typically T=15), the intersection yields
throughput λONR to the ramp (Step 5B), while the merge has capacity cmerge. If λONR > cmerge, then
queues will develop along the on-ramp until the number of vehicles reach the maximum ramp
storage LONR, when queue spillback begins. When that occurs, the maximum rate of vehicles that
can enter the on-ramp is limited by the merging capacity cmerge for the rest of the time period.
Figure E-8. On-ramp queue accumulation polygon – TWSC intersection
From this relationship shown in Figure E-8 the spillback time TSB is defined as the amount of
time within a time period when spillback is active:
𝐿 −𝑁 0
𝑇 =𝑇− (Equation E-9)
𝜆 −𝑐
Where:
313


LONR = available queue storage at on-ramp (veh)
N(0) = number of queued vehicles along the on-ramp at t = 0 (start of the cycle);
λ from the intersection into the on-ramp (veh/hr)
Estimating the spillback time TSB is critical to the methodology, as the aggregated calculations
of capacity for each movement depend on the amount of time that the intersection operates under
queue spillback.

In this step, the capacity of the movements affected by spillback are obtained and then
aggregated to a time period level. When on-ramp queue spillback occurs at an intersection,
movements discharging towards the on-ramp switch to a cooperative approach instead of the
priority-based regular operation.
When there is queue spillback, the maximum throughput to the on-ramp is equal to the merging
capacity cmerge. This capacity is then used by all movements traveling into the on-ramp. The
capacity of each affected movement i during spillback ci,SB is obtained proportionally to its
demand flow rate:
𝑐 ×𝑣 (Equation E-10)
𝑐 , =
∑ 𝑣
Where:
cSB,i = capacity during spillback for movement i (veh/h)
vi = demand flow rate for movement i (veh/h)
NSB = number of movements at the intersection discharging into the on-ramp
Finally, the adjusted capacity of each affected movement ci,EQ is obtained as a function of the
amount of time within the time period when spillback was present. The adjusted capacity
considers the proportion of time there is blockage during queue spillback and consists of the
aggregation, at a time period level, of movement capacities cm,i (which is observed during
undersaturated conditions) and spillback capacities cSB,i,(which is observed during oversaturated
conditions):
𝑐 , ×𝑇 + 𝑐𝑚,𝑖 × (𝑇 − 𝑇 ) (Equation E-11)

𝑐 , =
𝑇
Where:
cEQ,i = adjusted capacity for movement i (veh/h)
vi = demand flow rate for movement i (veh/h)
When queue spillback lasts for the entire time period T (for example, in a multi-period
analysis), the spillback time TSB is equal to T, and the capacity of each movement i is obtained as
the capacity during spillback and (Equation E- 3) becomes:
𝑐 , =𝑐 , (Equation E-12)
Step 11. Compute movement control delay
314

The average control delay is obtained using Equation 20-64 replacing the movement capacity
cm,i by the adjusted capacity cEQ,i:
3600 𝜆 (Equation
⎡ × ⎤
3600 𝑐 , 𝑐 E-13)
⎢ 𝑣 𝑣 , ⎥
𝑑 = + 900𝑇 ⎢ −1+ −1 + ⎥+5
𝑐 , 𝑐 , 𝑐 , 450𝑇
⎢ ⎥
⎣ ⎦
315

All-Way Stop-Controlled (AWSC) Intersections
The methodology to evaluate queue spillback into AWSC intersections follows the approach
developed for TWSC intersections. As shown in Figure E-9, after the capacities of individual
movements during undersaturated conditions are computed (Step 12), the process described for
TWSC intersections is performed by new steps 13A through D.
Source: Adapted from HCM 6th Ed. Exhibit 21-10

Figure E-9. AWSC intersections methodology with adjustments to address on-ramp queue
spillback
The only step in the methodology that differs from the TWSC (13D) is described below.
Step 13D – Compute spillback departure headway
The AWSC methodology calculates the delay for each approach based on its departure
headway instead of capacity. The estimated spillback capacity (cSB,i) is converted to a spillback
headway hSB through the following equation:
316

3600 (Equation E-14)

ℎ =
𝑐 ,
Roundabout ramp terminals

The methodology presented in Chapter 22 – Roundabouts is shown in Figure E-10. The
additional steps proposed to the methodology are marked in blue. Each of the steps added and
modified is discussed in the following paragraphs. This methodology is applicable only to single-
lane roundabouts. Exhibit 22-9 and Table E-1 provide the required input data and potential data
sources for roundabout motorized vehicle analysis.
317


Figure E-10. Roundabouts methodology with adjustments to address on-ramp queue
spillback
318

Table E-1. Required data and potential data sources – roundabout spillback evaluation
Required Data and Units Potential Data Source Suggested Default

Onramp Data
On-ramp metering rate (veh/h) Design plans, Field data Must be provided
On-ramp storage length LONR(ft) Field data Must be provided
Roundabout Data
Departure saturation headway
Field data 3s/veh
into the on-ramp hs (s/veh)
Step 13 – Compute the maximum throughput into the on-ramp for every movement
The maximum throughput into the on-ramp per movement is calculated using the roundabout
priority order in a counterclockwise order starting from the most upstream approach from the on-
ramp exit leg. The Rank 1 approach (Figure E-11) is the one whose flow has the highest priority,
given it enters the circulating stream upstream of all other approaches). The next priority
movement is the Rank 2 approach, and the last is the Rank 3 approach.
Figure E-11. Priority order for a roundabout upstream of an on-ramp
Next, the methodology calculates the capacity of the roundabout’s exit lane into the on-ramp.
Previous research (Robinson et al, 2006; Rodegerts & Blackwelder, 2005) suggests that the
capacity of an exit lane, accounting for pedestrian and bicycle traffic in a typical urban area, is in
the range of 1,200 to 1,300 vehicles per hour. Starting from the approach with Rank 1, and
proceeding counterclockwise with the rest of the approaches, the capacity for each approach is
used to determine the maximum throughput for every movement discharging to the on-ramp.
Rank 1 – SB approach. The Rank 1 approach has priority over the other movements
connecting to the on-ramp because it enters the circulating stream first. Also, because the on-ramp
does not have an approach into the roundabout, the Rank 1 movement is most often unopposed
by the circulating stream (except for occasional U-turns along the arterial). Therefore, the
maximum throughput λSB-ONR (veh/h) for this left-turn movement is limited by its own lane
capacity (cSB) and the maximum throughput to the on-ramp, and it is given by:
3,600 (Equation E-15)
𝜆 = min 𝑣 ,𝑐 × 𝑝 ,
ℎ
Where:
λSB- rate from the SB approach into the on-ramp (veh/h)
vSB- flow rate for the SB approach into the on-ramp (veh/h)
319

cSB = lane capacity for SB approach (veh/h) (HCM Equation 22-21)

pSB- of demand from SB approach into the on-ramp
hs = departure saturation headway into the on-ramp (s/veh)
Rank 2 – EB approach. The maximum throughput for this Rank 2 movement is limited by its
own lane capacity (cEB), as defined in HCM Equations 22-21 through 22-23, and the maximum
throughput after considering the departure rate of the upstream Leg 1. Therefore, the maximum
throughput λEB-ONR (veh/h) for this movement is given by:

𝜆 = min 𝑣 ,𝑐 ×𝑝 , −𝜆
ℎ
Where:
λEB- rate from the EB approach into the on-ramp (veh/h)
vEB- flow rate for the EB approach into the on-ramp (veh/h)
cEB = lane capacity for EB approach (veh/h) (HCM Equation 22-21)
pEB- of demand from EB approach into the on-ramp
Rank 3 – NB approach. Similar to rank 2 movements, the maximum throughput for the NBR
(i.e., NB-ONR) movement is limited by its own lane capacity (cNB), as defined in HCM Equation
22-21 through Equation 22-23, and the maximum throughput to the on-ramp after considering
departure rates from the upstream approaches. Therefore, the maximum throughput (λNB-ONR) for
this right-turn movement is given by:

𝜆 = min 𝑣 ,𝑐 ×𝑝 , −𝜆 −𝜆
ℎ
Where:
λNB- rate from the NB approach into the on-ramp (veh/h)
vNB- flow rate for the NB approach into the on-ramp (veh/h)
cNB = lane capacity for NB approach (veh/h) (HCM Equation 22-21)
pNB- of demand from NB approach into the on-ramp
The total on-ramp demand flow rate can be similarly calculated if there are additional
approaches to the roundabout.
Step 14 – Calculate the throughput into the on-ramp

The maximum throughput from the roundabout to the on-ramp, 𝜆 is calculated as:
𝜆 =𝜆 + 𝜆 + 𝜆 (Equation E-18)
Step 15 – Compute on-ramp merging capacity and compare to the maximum throughput to
the on-ramp
The calculation of the on-ramp merging capacity follows the exact same procedure used in Step
7B of the methodology developed for queue spillback into Signalized Intersections (Figure E-1).
The maximum number of vehicles that can merge into the on-ramp cmerge (estimated using
Equation 25-18) is compared to the maximum throughput from the roundabout to the on-ramp,
𝜆 . If cmerge ≤ λONR, then spillback is not expected to occur, and no adjustments are necessary in
the procedure. If cmerge > λONR, queues will develop along the on-ramp, and spillback may occur if
320

the queue storage is insufficient. The analyst must then proceed to Step 17 to evaluate the on-
ramp Queue Storage Ratio to evaluate whether spillback will occur.
Step 17 – Determine the on-ramp storage ratio and queue spillback length
With the exit flow rate into the on-ramp (λ ), the expected queue length QSP along the on-
ramp during a 15-minute period analysis is:
𝜆 −𝑐 (Equation E-19)
𝑄 =
4
If a multi-period analysis is performed, the queue length for the current time period p must be
added to the queue length obtained from the previous time period:
𝜆 , −𝑐 , (Equation E-20)
𝑄 , =𝑄 , +
4
The on-ramp storage ratio is calculated by dividing the available on-ramp storage LR (ft) by the
average vehicle spacing , Lh (Equation 31-155):
𝐿 ×𝑄 (Equation E-21)
𝑅 =
𝐿
If the on-ramp storage ratio (R ) is greater than 1, queues will form along each approach due
to spillback. The value of RQ corresponds to the specific analysis period. If congestion is
expected, but RQ < 1 for a single analysis period, multi-period analysis may have to be conducted.
Step 18 – Compute the queue spillback distribution per approach

When spillback occurs, the total number of vehicles queued during a 15-minute time period
analysis (Q ) is calculated as:
𝑄 =𝑄 −𝐿 ×𝑄 (Equation E-22)
These queues are assumed to be distributed proportional to the demand flow rates to the on-
ramp per approach and added to the 95th percentile queues estimated for the undersaturated
conditions (Equation 22-20):
𝜆 (Equation E-23)
𝑄 , =𝑄 × +𝑄 ,
𝜆
𝑄 , =𝑄 × +𝑄 ,
𝜆
𝑄 , =𝑄 × +𝑄 ,
𝜆
Where:
Qsp,SB , Qsp,EB , Qsp,NB = queue due to the on-ramp spillback on SB, EB and NB approaches,
respectively (veh)
λSB-ONR, λEB-ONR, λNB- throughput for SB, EB, and NB approaches into the on-
ramp, respectively
Q95,SB , Q95,EB , Q95,NB = 95th percentile queue on SB, EB, and NB approaches, respectively
(veh))
321

Step 19. Calculate the average control delay per approach

To estimate the average delay per approach, the delay due to the on-ramp capacity limitation is
estimated and added to the approach control delay calculated in Step 9 (HCM Chapter 22). As
indicated in HCM – Chapter 22, it is recommended to estimate the approach average control delay
through Equation 22-17.
Equation 22-17 assumes no residual queue at the start of the analysis period. If queue spillback
occurs, the average control delay is significantly affected by the analysis period length. However,
the HCM Chapter 22 – Roundabouts does not provide a multiperiod analysis method. Therefore,
the delay results may not be accurate when there is a queue at the start of the analysis period.
However, an iterative process that carries over queues from one time period to the next may be
considered (Kimber and Hollis, 1979). The additional delay (in sec/veh) due to the on-ramp
spillback is calculated as follows:
⎡ 3600 𝜆 ⎤
×
3600 ⎢𝜆 𝜆 𝑐 𝑐 ⎥
𝑑 = + 900𝑇 ⎢ −1+ −1 + ⎥
𝑐 𝑐 𝑐 450𝑇
⎢ ⎥ (Equation
⎣ ⎦ E-26)
𝜆
+ 5 × 𝑚𝑖𝑛 ,1
𝑐
Where
λ flow rate into the on-ramp (veh/h)
t = time period (h) (T = 0.25 h for a 15-min analysis)
322

Case Study: Evaluating Queue Spillback from Freeway On-Ramp

This case study illustrates the application of the on-ramp spillback methodology by evaluating
operations at an interchange when there is queue spillback originating from the on-ramp. There
are three parts to the case study with each one analyzing a different intersection type at the ramp
terminal: signalized, TWSC and AWSC. The main objective in each analyzed scenario is to
determine the new control delay for the movements affected by queue spillback. All other
parameters in the network (freeway design and traffic demand, and intersection demand) are kept
the same.
An urban network in Baton Rouge, LA is comprised of the following facilities:

• One freeway facility
• One arterial facility (Acadian Thruway), with four intersections:
• Perkins Rd.
• Acadian Center Rd.
• I-10 WB
• I-10 EB
The subject freeway has three lanes and it connects to the arterial corridor (Acadian Thruway)
through an interchange as illustrated in Figure E-1.
Figure E-12. Illustration of study site
The freeway facility (I-10 EB) is modeled according to the Freeway Facilities methodology
(Chapter 10), while the ramp terminal is modeled according to its respective intersection
methodology. First a check is performed to confirm the occurrence of queue spillback. Next, the
respective spillback analysis is applied to evaluate the impacts of queue spillback in the capacity
of each movement at the intersection. With the estimated reduced capacities at the intersection,
the control delay values considering queue spillback are computed and compared to the delay
values without consideration of queue spillback.
323

Part 1 – Signalized Intersection
Input data
The geometry of the intersection connected to the I-10 EB on-ramp (I-10 EB) is shown in
Figure E-13. There are three movements leading into the on-ramp:
• NBR: One channelized, unsignalized right-turn lane;
• SBL: One exclusive left turn lane with a protected phase; and
• EBT: One through lane.
Figure E-13. Signalized intersection geometry – Acadian Thruway @ I-10 EB
The phasing sequence of the subject intersection is presented in Figure E-14. The north-south
direction corresponds to the major street, while the minor streets correspond to the freeway off-
ramp and on-ramp. The intersection has a leading left turn phase with a protected left turn
movement (SBL).
Figure E-14. Phasing sequence – I-10 EB intersection
The demand volumes for each time period are presented in Table E-2. Additional input data are
summarized in Table E-3.
324

Table E-2. Demand flow rates (veh/h) – I-10 EB intersection

L T R T R L T
Time Period 1 8 48 87 362 315 652 804
Time Period 2 16 96 20 1812 521 586 1759
Time Period 3 16 96 20 271 630 1071 717
Time Period 4 8 24 28 845 80 463 201
Table E-3. Input data – I-10 EB intersection

L T R T R L T
General Information
Base Sat. Flow Rate (s0), veh/h 1900 1900 1900 1900 1900 1900 1900
Arrival Type (AT) 3 3 3 3 3 3 3
Lane Width (W), ft 11 11 11 11 11 11 11
Heavy Vehicles % 5 5 5 5 5 5 5
Grade (Pg), % 0 0 0
Speed Limit, mi/h 35 35 35 35 35 35 35
Phase Information
Maximum Green (Gmax), s 20 20 - 53 - 47 100
Yellow Change Interval (Y), s 4.7 4.7 - 4.7 - 4.7 4.7
Red Clearance Interval (Rc), s 1.0 1.0 - 1.0 - 1.0 1.0
Minimum Green (Gmin), s 5.0 5.0 - 15.0 - 5.0 15.0
Start-Up Lost Time (lt), s 2.0 2.0 - 2.0 - 2.0 2.0
Green Extension (e), s 2.0 2.0 - 2.0 - 2.0 2.0
Passage (PT), s 2.0 2.0 - 2.0 - 2.0 2.0
Recall Mode Off Off - Off - Off Off
Dual Entry No No - Yes - No Yes
Freeway Facility (I-10 EB)

The freeway facility (I-10 EB) is divided in seven segments (Figure E-15), where segment 3
(diverge) and segment 5 (merge) connect to the subject signalized intersection (Acadian
Thruway).
325

Figure E-15. Freeway facility segmentation– I-10 EB
The geometric features of the freeway facility are summarized in Table E-4.
Table E-4. Freeway facility (I-10 EB) - geometric features

Acceleration /
Segment Length Grade
Type deceleration lane length Ramp length (ft)
ID (ft) (%)
(ft)
1 Basic 5280 0 - -
2 Diverge 1500 0 800 1139
3 Diverge 720 0 0 965
4 Basic 732 0 - -
5 Merge 1000 0 1000 924
6 Basic 1200 0 - -
7 Basic 900 0 - -

The first step in the spillback check analysis is to determine the on-ramp demand flow rates for
each time period, based on the demands at the signalized intersection. For each time period, the
demand (v) and capacities (c) are compared for each movement that flows into the on-ramp (EBT,
NBR and SBL). The minimum value between demand and capacity for each movement is
computed and the merge demand vR is then computed as the sum of the three movements.
The capacities for protected movements (EBT and SBL) are computed for each time period.
Due to the actuated control operation, the average green times for these movements vary by time
period as they are computed as function of the demands on each intersection approach. The NBR
movement is unsignalized and therefore no capacity estimation is provided by HCM methods.
The capacity for this movement is computed by calculating the maximum throughput through one
cycle and then aggregating to an hourly flow rate. If there were no conflicting movements
discharging into the on-ramp, the NBR capacity would be computed as its respective saturation
flow rate, considering the applicable adjustment factors fRT (for right-turn movements) and fHV
(for the presence of heavy vehicles). During the transition time between consecutive phases, the
326

throughput of the unsignalized turning movement is also assumed to be equal to its saturation
flow rate. Therefore:
𝑠 , =𝑠 , ×𝑓 ×𝑓
where
sNBR,FF = saturation flow rate of NBR movement at free-flow conditions (veh/h/ln)
s0,NBR = base saturation flow rate (1,900 pc/h/ln)
fRT = adjustment factor for right-turn vehicle presence in a lane group
fHVg = adjustment factor for heavy vehicles and grade
The adjustment factor for right-turn vehicle presence is computed using Equation 19-13:
1 1
𝑓 = =
𝐸 1.18
where
ET = equivalent number of through cars for a protected right-turning vehicle (1.18)
The adjustment factor for heavy vehicles and grade is computed using Equation 19-10:
100 − 0.78𝑃 − 0.31𝑃 100 − 0.78 × 5 − 0.31 × 0

𝑓 = = = 0.961
100 100
where
PHV = percentage heavy vehicles in the corresponding movement group (5%)
Pg = approach grade for the corresponding movement group (0%)
Therefore, the saturation flow rate

1
𝑠 , = 1,900 × × 0.961 = 1,547 𝑣𝑒ℎ/ℎ
1.18
1.18
0.961
Since there are conflicting movements discharging into the on-ramp (for example, a protected
left-turn), the NBR capacity is constrained as drivers yield to the higher priority movement. The
estimated discharge flow rate for the NBR movement with a conflicting protected flow vprot can
be obtained by the following equation, based on HCM equation 31-100:
/ ,
𝑣 𝑒
𝑠 = / ,
1−𝑒
Where:
sp = saturation flow rate of a permitted movement (veh/h/ln)
v0 = opposing demand flow rate (veh/h)
The computation of the permitted saturation flow rates must take into consideration that the
conflicting phase may have two distinct flow rates on signalized intersection operation, as
discussed in HCM Chapter 31 (Signalized Intersections Supplemental):
327

• During the queue service time (gs) portion of the conflicting phase green, the opposing
movement flow rate is equal to its saturation flow rate;
• During the green extension time (ge), the opposing movement flow rate is equal to its
arrival flow rate during the effective green (qg);
Table E-5 illustrates the calculation of the NBR potential capacity for a single cycle during
time period 1. For each active phase, the procedure identifies the respective conflicting flow to
the on-ramp along with its duration and flow rate. The NBR saturation flow rate is then computed
using HCM Equation 31-100. The last column computes the maximum number of vehicles that
can be discharged during each phase as the product of the NBR saturation flow rate and the phase
duration. Transition times between consecutive phases are also taken into consideration assuming
that they have no conflicting flow rate to the on-ramp.
Table E-5. Calculation of NBR potential capacity for a single cycle – Time Period 2
Conflicting NBR saturation NBR

Conflicting Duration
Active phase flow rate flow rate sNBR discharge
flow (s)
(veh/h) (veh/h) volume (veh)
φ1 (SBL) - gs,SBL sSBL 40.2 1739 282 3.1
φ1 (SBL) -ge,SBL qg,SBL 3.7 128 1282 1.3
Transition time 1 - 5.7 - 1547 2.5
φ2 (NBT) - 50.7 - 1547 21.8
φ7 (EBT) - gs,EBT sEBT 6.3 1811 263 0.5
φ7 (EBT) - ge,EBT qg,EBT 2.0 97.2 1319 0.8
Total 120.0 34.8
gs: queue service time; ge: green extension time; qg: arrival flow rate during effective green;s: saturation flow rate
As shown, for a 120s cycle the capacity of the unsignalized NBR movement is 34.8 vehicles.
Aggregated to an hourly flow rate:
3600
𝑐 = 34.8 × = 1045 𝑣𝑒ℎ/ℎ
120
Because of the actuated control operation, the discharging rates to the on-ramp are different
during each time period since they depend on effective green times and flow profiles. Therefore,
this procedure must be repeated for every time period to compute the capacity of the NBR
unsignalized movement cNBR (Table E-6).
Table E-6. NBR capacity, computed for each time period

Time Period NBR capacity (veh/h)
1 1213
2 1045
3 978
4 1182
328

Table E-7 summarizes the calculations for this step. During time period 3, the SBL movement
operates at demand over capacity (v/c = 1.56), therefore its throughput to the ramp is constrained
by its capacity value (685 veh/h). For all other movements and time periods the throughput to the
on-ramp is equal to its demand because v/c < 1.
Table E-7. Calculation of the on-ramp demand (vR) based on the intersection operation.
Time Movements
Parameter
Period EBT NBR SBL
v/c 0.064 - 0.96
1 c (veh/h) 125 1213 677
min (v, c) 8 315 652
v/c 0.768 - 0.93
2 c (veh/h) 125 1045 630
min (v, c) 96 521 586
Demand (veh/h) 96 630 1071
v/c 0.77 - 1.56
3 c (veh/h) 125 978 685
min (v, c) 96 630 685
v/c 0.39 - 0.62
4 c (veh/h) 62 1182 746
min (v, c) 24 80 463
The calculated on-ramp demand is then provided as input into the freeway facility analysis
(Table E-8). As shown, the ramp flow rates for the merge segment (segment 5) are obtained from
Table E-7, and highlighted in bold.
Table E-8. Freeway facility (I-10 EB) – demand inputs

Time Period 1 Time Period 2 Time Period 3 Time Period 4
Segment Mainline Ramp Mainline Ramp Mainline Ramp Mainline Ramp
flow rate flow flow rate flow flow rate flow flow rate flow
ID
(veh/h) rate (veh/h) rate (veh/h) rate (veh/h) rate
(veh/h) (veh/h) (veh/h) (veh/h)
1 5209 - 6300 - 5300 - 5000 -
2 5209 348 6300 450 5300 1200 5000 50
3 4861 135 5850 116 4100 1000 4950 96
4 4726 - 5734 - 3100 - 4854 -
5 4726 975 5734 1203 3100 1411 4854 567
6 5701 - 6937 - 4511 - 5421 -
7 5701 - 6937 - 4511 - 5421 -
The results of the freeway facility analysis are provided in Table E-9. Oversaturated conditions
occur during time periods 2 and 3, therefore queueing may occur along the on-ramp.
329

Table E-9. Performance measures for the freeway facility (I-10 EB)
Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7

(Basic) (Diverge) (Diverge) (Basic) (Merge) (Basic) (Basic)
TP 1 D C D C D D D
TP 2 E F F F F F E
TP 3 D D F F F E E
TP 4 D C C B C C C
The next step will estimate the on-ramp queue length compared to the available queue storage
length to determine whether spillback is expected to occur. Table E-10 shows the expected on-
ramp queues from the freeway facility analysis. For each time period, the ramp storage ratio (RQ)
is computed by dividing the ramp queue by the available storage length (924 ft). During time
period 2, a queue is expected on the ramp, but it is not long enough to cause queue spillback (RQ
< 1). During time period 3, however, the on-ramp is expected to have RQ = 2.31, which indicates
that spillback will occur at the intersection during this time period.
Table E-10. Spillback check – I-10 EB on-ramp
Time vR Ramp queue Ramp Ramp storage Spillback

period (veh/h) (veh) queue (ft) ratio (RQ) expected?
1 975 0.0 0.0 0.00 No
2 1,203 15.0 388.6 0.42 No
3 1,411 82.1 2,133.6 2.31 Yes
4 567 0.0 0.0 0.00 No
Since spillback will occur for at least one time period, the impacts on the operation of the
signalized intersection must be evaluated. The next section illustrates the application of the
methodology to evaluate spillback effects at a signalized intersection.

The evaluation of queue spillback impacts on the signalized intersection follows the procedure
detailed in the methodology (Figure E-1). Since this is a multiperiod analysis, the procedure must
be applied for every time period. In this example, time periods 2, 3 and 4 will be evaluated. Time
period 1 is not analyzed here since it does not have oversaturated conditions.
Time Period 2
The procedure to evaluate queue spillback into intersections is applied for time period 2, even
though spillback is not expected to occur during this time period. The application of the
methodology is presented for this time period to facilitate the understanding of the calculations.

The throughput of movements into the on-ramp have been previously determined as part of the
queue spillback check, as shown in Table E-7.

When the freeway facility operates in oversaturated conditions, the capacity of the subject
merge section may be constrained by the presence of queues along the mainline. The
330

Oversaturated Segment Evaluation procedure (HCM Chapter 25) computes the on-ramp queue
(ONRQ) and on-ramp capacity (ONRO) every 15 seconds. The merge capacity cmerge is then
obtained by aggregating the ONRO parameter into an hourly flow rate for each time period.
Figure E-16 shows the values of ONRQ and ONRO over the analysis period (60 minutes),
converted to hourly flow rates.
Figure E-16a compares the on-ramp capacity ONRO to the on-ramp demand. During the first
time period there are no oversaturated conditions along the freeway, thus the on-ramp capacity
ONRO equals 2,000 pc/h (corresponding to the ramp roadway capacity as provided by HCM
Exhibit 14-12), or 1,903 veh/h. During time periods 2 and 3, oversaturated conditions occur and
the on-ramp capacity drops to 5 pc per time step, corresponding to 1,142 veh/h. During the last
time period, the lower demand along the freeway allows the mainline queue to clear within 4 time
steps (60 seconds). Therefore, during the first 60 seconds the on-ramp capacity remains at 1,142
veh/h. From the fifth time step to the end of the time period, there is no congestion at the merge
and thus the on-ramp capacity is again 1,903 veh/h.
Figure E-16b provides the on-ramp queue as estimated by the Oversaturated Segment
Evaluation procedure. Since spillback is expected to occur, an adjustment to the Freeway
Facility Oversaturated Segment evaluation procedure is necessary to account for the
maximum ramp storage (35.5 vehicles). This value is the upper boundary of the on-ramp
queue length. At the end of time period 3, the predicted on-ramp queue length would be 82
vehicles if there were no storage constraints (black curve). The red curve represents the
adjusted queue profile for the on-ramp considering the maximum storage capacity. At the
start of time period 4, having an on-ramp queue of 35.5 vehicles instead of 82 results in a
shorter queue clearance time, with a slight positive impact on the freeway performance. In
other words, the intersection has a metering effect, which may improve operations along
the freeway.
Table E-11 compares the performance results of the freeway segments downstream of the
merge (see Figure E-15) with and without consideration of the maximum storage constraint.
331

Figure E-16. Freeway facility, segment 5 (merge) performance: (a) merge capacities and
(b) queue lengths
Table E-11. Freeway performance during time period 4 – with and without the queue
storage constraint
Seg 5 (Merge) Seg 6 (Basic) Seg 7 (Basic)

Without With Without With Without With
storage storage storage storage storage storage
constraint constraint constraint constraint constraint constraint
Speed (mi/h) 67.2 67.4 67.7 67.8 72.2 72.5
Density (pc/mi/ln) 20.9 19.9 20.8 19.7 19.5 18.4
332

Step 7C – Plot queue accumulation polygon for the on-ramp and unsignalized movements
In this step, a queue accumulation polygon is plotted for the on-ramp as a function of all
protected and permitted movements entering the on-ramp, on a cycle-by-cycle basis. Since an
unsignalized movement (NBR) also discharges into the on-ramp, a queue accumulation polygon
must be developed for this movement as well. This is required to: (a) determine the discharge
pattern of the unsignalized movement throughout the cycle and (b) allow the estimation of control
delay for this movement.
Figure E-17 presents the queue accumulation profiles for (a) the on-ramp and (b) for the NBR
movement.
Figure E-17. Estimated queue lengths and merge capacities – time period 2
The cycle starts with a permitted left-turn movement (Φ1: SBL) discharging into the on-ramp
with a green time g1 = 43.9s, divided in a queue service time gs1 = 40.2s and a queue extension
time ge1 = 3.7s (as defined in HCM Chapter 31 – Signalized Intersections Supplemental). During
the green interval for SBL, the capacity of the NBR movement is constrained since drivers must
yield to the protected left-turn vehicles. The estimated saturation flow rate for the NBR movement
with a conflicting flow vSBL can be obtained by the following equation, based on HCM equation
31-100:
333

/ ,
𝜆 𝑒
𝑠 , = / ,
1−𝑒
Where:
sNBR,perm = saturation flow rate of the NBR movement (veh/h/ln)
λSBL = throughput of the opposing SBL movement(veh/h)
The saturation flow rates of the NBR movement during Φ1 are determined next. During the
SBL queue service time:
𝜆 = 𝑠 = 1,739 veh/h/ln → 𝑠 , = 282 veh/h/ln
Where:
sSBL = saturation flow rate of the SBL movement (veh/h/ln)
sNBR,perm1 = saturation flow rate of the NBR movement during the SBL queue service time
(veh/h/ln)
The throughput for the NBR movement is obtained as the minimum of the demand and
saturation flow rate. Since the demand flow rate is greater than the saturation flow rate, a queue
will develop for the NBR movement:
𝜆 , = 𝑚𝑖𝑛 𝑠 , ,𝑣 = 𝑚𝑖𝑛(282, 521) = 282 𝑣𝑒ℎ/ℎ
Where:
λNBR,1 = throughput for the NBR movement during the SBL queue service time (veh/h/ln)
vNBR = demand flow rate of the NBR movement (veh/h)
During the SBL green extension time ge, the SBL throughput λSBL is equal to the arrival flow
rate during the effective green (qg,SBL, from Equation 19-32):
𝑣 𝐶
𝜆 =𝑞 , =𝑃 × ×
3600 𝑔
586 120
𝜆 = 0.08 × × = 0.0356 veh/s/ln = 128 veh/h/ln
3600 43.9
where
P = proportion of vehicles arriving during the green indication (decimal)

VSBL = SBL demand flow rate (veh/h)
C = cycle time (s)
gSBL = SBL effective green time (s)
For this conflicting flow, therefore, the NBR saturation flow rate sNBR,perm2 is obtained using
Equation 31-100:
/ ,
𝜆 𝑒
𝑠 , = / ,
1−𝑒
× . / ,
128𝑒
𝑠 , = × . / ,
= 1282 𝑣𝑒ℎ/ℎ/𝑙𝑛
1−𝑒
334

with all variables previously defined.
Since a queue is present in the NBR movement, the throughput for the NBR movement is equal
to its saturation flow rate:
𝜆 , =𝑠 , = 1282 𝑣𝑒ℎ/ℎ
Where:
λNBR,2 = throughput for the NBR movement during the SBL green extension(veh/h/ln)
sNBR,perm2 = saturation flow rate of the NBR movement during the SBL green extension
time (veh/h/ln)
With the discharge patterns for the NBR determined, the queue profile in the on-ramp during
Φ1 can be determined. During the SBL queue service time (cycle time t = 0 to t = 40.2s), the
throughput to the on-ramp is given by:
𝜆 = 𝜆 + 𝜆 , = 1,739 + 282 = 2,021 veh/h or 0.561 veh/s
Given the merge capacity cmerge = 1,142 veh/h for the current time period, the on-ramp queue
will grow at the following rate during the SBL queue service time:
𝜆 −𝑐 = 2,021 − 1,142 = 879 𝑣𝑒ℎ/ℎ 𝑜𝑟 0.244 𝑣𝑒ℎ/𝑠
Therefore, at the end of the SBL queue service time (t = 40.2s), the queue at the on-ramp
will be 0.244 x 40.2 = 9.8 vehicles (Figure E-17a).
This process is then repeated for all phases throughout the cycle. The results for a single cycle
(120 sec) are presented in Table E-12, where the maximum on-ramp queue occurs at t = 50.48s,
with 10.82 vehicles (t = 50.48s). The expected on-ramp queue at the end of the cycle is 2.02
vehicles. The remaining cycles within time period 2 show the same pattern, where the on-ramp
queue at the end of each cycle becomes the initial queue at the start of the next cycle.
Each row in Table E-12 describes a portion of the cycle, as follows:
• gs1: queue service time for SBL (Φ1), as previously discussed
• ge1: green extension time for SBL (Φ1). The NBR movement discharges at the permitted
saturation flow rate due to the queue that has developed during gs1, and the on-ramp queue
grows at a rate of 0.07 veh/s
• r1: effective red time for SBL (Φ1). There is no throughput from protected movements
and the NBR movement discharges freely at the saturation flow rate. The on-ramp queue
• g2*: effective green for NBT (Φ2), with no throughput from protected movements. The
duration of 0.88s is calculated based on the queue service time of the NBR approach. The on-
ramp queue grows at a rate of 0.11 veh/s
• g2**: remaining effective green for NBT (Φ2). For this portion, no queue remains on
the NBR approach, therefore the NBR throughput is equal to its demand flow rate (vNBR). The
on-ramp queue discharges at a rate of 0.17 veh/s
• r2: effective red time for NBT (Φ2). There is no throughput from protected movements
and the NBR throughput is equal to its demand flow rate (vNBR). The on-ramp queue
discharges at a rate of 0.17 veh/s
• gs7: queue service time for EBT (Φ7). The EBT discharges into the on-ramp at the
saturation flow rate. The throughput of the NBR movement is restricted to the permitted
saturation flow rate, causing queues to develop in the NBR approach. The on-ramp queue
• ge7*: green extension time for EBT (Φ7). The duration of 0.03s is calculated based on
the queue service time of the NBR approach. The NBR movement discharges at the permitted
saturation flow rate. The on-ramp queue grows at a rate of 0.08 veh/s
335

• ge7**: remaining extension time for EBT (Φ7). The EBT movement discharges at a rate
equal to its arrival flow rate during the effective green. For this portion, no queue remains on
the NBR approach, therefore the NBR throughput is equal to its demand flow rate (vNBR). The
on-ramp queue discharges at a rate of 0.15 veh/s
• r7: effective red time for EBT (Φ7). No throughput from protected movements and the
NBR throughput is equal to its demand flow rate (vNBR). The on-ramp queue discharges at a
rate of 0.17 veh/s.
Table E-12. Discharge flow rates into the on-ramp for each phase throughout the cycle –
time period 2
Protected
Permitted movement On-ramp analysis
movement
Active Duration
t (s) NBR λONR - On-ramp
phase (s) λprot vNBR λNBR λONR
queue cmerge queue
(veh/s) (veh/s) (veh/s) (veh/s)
(veh) (veh/s) (veh)
gs1 0.00 40.16 0.483 0.145 0.078 0.00 0.56 0.24 0.00
ge1 40.16 3.74 0.036 0.145 0.356 2.66 0.39 0.07 9.80
r1 43.90 5.70 0.000 0.145 0.430 1.87 0.43 0.11 10.08
g2* 49.60 0.88 0.000 0.145 0.430 0.25 0.43 0.11 10.72
g2** 50.48 49.82 0.000 0.145 0.145 0.00 0.14 -0.17 10.82
r2 100.30 5.70 0.000 0.145 0.145 0.00 0.14 -0.17 2.22
gs7 106.00 6.25 0.503 0.145 0.073 0.00 0.58 0.26 1.24
ge7* 112.25 2.02 0.027 0.145 0.366 0.45 0.39 0.08 2.85
ge7** 114.27 0.03 0.027 0.145 0.145 0.00 0.17 -0.15 3.01
r7 114.3 5.7 0.000 0.145 0.145 0.00 0.14 -0.17 3.01
Cycle
120 - 2.02
end
At the end of the time period, a residual queue of 23.32 vehicles is expected along the on-
ramp, and this value is carried to the start of the next time period. The time period length of
900s does not correspond to an exact number of signal cycles, and the last cycle is interrupted at
t = 60s. Therefore, the next time period will start the analysis from the same timestamp to
maintain consistency.
Step 7D – Calculate equivalent capacities for the affected movements

Since spillback does not occur during time period 2, no adjustment to the intersection
capacity is necessary.
Time Period 3
The same steps performed for the analysis of time period 2 are applied again for the analysis of
time period 3.

The throughput for movements that discharge into the on-ramp have been previously
determined as part of the queue spillback check, and are shown in Table E-7.
336


As in the analysis of the previous time period, the merging capacity cmerge is obtained as an
output from the Freeway Facilities method (Figure E-16a). The merging capacity for time period
3 is 1,142 veh/h.
The procedure described earlier is applied but with an initial on-ramp queue of 23.32 vehicles,
which is the estimated queue at the end of time period 2. The analysis begins at the middle of the
cycle (t= 60s), which is the end of the previous time period. Figure E-18 illustrates the queue
accumulation polygon for both the on-ramp and the NBR movement.
Queue spillback occurs during the third cycle (SBL queue service time), when the on-ramp
queue reaches the maximum storage LONR = 35.5 vehicles. At this time, the maximum flow rate
that can enter the on-ramp is constrained by the merge capacity cmerge. In other words, the
maximum number of vehicles allowed to enter the ramp is equal to the number of vehicles that
are able to merge to the freeway mainline. Also, the queues developed in the NBR are longer
during cycles 3 through 8, causing an increased delay on this movement due to the queue spillback
conditions at the on-ramp.
The on-ramp queue at the start of cycle 3 is 27.9 vehicles. The cycle starts with the SBL
movement, with an effective green time g1 = 47.3s. Since this movement already operates with
v/c > 1, the queue service time gs1 is equal to g1, and no green extension time is available (ge1 =
337

0). The protected movement then discharges at saturation flow rate sSBL = 0.483 veh/s, while the
NBR movement discharges at a permitted saturation flow rate sNBR = 0.078 veh/s. At the same
time, the on-ramp discharges to the freeway at a rate cmerge = 1,142 veh/h = 0.317 veh/s. Therefore,
the on-ramp queue grows at the following rate:
𝜆 −𝑐 = (0.483 + 0.078) − 0.317 = 0.244 veh/s
At this rate, the time remaining until spillback occurs is calculated by dividing the remaining
on-ramp queue storage by the growth rate:
35.5 − 27.9
𝑇𝑖𝑚𝑒 𝑡𝑜 𝑠𝑝𝑖𝑙𝑙𝑏𝑎𝑐𝑘 = = 31.2𝑠
0.244
Spillback is then expected to occur within 31.2 seconds of the onset of g1. The total effective
green g1 value of 47.3s is then divided in two portions:
• gs1* (31.2s): discharging at saturation flow rate
• gs1,sp (16.1s): the remainder of g1 will be affected by queue spillback, limiting the
maximum discharge to the on-ramp to the merge capacity cmerge = 0.317 veh/s. Note that this
constraint is shared by two movements entering the on-ramp (SBL and NBR).
The effect of queue spillback on the intersection capacity during gs1,sp is then measured by the
capacity reduction factor β1,sp, defined as the ratio between the maximum on-ramp capacity
during queue spillback and the throughput from the intersection movements (SBL and NBR):
𝑐 0.317
𝛽 ,
= = = 𝟎. 𝟓𝟔𝟓
𝜆 + 𝜆 (0.483 + 0.078)
A capacity reduction factor β1,sp= 0.565 means that only 56.5% of the expected intersection
throughput is able to enter the on-ramp when queue spillback occurs during phase gs1,sp. This
capacity adjustment factor is applied to each movement to obtain their adjusted throughputs for
this time period:
𝜆 , =𝜆 ×𝛽 ,
= 0.483 × 0.565 = 0.273 𝑣𝑒ℎ/𝑠
𝜆 , =𝜆 ×𝛽 ,
= 0.078 × 0.565 = 0.044 𝑣𝑒ℎ/𝑠
The procedure is then repeated for the remaining movements of the cycle, as shown in Table
E-13.
As shown, at time t = 31.2 s the maximum storage length of the on-ramp is reached and
spillback occurs. From this time through t = 83.3s, the throughput from intersection movements
to the on-ramp λONR is greater than the merge capacity cmerge. Therefore, the maximum allowed
throughput λONR,ajd is constrained by the on-ramp discharge capacity cmerge = 0.137 veh/s. For these
cases, the spillback capacity reduction factor fsp is computed as the ratio of λONR,ajd and λONR. Note
that for this time range the on-ramp queue is kept constant at the maximum storage of 35.54
vehicles.
From t = 83.3s, the on-ramp queue begins to discharge at a rate of 0.142 veh/s, followed by a
small increase during the green time of phase 7 (EBT), but it is not sufficient to cause spillback.
At the end of the cycle, the residual on-ramp queue is 33.51 vehicles.
The subsequent cycles follow a recurring pattern, with the on-ramp reaching maximum storage
early in the cycle and slightly diminishing at the end of the cycle.
338

Table E-13. Discharge flow rates into the on-ramp for each phase throughout the cycle –
time period 3
Capacity
Protected
On- movement Permitted movement On-ramp analysis reduction
Active Duration ramp adjustment
t (s)
phase (s) queue λONR,adj
(veh) λprot vNBR λNBR Q(NBR) λONR λONR,adj
- cmerge βsp
(veh/s) (veh/s) (veh/s) (veh) (veh/s) (veh/s)
(veh/s)
gs1* 0.0 31.2 27.92 0.483 0.175 0.078 0.00 0.561 0.561 0.244 1.000
gs1,sp 31.2 16.1 35.54 0.483 0.175 0.078 3.01 0.561 0.317 0.000 0.565
r1 47.3 5.7 35.54 0.000 0.175 0.430 5.12 0.430 0.317 0.000 0.739
g2* 53.0 30.3 35.54 0.000 0.175 0.430 4.31 0.430 0.317 0.000 0.739
g2** 83.3 17.0 35.54 0.000 0.175 0.175 0.00 0.175 0.175 -0.142 1.000
r2 100.3 5.7 33.11 0.000 0.175 0.175 0.00 0.175 0.175 -0.142 1.000
gs7 106.0 6.3 32.30 0.503 0.175 0.073 0.00 0.576 0.576 0.259 1.000
ge7 112.3 2.0 33.92 0.027 0.175 0.366 0.64 0.393 0.393 0.076 1.000
r7* 114.3 1.0 34.08 0.000 0.175 0.430 0.25 0.430 0.430 0.113 1.000
r7** 115.3 4.7 34.18 0.000 0.175 0.175 0.00 0.175 0.175 -0.142 1.000
Cycle
- - - - - -
end 120 0 33.51

The adjusted capacities of the affected movements are estimated based on the volume of
vehicles that can actually be discharged during each time period. Table E-14 provides the
calculation of the adjusted capacity of the SBL movement during time period 3. The table lists all
occurrences of green times for the SBL movement during the analysis time period and their
respective durations. For each row, the expected throughput from the intersection λONR and the
actual throughput λONR,adj are computed. Next, the capacity reduction factor βsp is computed as the
ratio of λONR and λONR,adj. A value of βsp < 1.0 indicates the occurrence of queue spillback in the
subject phase. The expected and actual discharge volumes are obtained by multiplying the values
of λONR and λONR,adj, respectively, by their duration. At the end of the table, the expected and actual
volumes are aggregated and a capacity reduction factor βsp,SBL = 0.704 is obtained as the ratio of
these values.
The capacity of the SBL movement without consideration of queue spillback is 685 veh/h
(Table E-7). The adjusted capacity is calculated by applying the spillback capacity reduction
factor βsp, calculated in Table E-14:
𝑐 , =𝑐 ×β , = 685 × 0.704 = 𝟒𝟖𝟐. 𝟐 𝐯𝐞𝐡/𝐡
In this example, this step is not required for the EBT movement, since this movement does not
experience effects of queue spillback. As shown in Figure E-18, the on-ramp queue during the
EBT green does not reach the maximum storage length of 35.5 veh.
339

Table E-14. Calculation of spillback capacity reduction factor for the SBL movement for
time period 3
On-ramp
Spillback adjustment
analysis
Active Duration
Cycle On-ramp expected On-ramp actual
phase (s) λONR λONR,adj
βsp discharge volume discharge volume
(veh/s) (veh/s)
(veh) (veh)
2 gs1 47.3 0.561 0.561 1.000 26.56 26.56
3 gs1* 31.2 0.561 0.561 1.000 17.51 17.51
3 gs1,sp 16.1 0.561 0.317 0.565 9.04 5.11
4 gs1 8.3 0.561 0.561 1.000 4.67 4.67
4 gs1,sp 39.0 0.561 0.317 0.565 21.89 12.37
5 gs1 5.1 0.561 0.561 1.000 2.87 2.87
5 gs1,sp 42.2 0.561 0.317 0.565 23.68 13.39
6 gs1 4.7 0.561 0.561 1.000 2.62 2.62
6 gs1,sp 42.6 0.561 0.317 0.565 23.93 13.53
7 gs1 4.6 0.561 0.561 1.000 2.59 2.59
7 gs1,sp 42.7 0.561 0.317 0.565 23.97 13.55
8 gs1 4.6 0.561 0.561 1.000 2.58 2.58
8 gs1,sp 42.7 0.561 0.317 0.565 23.97 13.55
Total: 185.89 130.89
Capacity reduction factor (βsp,SBL): 0.704
Time Period 4
The same steps performed for time periods 2 and 3 are applied again in time period 4.

The throughput for movements that enter the on-ramp has been previously determined as part
of the queue spillback check, and shown in Table E-7.

The merge capacity for time period 4 has been previously determined, as shown in Figure E-
16a. Since the congestion along the freeway mainline is dissipating during this time period, the
merge capacity is not constant: from time steps 1 through 4, the merge capacity is 1,142 veh/h,
consistent with oversaturated conditions from previous time periods. After time step 5, the merge
capacity is set equal to the ramp roadway capacity (1,904 veh/h)
The procedure described earlier is applied to plot the queue accumulation polygons, shown in
Figure E-19. Queue spillback occurs during the first cycle, due to the residual queue from the
previous time period. However, due to low volumes at the intersection and improvement of
performance along the freeway mainline, the on-ramp clears quickly. The queue has cleared by
the end of the second cycle.
340


The procedure described earlier is used to calculate the capacity reduction factor for the SBL
movement, as shown in Table E-15. The estimated capacity reduction is minor, as spillback only
occurs during the first cycle. The EBT movement does not experience queue spillback, therefore
no adjustment is necessary.
Table E-15. Calculation of spillback capacity reduction factor for the SBL movement
during time period 4
On-ramp
Spillback adjustment
On-ramp analysis
Active Duration
Cycle queue On-ramp On-ramp actual
phase (s) λONR λONR,adj
(veh) βsp expected throughput
(veh/s) (veh/s)
throughput (veh) (veh)
1 gs1 6.0 34.42 0.505 0.505 1.000 3.02 3.02
1 gs1,sp 29.9 35.54 0.505 0.317 0.628 15.12 9.50
1 ge1 0.0 35.54 0.388 0.317 0.818 0.00 0.00
2 gs1 31.2 13.20 0.505 0.505 1.000 15.79 15.79
2 ge1 4.7 19.07 0.095 0.095 1.000 0.44 0.44
3 gs1 31.2 0.00 0.505 0.505 1.000 15.79 15.79
3 ge1 4.7 5.87 0.058 0.058 1.000 0.27 0.27
4 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55
4 ge1 3.7 9.80 0.392 0.392 1.000 1.46 1.46
5 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55
5 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46
341

6 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55

6 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46
7 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55
7 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46
8 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55
8 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46
Total: 170.49 164.86
Spillback capacity reduction factor: 0.967
The adjusted capacity of the SBL movement is calculated by applying the spillback capacity
reduction factor βsp, calculated in Table E-15:
𝑐 , =𝑐 ×𝛽 , = 746 × 0.967 = 𝟕𝟐𝟏. 𝟒 𝐯𝐞𝐡/𝐡
With the adjusted capacity values obtained, the performance measures for the intersection can
be computed using the remaining steps from the Signalized Intersections methodology (Chapter
19): compute the adjusted demand-to-capacity ratio (Step 8) and compute control delay (Step 9).
Table E-20 compares the performance measures for the affected movement (SBL) for the cases
with and without accounting for spillback effects. There is no change in the performance measures
in time period 2 even though the on-ramp demand is greater than the merge capacity, as the queue
can be stored in the on-ramp. Time period 3 yields a significant increase in the SBL control delay
due to the queue spillback: 589.2 s/veh, while the intersection analysis without consideration of
the spillback effects would return a control delay of 293.5 s/veh. Time period 4 shows a small
increase in control delay, from 575.2 s/veh to 609.5 s/veh. Even though spillback occurs for only
a short time during this time period, the high value of control delay obtained is due to the initial
queue delay (d3), as a result of the unmet demand at the end of time period 3.
Table E-16. Comparison of performance measures – with and without consideration of

spillback effects
Movement capacity (veh/h) Control delay (s/veh)

Time Period Without With Without With
spillback spillback spillback spillback
1 652 652 60.3 60.3
2 586 586 55.9 55.9
3 685 482 293.5 589.2
Part 2 – Two-Way Stop Control (TWSC) Intersection
Input Data
Figure E-20 shows the geometry of the TWSC intersection.
342

Figure E-20. TWSC intersection geometry – Acadian Thruway @ I-10 EB

each time period, based on the demand inputs of the TWSC intersection. For each time period,
the demand (v) and capacities (c) are compared for each movement that enters the on-ramp (EBT,
computed and the merge demand vR is then computed as the sum of the three movements.
The capacities for minor rank movements (EBT and SBL) are computed for each time period,
since they change as a function of the conflicting demand. The NBR movement is unsignalized
and therefore its capacity is computed by its respective saturation flow rate, considering the
applicable adjustment factors fRT (for right-turn movements) and fHV (for the presence of heavy
vehicles):
𝑠 =𝑠 , ×𝑓 ×𝑓
1
𝑠 = 1,900 × × 0.961 = 1,547 𝑣𝑒ℎ/ℎ
1.18
In this case there are no conflicting flows to the unsignalized right turn since it is a Rank 1
movement (highest priority). Therefore, the capacity for the NBR movement is equal to its
saturation flow rate. Table E-17 summarizes the calculations for this step.
343

Table E-17. Calculation of the on-ramp demand (vR) based on the TWSC intersection
operation
Time Movements
Parameter
Period EBT NBR SBL
v/c 0.06 - 0.96
1 c (veh/h) 125 1547 677
min (v, c) 8 315 652
v/c 0.10 - 0.48
2 c (veh/h) 42 1547 1222
min (v, c) 4 608 591
v/c 0.64 - 0.56
3 c (veh/h) 28 1547 1222
min (v, c) 18 708 685
v/c 1.00 - 0.60
4 c (veh/h) 24 1547 768
min (v, c) 24 80 463
The on-ramp demand estimates are then used as inputs for the freeway facility analysis. Since
the input demands for the freeway are identical to Part 1, it is already known that spillback will
occur during time period 3 (Table E-1).

The evaluation of queue spillback impacts on the TWSC intersection follows the procedure
detailed in Figure E-7. Since this is a multiperiod analysis, the procedure must be applied for each
time period as discussed in Part 1.

The throughput for movements that enter the on-ramp has been previously determined as part
of the queue spillback check, and these values are shown in Table E-17.
This step computes the merging capacity into the freeway cmerge. Since the inputs of the freeway
facility remain unchanged from Part 1, the same values are used:
• Time periods 2 and 3: 1,142 veh
• Time period 4: 1,142 veh/h during 4 time steps (60 seconds), then 1,903 veh/h.

In order to determine the spillback time TSB, a queue accumulation polygon is developed for
the on-ramp. Table E-18 shows the calculations for plotting the on-ramp queue. For each time
period, the difference between the on-ramp throughput λΟΝR and the merge capacity cmerge is
344

calculated. Then, the time to spillback is obtained considering the queue growth and the available
queue storage. Time period 4 is split into two rows (4a and 4b), since the merge capacity changes
within this time period. For the first minute of the time period (4a), the merge capacity remains
at 1,142 veh/h due to existing oversaturated conditions along the freeway mainline. For the
remaining of the time period (4b), the merge capacity is equal to the ramp roadway capacity
(1,903 veh/h).
The results show that queue spillback occurs only during time period 3. The initial queue of
time period 2 is 15.2 vehicles, and it takes 4.55 minutes for the on-ramp to reach maximum storage
capacity. Therefore, the spillback time TSB is computed as 15 – 4.55 = 10.45 minutes.
Table E-18. Queue accumulation plot calculations for on-ramp – TWSC intersection
On-ramp On-ramp Initial Spillback Final

Time to
Time Duration demand queue growth ONR time ONR
spillback
Period (min) (vR) rate (λΟΝR - queue (TsB) queue
(min)
(veh/h) cmerge) (veh/s) (veh) (min) (veh)
2 15 1203 0.017 0.0 - - 15.2
3 15 1411 0.075 15.2 4.55 10.45 35.5
4a 1 567 -0.160 35.5 - - 26.0
4b 14 567 -0.371 26.0 - - -
Figure E-21 illustrates the queue accumulation polygon for the on-ramp, based on the table
results.
Figure E-21. Queue accumulation polygon for the on-ramp – TWSC intersection

When queue spillback occurs at a TWSC intersection, movements discharging towards the on-
ramp tend to follow a cooperative approach instead of the priority-based regular operation.
Therefore, the merge capacity cmerge is shared among the three movements that enter the on-ramp:
𝑐 , + 𝑐 , +𝑐 , =𝑐 = 1,142 𝑣𝑒ℎ/ℎ
345

The capacities during spillback conditions are then obtained proportionally to their demand
flow rates (Equation E-10):
𝑐 ×𝑣 1,142 × 685
𝑐 , = = = 554.4 𝑣𝑒ℎ/ℎ
𝑣 +𝑣 +𝑣 685 + 708 + 18
𝑐 ×𝑣 1,142 × 708
𝑐 , = = = 573.0 𝑣𝑒ℎ/ℎ
𝑣 +𝑣 +𝑣 685 + 708 + 18
𝑐 ×𝑣 1,142 × 18
𝑐 , = = = 14.6 𝑣𝑒ℎ/ℎ
𝑣 +𝑣 +𝑣 685 + 708 + 18
The equivalent capacities cEQ,i for each movement i, aggregated for the 15-min time period, are
obtained proportionately to the spillback time TSB (Equation E-11):
, × ×( ) . × . × .
𝑐 , = = = 757 𝑣𝑒ℎ/ℎ
, × ×( ) × . × .
𝑐 , = = = 869 𝑣𝑒ℎ/ℎ
, × ×( ) × . . × .
𝑐 , = = = 24 𝑣𝑒ℎ/ℎ
be computed using the next step from the TWSC methodology (Chapter 20): compute movement
control delay (Step 11).
Table E-23 compares the performance measures of the affected intersection movements for the
cases with and without consideration of spillback effects during time period 3. All three
movements discharging to the on-ramp have significantly higher delays when considering
spillback effects.
Table E-19. Comparison of performance measures in a TWSC intersection – time period 3

- with and without spillback effects
Capacity (veh/h) Control delay (s/veh)

Demand
Movement Without With Without With
(veh/h)
spillback spillback spillback spillback
EBT 18 28.0 18.7 166.5 479.8
NBR 708 1547.0 868.9 0 24.5
SBL 685 1222.0 757.2 9.4 37.2
Part 3 – All-Way Stop Control (AWSC) Intersection with
Input Data
Figure E-20 shows the geometry of the study intersection.
346

Figure E-22. AWSC intersection geometry – Acadian Thruway @ I-10 EB

each time period, based on the demand inputs of the AWSC intersection. For each time period,
the demand (v) and capacities (c) are compared for each movement that feeds the on-ramp (EBT,
computed and the merge demand vR is then computed as the sum of three movements.Table E-20
summarizes the calculations for this step.
The estimated on-ramp demand values are provided as inputs for the freeway facility analysis.
The freeway facility is then analyzed and the expected on-ramp queues are provided in Table E-
21.
347

Table E-20. Calculation of the on-ramp demand (vR) based on the AWSC intersection
operation.
Time Movements
Parameter
Period EBT NBR SBL
Adjusted demand (veh/h) 54 467 313
v/c 0.143 - 0.672
1
c (veh/h) 377 539 466
min (v, c) 54 467 313
v/c 0.114 - 0.984
2
c (veh/h) 350 521 439
min (v, c) 40 512 432
v/c 0.048 - 1.18
3
c (veh/h) 396 550 462
min (v, c) 19 539 462
v/c 0.062 - 0.618
4
c (veh/h) 455 619 511
min (v, c) 28 160 316
Table E-21. Check for spillback occurrence – AWSC intersection

Ramp
Time vR Ramp queue Ramp queue Spillback
storage
period (veh/h) (veh) (ft) expected?
ratio (RQ)
1 834 0.0 0.0 0.00 No
2 984 14.9 21.9 0.62 No
3 1020 82.1 53.4 1.50 Yes
4 504 0.0 0.0 0.0 No
Since spillback will occur, the impacts on the operation of the intersection must be evaluated.
The next section illustrates the application of the evaluation methodology at the AWSC
intersection.

The evaluation of queue spillback impacts on the AWSC intersection follows the procedure
detailed in Figure E-9. Since this is a multiperiod analysis, the procedure must be applied for each
time period. In this example, time periods 2, 3 and 4 will be evaluated. Time period 1 will be
excluded since no oversaturated conditions occur along the freeway.
348


The intersection throughput to the on-ramp was previously determined at the spillback check
(Table E-20).
Step 13B - Obtain merging capacity with Freeway Facilities method

For this example, the ramp metering rate (900 veh/h) is an additional input to the freeway
facility analysis and is considered as a potential constraint of the merge capacity. Therefore, the
merge capacity for this analysis is kept constant at 900 veh/h.
Step 13C - Determine fraction of time period with queue spillback

The procedure to evaluate the spillback time (TSB) is similar to the TWSC procedure, and the
calculations are provided in Table E-22.
Table E-22. Queue accumulation plot calculations for on-ramp – AWSC intersection
On-ramp
On-ramp queue Initial Spillback Final
Time to
Time Duration demand growth rate ONR time ONR
spillback
Period (min) (vR) (λΟΝR - queue (TsB) queue
(min)
(veh/h) cmerge) (veh) (min) (veh)
(veh/s)
2 15 984 0.023 0.0 - - 21.0
3 15 1020 0.033 15.2 7.25 7.75 35.5
4 15 504 -0.110 35.5 - - 0.0
Figure E-21 illustrates the queue accumulation polygon for the on-ramp, based on the table
results.
Figure E-23. Queue accumulation polygon for the on-ramp – AWSC intersection
Step 13D - Compute spillback departure headway

This step is similar to the calculation of adjusted capacities in the TWSC procedure. The same
calculations are performed, and adjusted capacity values are converted into headways (hsp), as
shown in Table E-23.
349

Table E-23. Equivalent capacities and headways for on-ramp – Time Period 3 – AWSC
intersection
Capacity during Regular Equivalent
Spillback departure
Movement spillback (csp) Capacity Capacity (cEQ)
headway (hsp) (s)
(veh/h) (c) (veh/h) (veh/h)
EBT 15 396.0 212.1 17.0
NBR 439 550.0 496.5 7.3
SBL 445 462.0 453.7 7.9
be computed using the remaining steps from the AWSC methodology (Chapter 21): compute the
service times (Step 13) and compute control delay (Step 14).
Table E-24Table E-20 compares the performance measures of the intersection movements for
the cases with and without consideration of spillback effects during time period 3. The three
movements that discharge into the on-ramp (EBT, NBR and SBL) experience increased delay,
while the remaining movements have the same performance measures.
Table E-24. Comparison of performance measures – time period 3 - with and without
spillback effects
Departure headway
Capacity (veh/h) Control delay (s/veh)
Demand (s)
Movement
(veh/h) Without With Without With Without With
spillback spillback spillback spillback spillback spillback
EBL 75 359 359 15.6 15.6 10.0 10.0
EBT 19 396 212 12.6 21.7 9.1 17.0
NBT 229 497 497 16.3 16.3 7.2 7.2
NBR 539 550 497 58.9 92.3 6.5 7.3
SBL 546 462 454 128.0 136.5 7.8 7.9
SBT 220 494 494 16.0 16.0 7.3 7.3
350

APPENDIX F
Freeway Facilities Lane-by-Lane Analysis
Data Collection
The data collected for this part of the project include speed and flow data from selected detector station
sensors in California, Virginia, Utah, Wisconsin, Minnesota, and Florida. These locations represent diverse
operational and design conditions across the US. Sites were selected based on the following criteria:
• Speed and flow data available for each lane, aggregated in 15-min intervals, for a period of at least
one year;
• Absence of freeway management strategies, such as express or high-occupancy vehicle (HOV)
lanes, ramp metering, speed harmonization, or demand shoulder use;
• For merge and diverge and segments, good health detector data available for the upstream,
downstream and ramp sections;
• Percentages of heavy vehicles were available.
The dataset includes 48 locations: 19 basic, 14 merge, 15 diverge and 16 weaving segments with 2, 3 or
4 lanes on each direction. There are no 5-lane segments in the database, as many of the identified locations
operate with HOV lanes. The number of required detector stations is different for each segment type (
Figure F-1). Basic segments require only one detector station. Diverge segments require two stations:
one at the ramp influence area (upstream of the exit) and one along the ramp. Merge segments require three
stations: one at the ramp influence area (downstream the merge), one along the ramp and one upstream of
the merge.
Figure F-1 – Required detector data positions by segment type
The list of data collection locations is provided in Table F-1 (basic segments), Table F-2 (merge
segments), Table F-3 (diverge segments) and Table F-4 (weaving segments).
351

Table F-1 – Database used for determination of lane-by-lane flows – Basic freeway segments
Detector #
# Observation %
State Road Station %HV adjacent
lanes Period Grade
IDs ramps
CA HWY 1 NB 2018 500014082 0.5 1.7 2
CA SR-132 EB 2018 10119910 -0.5 0.3 0
MN US-10 2017 - 18 946 0.3 1.4 1
MN I-694 NB 2017 1413 -1.2 8.6 1
2L
UT SR-67 NB 2018 820 -0.3 18 0
VA I-66 WB 2018 19002981 0.5 1 2
VA I-64 EB 2018 64239221 -0.9 9 1
WI I-43 SB 2017 - 18 692 -0.02 6.5 0
CA I-205 WB 2018 - 19 1027310 -0.9 4.2 0
CA SR-85 NB 2018 - 19 407336 -0.8 5.6 1
FL I-4 WB 2017 4712 -0.2 10.8 0
MN I-94 NB 2017 - 18 1356 -1.7 11.8 0
3L
UT I-215 SB 2016 - 17 82 -3.1 10.5 0
UT I-15 SB 2018- 19 963 1.45 32.9 1
VA I-64 EB 2017- 18 64055221 0.2 4 3
WI I-43 NB 2017 - 18 659 -0.6 10.2 1
CA I-80 2018 - 19 413373 0.4 6.8 1
CA SR-24 EB 2018 - 19 400532 1.7 14.1 0
CA I-80 EB 2018 - 19 413375 1.1 5 1
FL I-295W NB 2017 2220 0 13.6 1
4L
FL I-275 SB 2016 - 17 3829 -1.1 4.4 0
FL I-275 NB 2016 - 17 3408 0 4.4 0
UT I-215 CW 2018 - 19 50 -0.8 28.2 1
VA I-295 EB 2018 - 19 4044741 -0.1 10 1
352

Table F-2 – Database used for determination of lane-by-lane flows – Merge segments
#
# Observation %
State Road Detector Station IDs %HV adjacent
lanes Period Grade
ramps
UT SR-67 S 2018 872, 876, 1872 0 13 0
UT SR-67 N 2018 830, 834, 1830 0.1 17 0
2L
FL I-295E NB 2018 10821, 10852, 10890 2.7 11.8 0
FL I-295E NB 2018 10854, 10841, 10879 1.5 11.8 0
CA I-5 SB 2018 - 19 10121110, 10121310, 1083110 -0.9 11.9 0
CA CA-99 WB 2018 10109610, 10109810, 10109710 0.1 11.23 1
MN I-694 2017 174, 172, 753 1.8 8.6 1
UT SR201-W 2018 - 19 348, 350, 1348 0 27.9 1
3L
UT I-215 CCW 2017 173, 175, 1173 1.5 9 1
UT I-215S EB 2017 168, 169, 1168 0.2 11 0
UT I-215 2017 188, 190, 1188 0 10 0
UT I-80 2017 231, 232, 1231 1.32 14 0
CA I280 SB 2018 - 19 403908, 403328, 403909 0 1.3 1
4L
CA 1-8 WB 2017 403908, 403328, 403909 2.71 2.1 1
Table F-3 – Database used for determination of lane-by-lane flows – Diverge segments
#
# Observation %
lanes Period Grade
ramps
CA US-101 SB 2018 – 19 406305, 406303 -0.3 5 1
CA I-8 WB 2016 - 17 1115624, 1122447 0.8 3.4 0
2L UT SR-67 NB 2017 810, 2810 0 9 0
FL I-295E NB 2017 10829, 10876 0 11.8 0
WI I-94 WB 2017 67663, 67662 -2 7.2 1
CA CA-242 2018 – 19 414251, 417124 0 2.43 0
CA I-5 NB 2018 – 19 10121410, 1090210 0 18.1 0
CA CA-73 2018 – 19 1208789, 1208940 -5.4 3.8 0
MN I-694 2017 151, 554 2.5 8.6 2
3L
MN I-694 2017 171, 755 2.5 8.6 2
UT I-215 CCW 2017 112, 2114 0 17 0
UT I-215 CW 2018 – 19 22, 2024 -2.2 61.6 0
UT I-215 CW 2018 – 19 86, 2087 0 8 0
CA SR-242 NB 2018 – 19 414252, 418256 1.5 2.21 4
4L
CA I-80 EB 2017 413375, 410766 0.7 5.1 1
353

Table F-4 – Database used for determination of lane-by-lane flows – Weaving segments
#
# Observation %
lanes Period Grade
ramps
CA CA-56 WB 2018 1125546, 1125575, 1125543, 1126293 0 2.03 0
MN I-694 NB 2018 1027, 1410, 5120, 6226 0.6 14.8 3
MN Lafayette Hwy 2017 S1169, S1170, 5626, 5629 0 8.81 0
2L MN US 52 2017 S1442, S1444, 6061, 6069 0 8.01 0
MN Lafayette Hwy 2017 S1159, S1160, 5581, 5584 0 8.81 0
MN MN-36 WB 2017 S616, S617, 2361, 2362 0.8 8.81 0
MN MN-36 EB 2017 S591, S592, 2256, 2257 0.8 8.81 0
CA I-80 SB 2018-2019 409107, 404408, 409108, 419489 1 15.8 3
UT I-215 CW 2013-2014 320, 322, 1320, 2322 0 14 1
3
UT I-215 CW 2015-16 344, 346, 1344, 2346 0 14 0
UT Belt Route 2011-2012 162, 165, 1162, 2165 1 14 1
CA SR4-EB 2018 416930, 414707, 416931, 414708 -0.5 3.3 2
CA SR4-EB 2018 400049, 405269, 418869, 406635 -0.8 4.8 0
4 CA I-680 SB 2018 407177, 407179, 409059, 407178 0.51 4.4 4
CA I-880 SB 2018 400949, 400678, 403028, 403030 0.1 6.1 0
UT I-80 EB 2015 228, 240, 1228, 2231 0 16 0
Speed and flow detector data were collected from online sources from the respective state agencies. Data
were obtained by lane in 15-min intervals, over a 1-year period for each location. Erroneous speed and flow
data and those associated with crashes, lane closures, and work zones were removed. Holidays and
weekends were excluded. The heavy vehicle percentage (HV%) was collected from the respective state
agencies. Average truck percentages are typically reported on an annual basis by agencies; therefore the
speed-flow data from detectors were downloaded only for periods when HV% information was available.
The presence of ramps upstream or downstream of a site might cause significant impact on lane flow
distribution. Therefore, the analysis included the number of such ramps within a half-mile upstream and
downstream of the segment (access point density).
Lane-By-Lane Flow Models by Segment Type

The lane flow ratio (LFR) model for each lane is estimated as a function of the logarithm of the segment
volume-capacity ratio (v/c). This relationship was established empirically after evaluating the performance
of logarithmic and polynomial regressions. Although a 4th degree polynomial provided an overall slightly
better fit, the number of adjustment factors required to accommodate parameters of geometry (grade and
number of accesses) and flow (truck percentile and ramp flow) was considered too high. Thus, a logarithmic
model was selected as a balance between model complexity and accuracy. The flow estimation curves for
each lane are fitted using the least squares method, except for the leftmost lane, which is estimated as the
remaining flow, to ensure the sum of the flow shares from each lane always equals 100%. The equations
estimating LFR are as follows:
𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 +𝑏 (Equation F-1)
𝐿𝐹𝑅 = 1 − ∑ 𝐿𝐹𝑅 (Equation F-2)
Where:
LFRi = share of the total flow on lane i, where i ranges from 1 to n-1 (n = total number of segment
lanes)
354

LFRn = share of the total flow on the leftmost lane (lane n);
fa = adjustment factor for 𝑎 (Equations F-3, F-5, F-7);
v/c = volume/capacity ratio (0 ≤ v/c ≤ 1)
fc = adjustment factor for 𝑐 (Equations F-4, F-6, F-8)
The model proposed in Equation F-1 can be applied for basic, merge, diverge and weaving segments.
For merge and diverge segments, the share of flow is estimated at the area upstream of the ramp. For
weaving segments, the share of flow is estimated at the mainline upstream the on-ramp.
For the proposed methodology, volume and capacity are given in veh/h. The adjustment factors fa and fc
applicable in the analysis of basic segments are as follows:
𝑓 =𝑎+𝐺∙𝑓 , +𝑡∙𝑓 , +𝑛∙𝑓, (Equation F-3)
𝑓 = 𝑐+𝐺 ∙𝑓, +𝑡∙𝑓, +𝑛∙𝑓, (Equation F-4)
For merge and diverge segments, the fa and fc factors are as follows, with additional coefficients f ,
and f , to address ramp demand:
𝑓 =𝑎+𝐺∙𝑓 , +𝑡∙𝑓 , +𝑛∙𝑓, + ∙𝑓 , (Equation F-5)
𝑓 = 𝑐+𝐺 ∙𝑓, +𝑡∙𝑓, +𝑛∙𝑓, + ∙𝑓, (Equation F-6)
where:
G = grade (%)
a = empirical constant
fa,G = adjustment factor for a due to impact of grade
fc,G = adjustment factor for c due to impact of grade
t = truck percentage (%)
fa,t = adjustment factor for a due to impact of trucks
fc,t = adjustment factor for c due to impact of trucks
n = access point density – number of ramps half a mile upstream and half mile downstream
fa,n = adjustment factor for a due to impact of access point density
c = empirical constant
fc,n = adjustment factor for c due to impact of access point density
vR = ramp flow (vph)
fa,vR = adjustment factor for a due to impact of ramp flow
fc,vR = adjustment factor for c due to impact of ramp flow
The adjustment factors for the weaving segments address the effect of weaving-specific properties:
𝑓 = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + , ∙ 𝑓 , + , ∙ 𝑓 , + ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 ,
(Equation F-7)
, ,
𝑓 = 𝑐 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + ∙𝑓, + ∙𝑓, + ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 ,
(Equation F-8)
where:
ID = interchange density, as defined in HCM Chapter 13
fa,I = adjustment factor for a due to impact of interchange density
fc,I = adjustment factor for c due to impact of interchange density
vR,m = on-ramp flow (veh/h)
fa,vm = adjustment factor for a due to on-ramp flow
fc,vm = adjustment factor for c due to on-ramp flow
vR,d = off-ramp flow (veh/h)
fa,vd = adjustment factor for a due to off-ramp flow
fc,vd = adjustment factor for c due to off-ramp flow
355

LS = length of the weaving segment (ft)

fa,LS = adjustment factor for a due to length of the weaving segment
fc,LS = adjustment factor for c due to length of the weaving segment
VR = volume ratio (weaving volume/total volume)
fa,VR = adjustment factor for a due to volume ratio
fc,VR = adjustment factor for c due to volume ratio
The remaining factors have been defined previously.
The empirical constants (a, c, and the adjustment factors f) were obtained by regression and are specific
for each combination of segment type, lane number and total number of lanes. The obtained values for
basic, merge and diverge segments are presented in Table F-5.
356

Table F-5 – Adjustment factors for lane flow distribution on basic, merge and diverge segments
Lane Para- Basic segments Diverge segments Merge segments

# meter 2 lanes 3 lanes 4 lanes 2 lanes 3 lanes 4 lanes 2 lanes 3 lanes 4 lanes
a 0.17991 0.02708 0.06815 0.00969 -0.07503 0.30943 0.01501 0.00290 -0.07664
c 0.51747 0.27040 0.21903 0.44267 0.26667 0.24818 0.58644 0.28248 0.23621
fa,g 0.02397 0.02095 -0.01107 0.00969 0.00768 -0.03381 0.01501 -0.00290 -0.00302
fa,t -0.04821 -0.00364 -0.00209 -0.00928 0.00080 -0.05689 -0.00929 -0.00290 0.01110
fa,n -0.09525 -0.00829 -0.05870 -0.00969 0.01382 -0.02756 -0.00474 -0.00290 0.01449
L1
fc,g 0.00301 0.00969 -0.03378 -0.00976 -0.00810 -0.00016 0.01965 0.03100 0.04041
fc,t 0.00788 -0.00289 0.00243 0.00775 0.00140 -0.01887 -0.01350 -0.00179 -0.02714
fc,n 0.00134 0.03222 -0.03481 0.00057 0.03129 0.00516 -0.03997 -0.04212 -0.04073
fa,vR -0.21359 -0.06664 -0.00871 -0.03477 -0.10409 0.02637
fc,vR -0.12519 0.01324 -0.02112 -0.07032 -0.02982 0.00914
a -0.06337 -0.02491 0.00960 0.28585 -0.00816 -0.08022
c 0.31448 0.28769 0.33948 0.24967 0.37687 0.24498
fa,g -0.00596 0.00150 -0.00960 -0.03465 -0.00816 0.00048
fa,t 0.00113 0.00027 -0.00054 -0.05211 -0.00082 0.01250
fa,n 0.00368 -0.00845 -0.00960 -0.03023 -0.00261 0.01782
L2
fc,g -0.01688 -0.02388 -0.00189 0.00189 0.00791 -0.01938
fc,t 0.00239 -0.00036 0.00089 -0.00408 -0.00048 -0.00670
fc,n 0.01139 -0.04134 0.00520 0.00437 -0.00597 0.00101
fa,vR -0.04766 -0.00652 -0.11832 -0.03270
fc,vR -0.07333 -0.00914 -0.03855 -0.01262
a -0.04510 0.26611 0.02860
c 0.27607 0.25113 0.25373
fa,g -0.00171 -0.03618 -0.00169
fa,t 0.00213 -0.04404 -0.00579
fa,n 0.00808 -0.03444 -0.00678
L3
fc,g 0.01052 0.00344 0.00060
fc,t -0.00112 0.00918 0.01424
fc,n 0.01485 0.00164 0.01764
fa,vR 0.02083 -0.07890
fc,vR -0.00644 -0.04144
357

The weaving LFRs are calculated at two locations: upstream of the on-ramp and within the weaving
segment (Figure F-1). The downstream LFRs are calculated as a function of the upstream LFRs.
Figure F-2. Notation for LFR estimation at weaving segments
The adjustment factors calculated for the upstream LFRs are presented in Table F-6. The number of lanes
refer to the freeway section immediately upstream of the weave, and any lanes connecting the on-ramp and
off-ramp are not considered as part of the total number of lanes.
Table F-6 – Adjustment factors for lane flow distribution on weaving segments
2-lane 3-lane 4-lane

Parameter segments segments segments
L1 L1 L2 L1 L2 L3
a 0.99465 0.64110 0.47799 -0.13493 0.00483 0.11993
c 0.40000 0.40000 0.33391 0.24344 0.25717 0.27102
fa,g -0.21470 -0.28453 0.11187 0.13490 -0.00483 -0.11991
fa,t -0.11511 -0.05549 -0.03308 -0.01189 -0.00483 0.01851
fa,I 0.13262 0.00370 -0.03519 -0.00252 -0.00483 -0.11993
fa,vm 0.02186 0.07467 -0.09000 0.07183 -0.03130 -0.01135
fa,vd -0.19422 -0.03564 0.01725 -0.12644 0.02999 0.05097
fa,Ls -0.19745 0.09771 -0.03081 0.05588 0.00195 -0.04056
fa,VR 0.00799 0.02427 0.08859 -0.11102 -0.00445 0.11993
fc,g 0.06882 -0.40000 0.03850 -0.03002 0.04479 0.04102
fc,t 0.00318 -0.05137 0.00449 -0.00433 -0.01122 -0.00426
fc,I -0.01613 0.40000 -0.02045 -0.00670 -0.00498 -0.00261
fc,vm -0.04763 -0.13800 0.00474 0.06457 -0.00885 -0.03777
fc,vd 0.03962 0.03917 -0.04740 0.06291 -0.01525 -0.03723
fc,Ls -0.01090 0.14690 0.00495 -0.03030 0.01073 0.01985
fc,VR 0.07777 0.40000 0.01786 -0.14324 0.04014 0.15454
The LFRs within the weave are estimated considering the number of lanes involved in weaving.
According to the HCM Chapter 13, the number of weaving lanes (NWL) is the total number of lanes from
which a weaving maneuver may be completed with one lane change or no lane changes. The auxiliary lane
358

is included in the NWL. Figure F-3 provides two weaving example configurations with the respective NWL.
The number of weaving lanes on the mainline freeway, excluding the auxiliary lane(s) is denoted as NWUP,
also shown in Figure F-3 for the two example configurations.
Figure F-3. Notation and number of weaving lanes upstream (NWUP) and within the merge (NWL) for
two weaving configurations
The methodology assumes that all mandatory weaving lane change maneuvers are completed before the
midpoint of the short weaving length (LS). This assumption is based on the results reported by (Menendez,
and He, 2016; Ahmed at al., 2019). Menendez and He (2016) concluded that about 70% of lane change
completion in the weaving segment occurred within 19% of the weaving section length during all times and
for all traffic conditions. Another study (Ahmed at al., 2019) related to weaving lane changes at the US-
101 freeway indicated that 50% of all lane changes were completed within 16% of the short length of the
weave.
The methodology also assumes that for segments with only one weaving lane upstream (NWUP=1) the
entire freeway-to-ramp flow (vFR) will be positioned in the rightmost lane (L1,UP). For segments with two
upstream weaving lanes (NWUP=2), the methodology assumes that 80% of freeway-to-ramp flow (vFR) will
be on the rightmost lane (L1,UP) while the remaining 20% will be on the adjacent lane (L2,UP). This
assumption is based on recent work by Menendez, and He, (2016); and Ahmed at al. (2019). The
distribution of flows for non-weaving vehicles (freeway-to-freeway) in the middle of the weaving segment
is assumed to be equal to that upstream of the weave.
Therefore (Figure F-4), flows within the weave are calculated assuming the entire vFR flow will be on the
auxiliary lane when it reaches the midpoint of the weave. For traffic that is on the adjacent lane, it is assumed
that it will be located on L1 when it reaches the mid-point of the weave, i.e. it will make one lane change
toward the exit by the mid-point. If the VFR exceeds the calculated upstream flow in lane 1 v1,UP, then the
extra flow is allocated to the adjacent lane when estimating the mid-point lane allocations. Thus, the
methodology checks whether there is excess traffic from vFR (vEXFR) that needs to be allocated to L2 at the
midpoint of the weave. The sum of lane flows estimated within the weave should be equal to the sum of
the upstream lane flows (freeway and merge flows).
Figure F-4. Weaving flows lane allocation for two example weaving configurations
359

The calculation steps are as follows:
Step 1. Determine the number of upstream freeway weaving lanes (NWUP) based on geometry
Step 2. Check whether vFR exceeds the estimated flow in lane 1.

These checks are based on the value of NWUP.
For NWUP = 1:
𝑣 ≤𝑣 (Equation F-9)
Set vEXFR1 = 0, if equation F-9 is true. Otherwise:

𝑣 =𝑣 − 𝑣 , (Equation F-10)
For NWUP =2:

0.8 × 𝑣 ≤𝑣 , (Equation F-11)
Set vEXFR2 =0, if equation F-11 is true. Otherwise:

𝑣 = 0.8 × 𝑣 −𝑣 , (Equation F-12)
𝑣 + (0.2 × 𝑣 ) ≤ 𝑣 , (Equation F-13)
Set vEXFR3 =0, if equation F-13 is true. Otherwise:

𝑣 =𝑣 + (0.2 × 𝑣 ) − 𝑣 , (Equation F-14)
Where:
v,FR = freeway to ramp flow (veh/h)
v1,UP = upstream weaving lane flow for lane 1 (veh/h)
vEXFR1 = excess of freeway to ramp flow that needs to be accommodated in the lane adjacent to lane 1
upstream of the weaving segment when NWUP =1
upstream of the weaving segment when NWUP = 2
Step 3. Calculate the auxiliary lane flow (v0)

𝑣 = 𝑣 +𝑣 −𝑣 (NWUP =1) or (Equation F-15)
v = 𝑣 + (0.8 ∗ 𝑣 ) (NWUP =2) 𝑖𝑓 (0.8 × 𝑣 ) ≤ 𝑣 , (Equation F-16)
𝑣 = 𝑣 + 𝑣 , (NWUP =2) 𝑖𝑓 (0.8 × 𝑣 ) > 𝑣 , (Equation F-17)
where:
v0 = auxiliary lane flow (veh/h)
vFR = freeway-to-ramp flow (veh/h)
v1,UP = upstream lane 1 flow (veh/h)
vRR = ramp-to-ramp flow (veh/h)
Step 4. Calculate the rightmost freeway weaving lane flow (v1)

𝑣 = 𝑣 + 𝑣 − (𝑣 − 𝑣 ) + 𝑣 (NWUP =1) or (Equation F-18)
𝑣 = 𝑣 , − (0.8 ∗ 𝑣 ) + (0.2 ∗ 𝑣 ) + 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) ≤ 𝑣 ,
(Equation F-19)
360

𝑣 = (0.2 ∗ 𝑣 ) + 𝑣 + 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) > 𝑣 , (Equation F-20)

𝑣 =𝑣 + 𝑣 , (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) > 𝑣 , and 𝑣 + (0.2 ∗ 𝑣 ) > 𝑣 ,
(Equation F-21)
where:
v1 = lane 1 flow (veh/h) within the weaving segment
vRF = ramp-to-freeway flow (veh/h)
upstream of the weaving segment when NWUP =1
Step 5. Calculate the freeway weaving lane flow for lane 2 (v2)
𝑣 = 𝑣 , − 𝑣 (NWUP =1) or (Equation F-22)
𝑣 = 𝑣 , − (0.2 ∗ 𝑣 ) − 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) < 𝑣 , and (0.8 ∗ 𝑣 ) > 𝑣 ,
(Equation F-23)
𝑣 = 𝑣 (NWUP =2) 𝑖𝑓 (0.8 ∗ 𝑣 ) > 𝑣 , and (0.2 ∗ 𝑣 ) + 𝑣 >𝑣 ,
(Equation F-24)
where:
Step 6. Calculate the freeway weaving lane flow for lane 3 (v3)
This step is only valid with the presence of vEXFR3 .
𝑣 = 𝑣 , − 𝑣 (Equation F-25)
where:
v3,UP = upstream lane 3 (veh/h)
Step 7. Obtain flows for the remaining lanes, which will be equal to the respective upstream flow
values.
The flows of the remaining lanes will be same as their respective upstream lane flows.
Step 8. Check whether there are v/c ratios greater than 1 for each lane.
This step checks whether any of the lane v/c ratios are greater than 1. When that occurs, flows should be
adjusted based on the procedure described above.
Capacity for lane-by-lane flow models

The method for estimating the capacity used in Equation F-1 is unique to each segment type. For basic,
merge and diverge segments, a segment capacity is a single value, measured in veh/h, obtained through the
breakdown method by measuring speed drop occurrences at different detectors within the area of study
according to the segment type:
• Basic: a mainline detector within the area of study;
• Merge: a mainline detector right after the merge location; and
• Diverge: a mainline detector right before the diverge location.
361

For the weaving segments, capacity is estimated using the method proposed in HCM 6th Edition –
Chapter 13 (Step 5, Equations 13-5 through 13-9) in passenger-cars per hour (pc/h). It should be noticed
that capacity in this method is function of the volume ratio (VR). As such, the capacity for weaving
segments may vary for different time intervals.
Reasonableness checks
After lane flow ratios are obtained, a two-step reasonableness check must be performed to ensure the
obtained flow distribution remains under feasible constraints. The first step checks for any negative flows
that may occur in any segment lane – this issue is more likely to occur in the leftmost lane, as the flows on
this lane are obtained by the difference between the total segment flow and the sum of estimated flows in
the other lanes. Therefore, if flows on the remaining lanes are overestimated the resulting flow in the
leftmost lane may become negative. Figure F-5 illustrates the recommended procedure for the first check.
Figure F-5. Reasonableness check for negative flows
The second step of the reasonableness check compares the estimated flow by lane with the respective
lane capacities to make sure no lane operates with a demand-to-capacity ratio greater than 1.The procedure
illustrated in Figure F-5. If any lane is observed to operate above its capacity, the flow in this given lane is
constrained by the capacity value and the exceeding demand is rearranged to the adjacent lane.
362

Figure F-6. Reasonableness check for lane capacity
Model application examples
Diverge segment
A practical application of the LFR model is presented next for a 3-lane diverge segment (single period
analysis), with the following input data:
• Grade (G): 3%
• Heavy vehicles (t): 4%
• Access point density (n): 2 adjacent ramps
• Mainline demand flow rate (v): 5500 veh/h
• Off-ramp demand (vR): 850 veh/h
• Measured segment capacity (c): 2050 veh/h/ln (6150 veh/h)
The flow ratio for lane 1 (right lane) is obtained by the following equation:
𝑣
𝐿𝐹𝑅 = 𝑓 ∙ ln +𝑓
𝑐
The adjustment factors fa and fc for lane 1 are obtained as follows:

𝑓 =𝑎+𝐺∙𝑓 , +𝑡∙𝑓 , +𝑛∙𝑓, + ∙𝑓 ,
𝑓 = −0.07503 + 3 ∙ 0.00768 + 4 ∙ 0.00080 + 2 ∙ 0.01382 + ∙ (−0.06664)
𝑓 = −0.07779
𝑓 = 𝑐+𝐺 ∙𝑓, +𝑡∙𝑓, +𝑛∙𝑓, + ∙𝑓,

𝑓 = 0.26667 + 3 ∙ (−0.00810) + 4 ∙ 0.00140 + 2 ∙ 0.03129 + ∙ (0.01324)
363

𝑓 = 0.3218
The lane flow ratio on lane 1 can then be obtained by:

5500
𝐿𝐹𝑅 = −0.07779 ∙ ln + 0.3218
3 ∙ 2050
𝐿𝐹𝑅 = 33.0%
The same procedure is applied to obtain the lane flow ratio on lane 2, using the respective coefficients
from Table F-5:
𝑓 =𝑎+𝐺∙𝑓 , +𝑡∙𝑓 , +𝑛∙𝑓, + ∙𝑓 ,
𝑓 = 0.0096 + 3 ∙ (−0.00960) + 4 ∙ (−0.00054) + 2 ∙ (−0.0096) + ∙ (−0.04766)
𝑓 = −0.08107
𝑓 = 𝑐+𝐺 ∙𝑓, +𝑡∙𝑓, +𝑛∙𝑓, + ∙𝑓,

𝑓 = 0.33948 + 3 ∙ (−0.00189) + 4 ∙ (0.00089) + 2 ∙ 0.00520 + ∙ (−0.07333)
𝑓 = 0.2854
5500
𝐿𝐹𝑅 = −0.08107 ∙ ln + 0.2854
3 ∙ 2050
𝐿𝐹𝑅 = 29.4%
Finally, the lane flow ratio on the leftmost lane (lane 3) can be obtained as follows:
𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.294 − 0.33
𝐿𝐹𝑅 = 37.6%
Weaving Segment
A practical application of the LFR model is presented next for a weaving segment (Figure F-7), where
the lane flow share among 5 lanes is estimated both upstream and within the weave (single period analysis).
Figure F-7. Study case on a weaving segment, with four mainline lanes upstream
The following input data are provided:

• Number of lanes within the weave (N): 5
• Number of upstream lanes (NUP): 4
• Grade (G): -0.5%
• Heavy vehicles (t): 3.3%
• Interchange density (𝐼𝐷): 0.67
• Weaving length (𝐿 ): 3920 ft
• Upstream mainline demand flow rate (vUP): 4512 veh/h
364

• On-ramp demand flow rate (vR,m): 428 veh/h

• Freeway-to-freeway demand (vFF): 3912 veh/h
• Freeway-to-ramp demand (vFR): 600 veh/h
• Ramp-to-freeway demand (vRF): 404 veh/h
• Ramp-to-ramp demand (vRR): 24 veh/h
• Off-ramp flow rate (vR,d): 624 veh/h
• Number of weaving lanes (NWL): 2
• Measured segment free-flow speed (FFS): 70 mi/h
• PHF = 1.0
LFRs and lane flows are first calculated for the upstream section of the weaving segment. The heavy-
vehicles adjustment factor can be estimated (adopting 𝐸 = 2) as:
1 1
𝑓 = = = 0.968
1 + 𝑃 (𝐸 − 1) 1 + 0.03(2 − 1)
The weaving and non-weaving demands can be adjusted to flow rates under ideal conditions. Because
the demands are estimated based on 15-minute volumes, PHF is equal to 1.
𝑉
𝑣=
𝑃𝐻𝐹 ∙ 𝑓
24
𝑣 = = 24.8 𝑝𝑐/ℎ
1 ∙ 0.968
404
𝑣 = = 417.3 𝑝𝑐/ℎ
1 ∙ 0.968
600
𝑣 = = 619.8 𝑝𝑐/ℎ
1 ∙ 0.968
3912
𝑣 = = 4041.3 𝑝𝑐/ℎ
1 ∙ 0.968
The weaving and non-weaving flows are given by

𝑣 = 𝑣 + 𝑣 = 619.8 + 417.3 = 1037.1 𝑝𝑐/ℎ
𝑣 = 𝑣 + 𝑣 = 24.8 + 4041.3 = 4066.1 𝑝𝑐/ℎ
The volume ratio is:

𝑣 1037.1
𝑉𝑅 = = = 0.203
𝑣 1037.1 + 4066.1
The capacity of the weaving segment is given by the minimum between the density-capacity (𝑐 ) and
weaving-demand-capacity (𝑐 ), which are:
𝑐′ = 𝑐 − 438.2(1 + 𝑉𝑅) . + (0.0765𝐿 ) + (119.8𝑁 )
𝑐 = 2400 𝑝𝑐/ℎ
𝑐′ = 2400 − 438.2(1 + 0.203) . + (0.0765 ∙ 3920) + (119.8 ∙ 2) = 2351 𝑝𝑐/ℎ/𝑙𝑛
𝑐 = 𝑐′ ∙ 𝑓 = 2350.5 ∙ 0.968 = 2275 𝑣𝑒ℎ/ℎ/𝑙𝑛
2400 2400
𝑐′ = = = 11822 𝑝𝑐/ℎ
𝑉𝑅 0.203
365

𝑐′ ∙𝑓 11822.5 . 0.968
𝑐 = = = 2861 𝑣𝑒ℎ/ℎ/𝑙𝑛
𝑁 4
𝑐 = min(𝑐 , 𝑐 ) = min(2275.3 ,2861.1 ) = 2275 𝑣𝑒ℎ/ℎ/𝑙𝑛
Therefore, the capacity of the weave is 2275 veh/h/ln.

The flow ratio for lane 1 (right lane) is obtained by applying Equation F-1:
𝑣
𝐿𝐹𝑅 = 𝑓 ∙ ln +𝑓
𝑐
The adjustment factors fa and fc for lane 1 are obtained as follows:

𝑣 , 𝑣 , 𝐿
𝑓 , = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + ∙𝑓, + ∙𝑓 , + ∙𝑓
+ 𝑉𝑅 ∙ 𝑓 , ,
1000 1000 1000
428
𝑓 , = −0.1349 + (−0.5) ∙ 0.1349 + (3.3) ∙ (−0.0119) + 0.67 ∙ (−0.0025) + ∙ 0.0718
1000
624 3920
+ ∙ (−0.1264) + ∙ (0.0558) + 0.203 ∙ (−0.1111)
1000 1000
𝑓 , = −0.0953
𝑣 , 𝑣 ,
𝐿
𝑓, =𝑐+ 𝐺∙𝑓, +𝑡∙𝑓, +𝐼 ∙𝑓, + ∙𝑓 + ∙𝑓 +
∙ 𝑓 + 𝑉𝑅 ∙ 𝑓 ,
1000 , 1000 ,
1000 ,
428
𝑓 , = 0.2434 + (−0.5) ∙ (−0.03) + (3.3) ∙ (−0.004) + 0.67 ∙ (−0.0067) + ∙ 0.0645
1000
624 3920
+ ∙ (0.0629) + ∙ (−0.0303) + 0.203 ∙ (−0.1432)
1000 1000
𝑓 = 0.1606
The lane flow ratio of lane 1 upstream of the weave is:

4512
𝐿𝐹𝑅 = −0.0953 ∙ ln + 0.1606
4 ∙ 2275.3
𝐿𝐹𝑅 = 22.8%
The same procedure is applied to obtain the lane flow ratio on lane 2, using the respective coefficients
from Table F-6:
𝑣 , 𝑣 , 𝐿
𝑓 , =𝑎+𝐺∙𝑓 , +𝑡∙𝑓 , +𝐼 ∙𝑓 , + ∙𝑓, + ∙𝑓 , + ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 ,
1000 1000 1000
428
𝑓 , = 0.0048 + (−0.5) ∙ (−0.0048) + (3.3) ∙ (−0.00482) + 0.67 ∙ (−0.00482) +
1000
624 3920
∙ (−0.0313) + ∙ (0.03) + ∙ (0.0019) + 0.203 ∙ (−0.0044)
1000 1000
𝑓 = −0.00012
𝑣 , 𝑣 , 𝐿
𝑓, =𝑐+ 𝐺∙𝑓, +𝑡∙𝑓, +𝐼 ∙𝑓, + ∙𝑓 + ∙𝑓 + ∙𝑓
+ 𝑉𝑅 ∙ 𝑓 ,
1000 , 1000 , 1000 ,
428
𝑓, = 0.2571 + (−0.5) ∙ (0.0447) + (3.3) ∙ (−0.0112) + 0.67 ∙ (−0.0049) +
1000
624 3920
∙ (−0.0088) + ∙ (−0.0152) + ∙ (0.0107) + 0.203 ∙ (0.0401)
1000 1000
𝑓, = 0.2310
The LFR of upstream lane 2 can then be obtained by:
366

4512
𝐿𝐹𝑅 = − 0.00012 ∙ ln + 0.2310
4 ∙ 2275.3
𝐿𝐹𝑅 = 23.1%
The same procedure is applied to obtain the LFR on lane 3, using the respective coefficients from
Table F-6:
𝑣 , 𝑣 ,
𝑓 , = 𝑎 + 𝐺 ∙ 𝑓 , + 𝑡 ∙ 𝑓 , + 𝐼𝐷 ∙ 𝑓 , + ∙𝑓, + ∙ 𝑓 , + 𝐿 ∙ 𝑓 , + 𝑉𝑅 ∙ 𝑓 ,
1000 1000
428
𝑓 , = 0.12 + (−0.5) ∙ (−0.1199) + (3.3) ∙ (0.0185) + 0.67 ∙ (−0.1199) + ∙ (−0.0113)
1000
624 3920
+ ∙ (0.0509) + ∙ (−0.0405) + 0.203 ∙ (0.1199)
1000 1000
𝑓 , = 0.0524
𝑣 , 𝑣 ,
𝑓, =𝑐+ 𝐺∙𝑓, +𝑡∙𝑓, +𝐼 ∙𝑓, + ∙𝑓 + ∙𝑓 +𝐿 ∙𝑓, + 𝑉𝑅 ∙ 𝑓 ,
1000 , 1000 ,
428
𝑓 , = 0.2710 + (−0.5) ∙ (0.0410) + (3.3) ∙ (−0.0042) + 0.67 ∙ (−0.0026) +
1000
624 3920
∙ (−0.0377) + ∙ (−0.0372) + ∙ (0.0198) + 0.203 ∙ (0.1545)
1000 1000
𝑓 , = 0.3039
The LFR of lane 3 can then be obtained by:

4512
𝐿𝐹𝑅 = 0.0524 ∙ ln + 0.3039
4 ∙ 2275.3
𝐿𝐹𝑅 = 26.7%
Finally, the LFR on the leftmost lane (lane 4) can be obtained as follows:
𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.228 − 0.231 − 0.267
𝐿𝐹𝑅 = 27.4%
In summary, the lane flows upstream of the weave are as follows:

𝑣 , = 4512 ∙ 0.228 = 1029 veh/h
𝑣 , = 4512 ∙ 0.231 = 1043 veh/h
𝑣 , = 4512 ∙ 0.267 = 1204 veh/h

𝑣 , = 4512 ∙ 0.274 = 1236 veh/h
Based on these, we calculate the LFRs and lane flows within the weave.
Step 1: Determine the number of upstream freeway weaving lanes (NWUP) based on geometry
N =1, obtained from Figure F-7
Step 2: Check for VFR

𝑣 , = 1029 veh/h
𝑣 = 600 veh/h
Here, v < v ,
367

Hence, the entire freeway-to-ramp flow will be located at the upstream freeway-weaving lane and
v =0.
Step 3: Calculate auxiliary lane flow (v0)

𝑣 = 𝑣 +𝑣 −𝑣 (NWUP =1)
𝑣 = 24 + (600 -0) = 624 veh/h
Step 4: Calculate the lane 1 flow (v1)

𝑣 = 𝑣 + 𝑣 − (𝑣 − 𝑣 ) + 𝑣 (NWUP =1)
𝑣 = 404 + {1029 – (600-0)} + 0 = 833 veh/h
Step 5: Calculate the lane 2 flow (v2)

𝑣 = 𝑣 , − 𝑣 (NWUP =1)
𝑣 = 1043 – 0 = 1043 veh/h
Step 6 Calculate the lane 3 flow (v3)

This step does not apply since NWUP =1.
Step 7. Obtain flows for the remaining lanes, which will be equal to the respective upstream flow
values.
𝑣 = 𝑣 , = 1204 veh/h
𝑣 =𝑣 , = 1236 veh/h
Step 8. Check whether there are v/c ratios greater than 1 for each lane.
Given the following flows and capacities for each lane within the weave:
𝑣 = 624 veh/h, 𝑣 = 833 veh/h, 𝑣 = 1043 veh/h, 𝑣 = 1204 veh/h, 𝑣 = 1236 veh/h
𝑐 = 𝑐 = 𝑐 = 𝑐 = 𝑐 = 2275 veh/h
Checking v/c ratios for each lane:

Lane 1: 624/2275 = 0.27 < 1.0 (OK)
Lane 2: 833/2275 = 0.37 < 1.0 (OK)
Lane 3:1043/2275 = 0.45 < 1.0 (OK)
Lane 4:1204/2275 = 0.59 < 1.0 (OK)
Lane 5: 1236/2275 = 0.54 < 1.0 (OK)
Speed-Flow Curves by Lane and by Segment Type

This section presents the models developed to obtain speed-flow curves for each lane in a freeway
segment, as a function of two key inputs: free-flow speed (FFS) and lane capacity. The first part of the
section discusses the estimation of lane FFS, while the next part presents models for obtaining lane
capacities. The last part provides the speed-flow models obtained as a function of lane FFS and lane
capacities.
368

Lane FFS
Field observations have shown that operating speeds differ among lanes, and they are typically lower in
shoulder lanes and higher in median lanes. Free-flow speeds were measured as the average speed for
segment flow rates below 450 veh/h/ln. This criterion is consistent with HCM guidance, which recommends
measuring FFS for flows no greater than 500 pc/h/ln.
Next, lane FFS were modeled as a function of the segment FFS and as a function of the number of lanes
on the segment, as shown in Figure F-8. Due to the ramp influence on traffic flow, merge and diverge
segments are likely to have different distributions of FFS. Therefore, distinct models were developed by
segment type. Linear regression models were developed with the intercept set to zero.
As it can be observed in Figure F-8, there is a good correlation between segment and lane FFS, confirming
field observations: shoulder lanes’ FFS are lower than the segment average, while median lanes’ FFS are
higher. Center lanes typically have FFS values very close to the segment average.
Figure F-8. Segment FFS and lane FFS, by segment type and number of lanes
369

Based on the obtained results, models were developed to estimate individual lane FFS by applying a
multiplying factor to the segment FFS. These models are shown in Figure F-8 for each lane. Table F-7
summarizes the recommended multipliers which are provided as a function of the segment type and the
number of lanes in the segment. As shown, when the number of lanes increases, the range of FFS multipliers
increase as well (i.e. there are lower speeds in the shoulder lanes and higher speeds on the median lanes).
For 2-lane segments, merge and diverge segments have a higher difference in FFS between the two lanes
when compared to basic segments. For 3-lane segments, basic segments show the highest FFS range, while
merge segments have more uniform lane FFS. As for 4-lane segments, merge segments show the highest
FFS range, followed by basic and merge segments yield similar results.
Table F-7. Multipliers to estimate lane FFS from segment FFS
FFS Multiplier
Segment Number of
type lanes L1 L2 L3 L4
2 lanes 0.965 1.032
Basic 3 lanes 0.934 1.010 1.087
4 lanes 0.924 0.989 1.028 1.079
2 lanes 0.964 1.044
Merge 3 lanes 0.955 1.015 1.045
4 lanes 0.935 0.991 1.036 1.091
2 lanes 0.961 1.035
Diverge 3 lanes 0.943 1.024 1.068
4 lanes 0.933 0.975 1.018 1.074
2 lanes 0.969 1.018
Weaving 3 lanes 0.968 1.023 1.062
4 lanes 0.910 0.988 1.053 1.110
Capacity for speed flow curves by lane

Individual lane capacities were obtained through the breakdown observation approach, as previously
described. Although the literature shows that lanes may break down at different times, especially on ramp
segments, using 15-min aggregated data allows using the assumption that all lanes break down within one
time period.
The process for measuring lane capacities is illustrated in Figure F-8 based on an example merge segment
with 3 lanes. At the 85th percentile, the estimated segment capacity is 1561 veh/h/ln. However, the 85th
percentile approach for different lanes yields significantly different flows at breakdown (Figure F-9a): 1132
veh/h/ln (lane 1), 1604 veh/h/ln (lane 2) and 2064 veh/h/ln (lane 3). These values are taken as the estimated
capacities of individual lanes. When considered as the relative proportion of total flow, lane capacities can
be estimated as 24%, 33% and 43% of total capacity for lanes 1, 2 and 3, respectively. Figure F-9b shows
the distribution of LFRs as a function of segment capacity. As observed, at higher volumes the flow
distribution is stable at the time of breakdown, showing that lane capacities can be consistently measured
using this approach.
370

Figure F-9. Example of lane capacity estimation (French Camp, CA): (a) lane flow distribution at
breakdown and (b) LFRs as a function of segment capacity
The same rationale was applied to all locations in the database. Figure F-10 shows the relationship
between the measured segment capacities and their respective capacities for individual lanes. As it can be
observed, capacity typically increases from the rightmost to the leftmost lanes, with center lanes showing
capacity values similar to the segment average.
371

Figure F-10. Relationship between segment capacity and individual lane capacity, by segment type
and number of lanes
For weaving segments, capacity distributions were observed to be significantly more complex and the
breakdown observation method was not capable of providing reliable results from the selected dataset.
Capacity is assumed uniform for all lanes within a weaving segment, obtained by HCM Equation 13-5
(based on a maximum density of 43 pc/h/ln):
𝑐 = 𝑐 − 438.2 (1 + 𝑉𝑅) . + (0.0765 𝐿 ) + (119.8𝑁 ) (Equation F-27)
372

Next, results were averaged by segment type and number of lanes. Figure F-11 presents the percent
distribution of the total segment capacity across lanes (the numbers below the whisker boxes represent the
average values of lane capacity).
Figure F-11. Capacity of individual lanes as a percentage of segment capacity, by segment type and
number of lanes
The segment capacities measured from field data may not be equal to the estimated capacities using HCM
methodologies. According to the HCM Equation 12-6, base capacity can be estimated as:
𝑐 = 𝑚𝑖𝑛 2200 + 10 𝑥 (𝐹𝐹𝑆 − 50), 2400 (Equation F-28)
373

For each location from the dataset, base capacity was calculated using Equation F-28, as FFS is available
from field measurements. Since this equation provides capacity values in passenger-car equivalents, a heavy
vehicle factor fHV (as defined in HCM Equation 12-10) was applied to convert the base capacity to veh/h
and then make the unit consistent with field data.
Figure F-12 shows the comparison of capacity values measured from the field against theoretical
estimates using the HCM methods. All observations yielded field measurements smaller than the estimated
capacities provided by the HCM. When different segment types are compared, however, no clear
conclusions can be drawn on which lanes have higher differences between field and estimated capacities.
The field measurements of capacity are, on average, 21.7% smaller than their respective HCM estimations.
It is a significant difference that can lead to inaccurate capacity analyses, as the HCM methodologies may
overestimate capacity and therefore overestimate the overall segment performance. For this reason, it is
recommended that capacity adjustment factors (CAFs) are applied to adjust the estimated capacities to local
conditions. Additional research is recommended to further investigate the calibration of CAFs.
374

Figure F-12. Field measured and HCM estimated capacity values, for (a) basic segments, (b) merge
segments and (c) diverge segments
375

With flow, capacity and FFS by lane determined, HCM equations can be used to estimate operating
speeds on individual lanes. Segment-wise inputs of flow, capacity and FFS are based on the field
measurements, and the developed methods previously described are applied to estimate their distribution
among individual lanes.
For basic segments, average speed is determined as:
𝑆 = 𝐹𝐹𝑆 − ( )
(Equation F-29)
This model is applied to individual lanes, as the three key parameters (FFS, c and vp) are input by lane.
The breakpoint value (BP) is also determined for each lane (Equation F-30).
𝐵𝑃 = 1000 + 40 𝑥 75 − 𝐹𝐹𝑆 𝑥 𝐶𝐴𝐹 (Equation F-30)
It is worth noting that a capacity adjustment factor (CAF) is considered in the estimation of the
breakpoint. The HCM method defines the adjusted capacity cadj as the product of the base capacity by a
capacity adjustment factor (CAF), which typically reflects impacts of weather, incident, work zone, driver
population, and calibration adjustments.
𝑐 = 𝑐 𝑥 𝐶𝐴𝐹 (Equation F-91)
As field values of segment capacities were obtained, these can be inserted into Equation F-31 as the value
of adjusted capacity. Therefore, CAFs become the single unknown in the equation and can be easily
obtained.
Practical example
A practical example was developed to verify and illustrate the developed methodology. A 2-lane basic
segment was modeled and the lane-by-lane performance is compared to field data (CA-1 NB – Santa Cruz,
CA). Field measured parameters are as follows:
• Free-flow speed: 69.1 mph
• Capacity: 3993 veh/h (1996.5 veh/h/ln)
• % heavy vehicles: 1.7
• Grade: 3% (rolling)
By applying the multiplying factors obtained in Table F-7 to the segment FFS, individual FFS can be
FFS1 = FFS x 0.965 = 69.1 x 0.965 = 66.68 mph
FFS2 = FFS x 1.032 = 69.1 x 1.032 = 71.31 mph
Next, lane capacities are obtained by applying the multiplying factors obtained in Figure F-11 to the
capacity as follows:
c1 = c x 44% = 3993 x 44% = 1757 veh/h
c2 = c x 56% = 3993 x 56% = 2236 veh/h
For comparison purposes, HCM methods would obtain the following theoretical capacity value:
c = [2200 + 10 x (FFS – 50)] x fHV = [2200 + 10 x (69.1 - 50) )] x 0.967 = 2312 veh/h/ln
Therefore, the recommended CAF for this location is obtained by dividing field measured by theoretical
values of capacity:
CAF = cadj/c = 1996.5/2312 = 0.864
376

Next, the breakpoint values for each lane can be obtained:

BP1 = [1000+ 40 x (75-FFS1)] x CAF2 = [1000+ 40 x (75-66.68)] x 0.8642 = 995 veh/h
BP2 = [1000+ 40 x (75-FFS2)] x CAF2 = [1000+ 40 x (75-71.31)] x 0.8642 = 857 veh/h
Flows on each lane can be obtained by applying the model described in Equation F-1 to the flow rate
entering the segment. Next, speeds on individual lanes using the speed-flow relationship described in
Equation F-29. For this location, a sample of 14690 observations (15-min each) was randomly selected,
and then predicted values are compared to field data in Figure F-12.
Figure F-13. Field vs. predicted speed-flow curve for (a) Lane 1 and (b) Lane 2 (CA-1 NB – Santa
Cruz, CA)
As observed, the individual speed-flow models can replicate field conditions with good accuracy.
Naturally, the oversaturated portion of the curve cannot be addressed by the model, as this is already a
limitation of the existing method.
377

APPENDIX G
Glossary
General Acronyms
𝐴𝑇𝐷𝑀 = Active Traffic and Demand Management;
𝐴𝑊𝑆𝐶 = all-way stop controlled intersection;
𝐷𝐷𝐼 = diverging diamond interchange;
𝐷𝑂𝑇 = Department of Transportation;
𝐸𝐵 = eastbound;
𝐹𝐻𝑊𝐴 = Federal Highway Administration;
𝐻𝐶𝑀 = Highway Capacity Manual;
𝐼𝐶𝑀 = Integrated Corridor Management;
𝐼𝑅𝑇 = interchange ramp terminal;
𝑀𝑂𝐸 = Measures of Effectiveness;
𝑁𝐵 = northbound;
𝑄𝐴𝑃 = queue accumulation polygon;
𝑆𝐵 = southbound;
𝑆𝑃𝑈𝐼 = single-point urban interchange;
𝑇𝑊𝑆𝐶 = two-way stop controlled intersection;
𝑊𝐵 = westbound.
General Values
𝑑/𝑐 = demand to capacity ratio;
𝐸𝐷 = expected demand (veh/h);
𝐹𝐹𝑆 = free flow speed (mi/h);
𝐺 = grade (%);
𝐿𝑂𝑆 = level of service;
𝑂 − 𝐷 = origin-destination;
𝑃𝑀𝑇 = personal miles traveled (mi);
𝑣/𝑐 = volume/capacity ratio
𝑉𝑀𝑇 = vehicle miles traveled (mi).
378

1. Arterial Facilities
1.1. General concepts

𝑐 = merging capacity at the freeway (veh/h);
𝑐 = capacity of ramp proper (pc/h) (Eq. 38-2); capacity of the off-ramp roadway (pc/h) (Eq. 38-A1, 38-A3,
38-A6);
𝐿 = average vehicle spacing in stationary queue (ft/veh);
𝜆 = departure rate from the major-street left-turn into the on-ramp (veh/h);
𝜆 = total on-ramp demand throughput (pc/h);
𝜆 = departure rate from major street right turn into the on-ramp (veh/h);
𝜆 = departure rate from the minor street through into the on-ramp (veh/h);
𝑄 ,( ) = 95th percentile of queue, where (a) = approach direction (veh);
𝑠 = saturation flow rate of movement 𝑖 (veh/h/ln);
𝑣 = maximum entering flow rate for the intersection approach (veh/h);
𝑥( ) = volume-to-capacity ratio for approach direction a
1.2. Signalized Intersections

𝑐 = capacity for approach 𝑖 (veh/h);
𝑔 = green extension time (s);
𝑔 = green service time (s);
𝑙 = start-up lost time (s);
𝑙 = clearance lost time (s);
𝑁 , = total number of vehicles discharged from each protected movement 𝑖;
𝑁 , = total number of vehicles discharged from each permitted movement 𝑖;
𝑁 ,, = total number of vehicles discharged for movement 𝑖 during the green extension time;
𝑁 ,, = total number of vehicles discharged for movement 𝑖 during the queue service time;
𝑞 = arrival flow rate during the effective green time = 𝑃 𝑞 𝐶/𝑔 (veh/s);
𝑟 = effective red time (s);
𝑅 = platoon ratio;
𝑋 = demand-to-capacity ratio for spillback conditions.
1.3. TWSC Intersections

N(t) = number of queued vehicles along the on-ramp at time t;
379

1.4. AWSC Intersections

𝑐 , = potential capacity for the minor street through (veh/h);
N(t) = number of queued vehicles along the on-ramp at time t;
ℎ = departure headway during queue spillback (s/veh);
1.5. Roundabouts
𝜆( ), = maximum throughput for (a) movement (pc/h);
𝑐 ,( ) = entry lane capacity for roundabout approach, where (a) = approach direction (pc/h);
𝑑( ) = average control delay for (a) approach (sec/veh);
𝑑 = additional delay due to on-ramp spillback (sec/veh);
ℎ , = departure headway for the major street left turn (s);
ℎ , = departure headway for the major street right turn (s);
ℎ , = departure headway for the minor street through (s);
ℎ = departure saturation headway into the on-ramp (s/veh);
p(a)- of demand from NB approach a into the on-ramp
𝑄 = expected queue length QSP along the on-ramp during a 15-minute period analysis;
𝑄 = total number of vehicles queued during a 15-minute time period analysis;
𝑣( ), = flow rate for roundabout approach a (veh/h)
𝑣 ,( ), = circulating flow rate for roundabout approach a (veh/h)
𝑣 ,( ), = entry flow rate for roundabout approach a (veh/h)
total number of vehicles queued during a 15-minute time period analysis
2. Freeway Facilities
2.1. Lane by lane analysis

∆𝑁𝑉(𝑖, 𝑡, 𝑝)= additional density of segment 𝑖 at the end of time step 𝑡 during time interval 𝑝 (veh/mi/ln);
𝐿𝐹𝑅 = lane flow ratio;
𝑎 = empirical constant;
𝐵𝑃 = breakpoint value;
𝑐 = empirical constant;
𝐶𝐴𝐹 = capacity adjustment factor for the upstream freeway area;
𝑓 = adjustment factor for 𝑎; (Eq. 38-3, 38-C2, 38-C3, 38-C5, 38-C7)
380

𝑓, = adjustment factor for 𝑎; due to impact of grade;

𝑓 , = adjustment factor for 𝑎; due to impact of interchange density;
𝑓, = adjustment factor for 𝑎; for length of the weaving segment;
𝑓, = adjustment factor for 𝑎; due to impact of access point density;
𝑓 , = adjustment factor for 𝑎; due to impact of trucks;
𝑓, = adjustment factor for 𝑎; for off-ramp flow;
𝑓, = adjustment factor for 𝑎; for on-ramp flow;
𝑓, = adjustment factor for 𝑎; due to impact of ramp flow;
𝑓, = adjustment factor for 𝑎; for volume ratio;
𝑓 = adjustment factor for 𝑐; (Eq. 38-3, 38-C2, 38-C4, 38-C6, 38-C8)
𝑓, = adjustment factor for 𝑐; due to impact of grade;
𝑓 , = adjustment factor for 𝑐; due to impact of interchange density;
𝑓, = adjustment factor for 𝑐; for length of the weaving segment;
𝑓, = adjustment factor for 𝑐; due to impact of access point density;
𝑓 , = adjustment factor for 𝑐; due to impact of trucks;
𝑓, = adjustment factor for off-ramp flow;
𝑓, = adjustment factor for on-ramp flow;
𝑓, = adjustment factor due to impact of ramp flow;
𝑓, = adjustment factor for volume ratio;
ℎ = reaction headway (s);
𝐼𝐷 = interchange density (veh/mi/ln);
𝐾𝐵 = background density (veh/mi/ln);
𝑛 = access point density – number of ramps half a mile upstream and half mile downstream (veh/mi/ln);
𝑡 = truck percentage (%);
𝑣 = segment entering demand (pc/h);
𝑣 = ramp flow for freeway analysis (veh/hr);
𝑣 , = off-ramp flow for freeway analysis (veh/hr);
𝑣 , = on-ramp flow for freeway analysis (veh/hr); and
𝑉𝑅 = volume ratio (weaving volume/total volume).
2.2. Off-ramp queue spillback

𝑐 = capacity of ramp proper (pc/h) (Eq. 38-2); capacity of the off-ramp roadway (pc/h) (Eq. 38-A1, 38-A3,
38-A6);
𝑓 = adjustment factor for driver population;
𝐾𝐵𝐵𝐿(𝑖, 𝑡, 𝑝) = background density (pc/mi/ln) of the blocked portion of segment 𝑖 during time step 𝑡 in time interval 𝑝;
𝐾𝐵𝑈𝐵(𝑖, 𝑡, 𝑝) = background density (pc/mi/ln) of the unblocked portion of segment 𝑖 during time step 𝑡 in time interval 𝑝;
𝐿 = section 𝑖 length (ft);
𝐿 (𝑖, 𝑝) = available deceleration lane length (ft) for segment 𝑖 during time period 𝑝;
𝐿 ,𝐿 = available queue storage distance (ft/ln);
𝐿 = length of the weaving segment (ft);
381

𝐿𝐹𝑅 = share of the total flow on lane 𝑖

𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) = actual flow that can exit at off-ramp 𝑖 during time step 𝑡 in time interval 𝑝 (veh/h);
𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) = maximum output flow rate that can enter the merge point from on-ramp 𝑖 during time step 𝑡 in time
interval 𝑝 (veh/h);
𝑂𝑁𝑅𝑄 = onramp queue length (veh);
𝑀𝐹𝐵𝐿(𝑖, 𝑡, 𝑝) = mainline flow rate that can cross the blocked portion of node 𝑖 during time step 𝑡 in time interval 𝑝;
𝑀𝐹𝑈𝐵(𝑖, 𝑡, 𝑝) = mainline flow rate that can cross the unblocked portion of node 𝑖 during time step 𝑡 in time interval 𝑝;
𝑀𝐼𝐵𝐿(𝑖, 𝑡, 𝑝) = maximum flow desiring to enter the blocked portion of node 𝑖 during time step 𝑡 in time interval 𝑝;
𝑀𝐼𝑈𝐵(𝑖, 𝑡, 𝑝) = maximum flow desiring to enter the unblocked portion of node 𝑖 during time step 𝑡 in time interval 𝑝;
𝑀𝑄1(𝑖, 𝑡, 𝑝) = mainline queue length of off-ramp unserved vehicles in the rightmost mainline lane, for segment 𝑖 during
time period p in time interval 𝑡;
𝑀𝑄2(𝑖, 𝑡, 𝑝) = mainline queue length of off-ramp unserved vehicles in the rightmost mainline lane, for segment 𝑖 during
time period p in time interval 𝑡;
𝑁, = number of lanes in section 𝑖 that are associated to ramp lane 𝑘;
𝑁 = number of approaching lanes for lane group 𝑚;
𝑁𝑉 = number of vehicles (veh);
𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖) = index of the nearest downstream diverge segment relative to subject node 𝑖;
𝑂𝐹𝑅𝐷𝐼𝑆𝑇(𝑖) = distance (ft) from node 𝑖 to the start of the deceleration lane at the nearest downstream off-ramp;
𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡, 𝑝) = queue length of off-ramp unserved vehicles for diverge segment 𝑖 during time period 𝑝 in time interval 𝑡;
𝑂𝐹𝑅𝐹𝑈𝑃(𝑖, 𝑡, 𝑝) = flow that can exit at the closest off-ramp downstream of 𝑖 during time step 𝑡 in time interval 𝑝;
𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡, 𝑝)= number of off-ramp unserved vehicles for segment 𝑖 during time period p in time interval 𝑡;
𝑄 = queue growth during analysis period 𝑖 (pc);
𝑄𝐼𝐴(𝑖, 𝑝) = length of the queue influence area (ft) for segment 𝑖 during time period 𝑝 (ft);
𝑄, = number of queued vehicles in Ramp Lane 𝑘, during a 15-min interval (pc);
𝑄 , = number of queued vehicles from Lane Group 𝑚 associated with ramp lane 𝑘, during a 15-min interval
(pc);
𝑄 = maximum queue length on the ramp (pc);
𝑄 %, = estimated back of queue length (nth percentile), as defined in Equation 31-150 (veh/ln);
𝑄 = length of queue beyond ramp storage distance (ft);
𝑄 = queue length during for the analysis period 𝑡 (pc);
𝑅 = on-ramp storage ratio (veh);
𝑅𝐶(𝑖, 𝑝)= Capacity of the ramp proper (pc/h) during time period 𝑝 in time interval 𝑡;
𝑅𝐹(𝑖, 𝑡, 𝑝) = flow (pc/ts) that can enter the ramp proper at segment 𝑖 during time period p in time interval 𝑡;
𝑅𝐼(𝑖, 𝑡, 𝑝) = maximum flow (pc/ts) desiring to enter the off-ramp on segment 𝑖 during time period 𝑝 in time interval 𝑡;
𝑅𝐾𝐵(𝐼, 𝑡, 𝑝) = ramp proper queue density (pc/mi/ln) for segment 𝑖 during time period p in time interval 𝑡;
𝑅𝐾𝐶 = ramp density at capacity (pc/mi/ln);
𝑅𝐿(𝑖) = length of ramp proper (ft) for segment 𝑖;
𝑅𝑀(𝑖, 𝑡, 𝑝) = metering rate at on-ramp 𝑖 during time step 𝑡 in time interval 𝑝 (veh/h);
𝑅𝑁(𝑖) = number of ramp lanes for segment 𝑖;
𝑅𝑁𝑉(𝑖, 𝑡, 𝑝) = maximum number of vehicles (pc) within the ramp of segment 𝑖 at the end of time step 𝑡 during time
interval 𝑝;
𝑅𝑈𝑉(𝑖, 𝑡, 𝑝) = number of unserved vehicles at the entrance of the ramp proper of segment 𝑖 at the end of time step 𝑡
382

during time interval 𝑝;

𝑆 = number of computational time steps in an analysis period;
𝑠 = measured speed at the beginning of congestion at the upstream detector (mi/h)
𝑆𝐵𝐾𝑄 (𝑖, 𝑡, 𝑝) = spillback queue density for segment 𝑖 during time period 𝑝 in time interval 𝑡;
𝑆𝐵 (𝑖, 𝑡, 𝑝) = capacity adjustment when one or more lanes of segment 𝑖 are entirely blocked during time period 𝑝 in
time interval 𝑡;
𝑆𝐵 (𝑖, 𝑡, 𝑝) = capacity adjustment factor for approaching vehicles within the queue influence area upstream of an off-
ramp queue;
𝑆𝐵𝐿𝐶(𝐼, 𝑡, 𝑝) = number of lane change maneuvers within the Queue Influence Area at node 𝐼, during time step 𝑡 in time
interval 𝑝;
𝑆𝐵𝐿𝑄(𝑖, 𝑡, 𝑝) = queue length within segment 𝑖 during time period 𝑝 in time interval 𝑡;
𝑆𝐿(𝑖, 𝑝) = available shoulder length (ft) for segment 𝑖 during time period 𝑝;
𝑇𝐼𝐴 = total influence area (ft);
𝑣 = on-ramp flow rate (veh/h) (Eq. 38-B10); off‐ramp demand for the period (pc/h) (Eq. 38-A1, 38-A3, 38-
A6);
383

HCM 2020 PDF

Uploaded by

Copyright:

Available Formats

HCM 2020 PDF

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

HCM 2020 PDF

Uploaded by

Copyright:

Available Formats

THE NATIONAL ACADEMIES PRESS

This PDF is available at http://nap.edu/25963 SHARE

Highway Capacity Manual Methodologies for Corridors

390 pages | 8.5 x 11 | PAPERBACK

National Academies of Sciences, Engineering, and Medicine 2020. Highway

– Access to free PDF downloads of thousands of scientiﬁc reports

Copyright © National Academy of Sciences. All rights reserved.

Highway Capacity Manual Methodologies for Corridors

University of Florida Transportation Institute

Contractor’s Final Report for NCHRP Project 15-57

NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM

Copyright National Academy of Sciences. All rights reserved.

Learn more about the Transportation Research Board at www.TRB.org.

Copyright National Academy of Sciences. All rights reserved.

COOPERATI VE RESEAR CH PROGRAMS

CRP STAFF FOR NCHRP WEB-ONLY DOCUMENT 290

NCHRP PROJECT 15-57 PANEL

Copyright National Academy of Sciences. All rights reserved.

APPENDIX A. CHAPTER 38: SYSTEM ANALYSES .......................................................... 47

Copyright National Academy of Sciences. All rights reserved.

Figure 1 – HCM service measures by system element and mode .................................................. 8

Copyright National Academy of Sciences. All rights reserved.

Figure 32 – Comparison of lane flow distribution on two different 2-lane segments:

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

The limitations of the methods include the following:

Queue spillback into freeways:

Queue spillback into urban streets:

Freeway lane by lane analysis:

Copyright National Academy of Sciences. All rights reserved.

Research Objectives and Report Organization

Copyright National Academy of Sciences. All rights reserved.

Spillback Effects from Urban Streets to Freeways

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

Spillback Effects from Freeways to Urban Streets

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

3. Critical Review of the HCM

Overview of Performance Measures and Service Measures for HCM Analyses

Source: Highway Capacity Manual 6th edition - Exhibit 2-2

Copyright National Academy of Sciences. All rights reserved.

Source: Highway Capacity Manual 6th Ed. - Exhibit 14-7

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

Type of Measures Key Features

Lane-to-Lane Speed Variability

Figure 3 – Recommended performance measure framework for different evaluation purposes

Copyright National Academy of Sciences. All rights reserved.

5. Queue Spillback into Freeways

Copyright National Academy of Sciences. All rights reserved.

Copyright National Academy of Sciences. All rights reserved.

Table 1 – Data sources by State DOT – off-ramp queue spillback

State Detector Data Source Video Recordings Source

Copyright National Academy of Sciences. All rights reserved.

Table 2 – Summary of study locations – data collection – off-ramp queue spillback

Copyright National Academy of Sciences. All rights reserved.