Lesson 2 - Transportation Planning
Lesson 2 - Transportation Planning
Lesson 2 - Transportation Planning
Transportation Planning
1
Transportation Planning
2
■ Application of the concept of planning to the transportation system
makes it possible to formulate policies and develop programs that will
lead to improvements in the system.
■ Thus, transportation planning is the process by which;
• current information and data on socio-economic activities,
• transportation needs,
• trips,
• travel patterns and behaviour
are used to obtain the relevant information and data on future socio-
economic activities and transportation needs.
3
Objectives of Transportation Planning
4
■ Land use analysis has become a convenient way of studying
the activities that provide the basis for trip generation as
travel patterns are dictated by the transportation network and
land-use arrangements.
■ Planning highway network extensions in order to improve the
transportation system should be based on both connectivity
and future demands for travel.
■ Urban activity forecast is used to provide information
regarding activities that might influence travel in the urban
area.
5
Travel Demand Forecasting
■ Travel demand forecasting is a conditional prediction of the
amount of travel likely to be associated with a predicted land-use
pattern in a target or horizon year (future time).
■ The demand is necessary for transportation planners to decide
which part of the transportation system has to be improved,
what type of improvement is needed and at what time.
■ It also helps to evaluate the consequences on the transportation
system of several candidate transportation alternatives being
considered for implementation including the do-nothing
alternative.
6
■ To forecast the demand for travel, it is necessary to first
forecast socio-economic projections and urban activities.
■ Forecasts on socio-economic projections and urban activities
provide estimates of future land-use patterns, i.e., where
people will live and where businesses will be located.
■ The forecasts will also provide information on the intensity of
activity such as the number of households and the number of
employees in businesses, car ownership, amount of vacant
land, etc.
7
■ In the forecasting process, we attempt to predict by modelling
a trip maker’s travel behaviour regarding his
• decision to travel,
• choice of destination,
• choice of travel mode and
• choice of travel path or route.
8
■ The traditional method of forecasting travel demand is to
apply a sequential four-step procedure made up of the
following:
• Trip generation
• Trip distribution
• Modal choice
• Network/Trip Assignment
9
■ In the sequential process (see the figure below), the output of
one step becomes the input of the next.
Trip Generation
Trip Distribution
Modal Choice
Network/Trip Assignment
10
a) Trip generation
11
■ A trip is an event consisting of two ends (A and B as shown
below); a beginning point and a termination point.
A B
12
■ Consider a trip to work in the morning from the home located
in Zone A to the work place located in Zone B.
Trip
Zone A Zone B Remarks
Period
Morning Origin Destination Trip from home to work
Evening Destination Origin Trip from work to home
• In the morning, the trip has Zone A as the origin and Zone B as
the destination; at the close of work, the return trip home has
Zone B as the origin and Zone A as the destination.
13
■ From the foregoing, the terms “origin” and “destination” are
used for directional references in respect of trips and do not
bear any association with the land-use activity generating the
trips.
■ The terms trip production and trip attraction are more
appropriate to use when the nature of land use is considered.
■ Thus, a trip production, is the trip end associated with
residential land-use.
■ A trip attraction is the trip end associated with non-residential
land use.
14
■ In the case of the work trip between Zone A and Zone B cited
above, Zone A is always the trip production end and Zone B the
trip attraction end irrespective of where the trip begins or ends.
■ We note that not all trips occurring within urban areas may be
characterized by a trip production and a trip attraction end;
certain types of trips such as those taking place between two
places associated with non-residential land use patterns, for
example, from work place to a shopping centre, do not conform
to such characterization.
■ We also note that some zones may be characterized by both
residential and non-residential land uses that are intermingled
(e.g. Adum in Kumasi).
15
■ For planning purposes, such situations are resolved by
assuming the zone to be made up of two separate and distinct
sections; a purely residential section and a purely non-
residential section.
■ In trip generation studies, it is impossible to trace the travel
patterns of every individual within a region.
■ Rather the geographical pattern of trip generation is
summarized by dividing the region into smaller travel analysis
zones and associating the estimated trips with these zones.
16
■ Trip generation associated with such travel analysis zones may
be calibrated on the basis of either zonal attributes such as
zonal population, average zonal income, average vehicle
ownership, etc. or household attributes.
■ Zone-based models, however, are known to be insensitive to
internal or intra-zonal variability and, therefore, may lead to
inaccurate estimates of trip levels.
■ Household-based models on the other hand provide better
estimates of trip generation because the household is a more
fundamental travel analysis unit than a zone.
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■ Households with similar characteristics tend to have similar
travel tendencies irrespective of geographical location within a
region.
■ Common models of trip generations are those based on
multiple linear regression models and category analysis
models.
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i) Multiple Linear Regression Models
19
■ During trip generation studies, data on all household attributes
likely to influence trip generation must be collected but in reality,
not all of them may influence trip generation.
■ The following rules help decide which independent variables to
include in the model:
The selected explanatory (independent) variables;
i. must be linearly related to the dependent variable,
ii. must be highly correlated with the dependent variable,
iii. must not be highly correlated between themselves, and
iv. must lend themselves to relatively easy projection.
20
■ The first three rules are easily applied by drawing a simple
correlation matrix based on the data collected.
■ The following example will serve to illustrate the use of the
rules. Consider the following simple correlation matrix derived
from a trip generation study in which data on four household
attributes x1, x2, x3, and x4 were collected.
21
■ The simple correlation matrix is symmetric
so only one half need be specified. The
following observations are made from the
data in the table:
a) Variable x1 is not highly correlated with the
dependent variable so it may be eliminated
from further consideration (Rule ii)
b) Variables x2 and x3 are each highly
correlated with Y but because they are also
highly correlated with each other, the two
cannot appear together in the same
equation (Rule iii). This is because, x2 and x3
essentially measure the same effect and
appearing together in the same equation
would mean double counting.
22
■ Based on the above rules, the following potential models may
be suggested for further screening by other statistical
methods:
i. Y=ao+a2x2
ii. Y=bo+b3x3
iii. Y=co+c2x2+d4x4
iv. Y=do+d3x3+e4x4
23
■ One technique for developing a multiple linear regression model is
to add the independent variables to the model one at a time and
then assess the degree to which the addition of the last variable
improves the predictive power of the resulting model.
■ On this basis, a final relationship emerges which includes the set of
independent variables that provide the best fit.
■ The coefficient of multiple determination (R2) and various statistical
parameters may aid in assessing the goodness of fit of the model.
■ The coefficient of multiple determination, R2, is given by the
expression
24
(2.2)
where,
=model estimation of the dependent variable for a given set of
independent variables.
=the observed dependent variable corresponding to the given set
of independent variables.
=mean of the observed dependent variables ().
N=number of observation sets.
25
■ In a sense, R2 is a statistic that measures the degree of
explanatory power achieved by the regression equation. Its
value ranges between 0 and 1.
■ The better the explanatory power of the regression model, the
closer R2 is to unity.
■ When a new independent variable is added to the regression
equation and results in an increase in the value of R2, then
that variable contributes to the explanatory power of the
resulting model and must be retained in the model.
26
■ Another measure of goodness of fit is the standard error of
estimate (standard deviation of residuals). This statistic is given by
the expression;
(2.3)
where,
Se=standard error of estimate
N=number of observation sets
n=the number of independent variables in the model.
As an example, for a multiple regression model given by
Y
n=4, since there are four independent variables (x 1, x2, x3, x4) in
the model.
27
■ The smaller the value of Se, the better the model.
■ When the inclusion of an independent variable lowers the
value of Se, then that variable has improved the prediction
reliability of the model and must be included in the model.
■ Once a trip generation model has been calibrated using base
year data, estimates of future trips are obtained by inserting
the appropriate estimates of the independent variables (x1,
x2, ...xn) in the model equation.
28
ii) Category Analysis (Cross-classification) Model
■ This model considers the household as the fundamental
analysis unit and the assumption is made that the amount of
home-end travel generated is a stable function of the number
of households, household characteristics, the income level and
car ownership.
■ Each category of household type is associated with a trip
generation rate (estimated by statistical methods).
■ The total trip productions in a zone are estimated by summing
the contributions of each household type, i.e.,
29
A zone divided into three distinct areas by type of household
30
Example 1
■ The following table is an urban zone’s expected high-density
area household composition at some future year.
Vehicles
per Persons per household
household
1 2,3 4 5
31
■ The calibrated total home-based non-work trip rates for the high-
and medium-density areas of the zone are as given in this table:
32
■ Estimate the total non-work home-based trips that the high-
density area of the zone will produce on a typical day in the
horizon year.
Solution
■ When the households are cross-classified on the basis of car
ownership and number of persons per household, there will be
a total of 12 household types for the high-density area. Hence,
Pi N h Rh
h
P1=100x0.57+300x1.45+150x1.82+200x2.07+500x3.02+100x3.39+150x4.5
7+210x5.52+60x5.89 +20x6.95+50x7.90+0x8.27
=5,760 trips/day
33
Trip Data Collection
■ Data on journey or trip patterns are obtained through origin-
destination surveys.
■ The surveys begin with the breaking up of the survey area into zones of
homogeneous land use characters with zone boundaries being dictated
by geographical or physical limitations such as rivers, hilly terrain, etc.
■ The method of data collection is dependent on the purpose of the
survey.
■ The survey may be needed to establish or update general travel
parameters or to establish patronage of particular modes or develop
models of travel behaviour or to study a particular transport
disadvantaged group.
34
■ Methods of acquiring data on travel behaviour are collected
principally through home interviews.
■ The method involves interviewing the inhabitants in a
representative number of homes within the survey area such
that the persons included in it are distributed geographically
within the area in the same proportion as the whole
population is distributed.
■ Within each dwelling unit, information is obtained about size
of household, its gross income, sex, age and occupation status
of each resident and car ownership.
35
■ For each person, data pertaining to the previous day’s travel is
collected regarding the following:
• origins and destinations of all trips,
• mode of travel,
• number of occupants if private car was used,
• cost of travel if public transport was used,
• route, and
• details of parking if applicable.
36
■ It is recommended to carry out the survey in the evening
when the chances of finding people are higher.
■ Other methods of travel data collection include;
• mail-returns,
• roadside interview and
• car-sticker methods
but the level of detail provided by these methods do not match
that provided by the home-interview method and the methods
are at best used to provide supplementary information.
37
Example 2
A base-year trip study obtained the following data relating daily person-trip
productions per dwelling unit (Y) and residential density (X dwelling units per acre):
38
a) Solution by Computational Method
Y a (a)
bX
1
X
aX bX 2 (c)
Y
■ Sum both sides of Eqns. (b) and (c) to obtain
1
(d) Y na b X
X
(e) a X b X 2
Y
39
■ Solve Eqns. (d) and (e) simultaneously to obtain
X 1
Y Y X 2
X
a
X 2 n X 2
1
Y na
b
X
40
Y X 1/Y X/Y X2
6.5 10 0.154 1.538 100
4.0 50 0.250 12.500 2500
3.5 30 0.286 8.571 900
2.2 70 0.454 31.818 4900
160 1.144 54.427 8400
a
X n X
2 2 160 2
4 8400
a 0.1127
41
1
Y na 54.428 4 0.1127
b 0.0043
X 160
■ The calibrated model is then;
Y 0.1127 0.0043 X
1
42
b) Trip Distribution
43
■ The model is formulated as follows:
A j K ij Fij
Qij Pi (2.5)
A j K ij Fij
j
where,
Qij=number of trips attracted from Zone i to Zone j
Pi=total number of trips produced in zone i for a particular purpose
i=trip production zone
j=trip attraction zone
Aj=attractiveness of Zone j
Fij=friction factor between Zones i and j
Kij=inter-zonal socio-economic adjustment factor
44
■ In the case of the destination zones j competing for the trips
produced at i, the intervening difficulty of travel between the
producing zone and each of the competing zones has a definite
effect on the choice of attraction zone.
■ This difficulty is measured by what is known as travel impedance.
■ The friction factor (also known as travel-time factor) is a function
of the impedance between any pair of zones. In this sense,
impedance is used to represent travel time, cost, distance, or a
combination of factors.
■ More generally, it represents a weighted sum of various types of
times (walking, waiting, riding) and types of costs (fares, operating
cost, tolls, parking charges, etc.).
45
■ The friction factor (Fij) is related to impedance (Wij) by the
expression;
c
1
Fij (2.6)
W
ij
where,
c=constant
The socio-economic adjustment factors (Kij)are introduced
during model calibration to take care of the effects of factors that
could not be captured by the limited number of independent
variables used in the model.
46
■ Note that the total trips attracted by zone j equals the sum of
all trips attracted to that zone from all trip-producing zones
that contribute trips to zone j, i.e.,
A*j Q
(2.7)
x, j
x
47
Example 3 (Class involvement)
48
Solution
i. Zones 1 and 3 have residential land-use.
ii. Zone 1 is a purely residential zone
iii. Zone 3 has intermingled land use (i.e., it has both residential
and non-residential land uses).
iv. Zones 2 and 4 have non-residential land use.
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Example 3 cont’d
The relationship between impedance (W) and friction factor (F)
for the city is
2
1
Fij
W
ij
Apply, the gravity model if Kij=1 to find the trip interchanges Qij
between the zones, using the following impedance matrix (Wij)
Zone j
Zone i
1 2 3 4
1 5 10 15 20
2 10 5 10 15
3 15 10 5 10
4 20 15 10 5
50
Solution cont’d
■ For i=1, P1=1500
0.0514 1500
51
■ For i=3, P3=2600
0.03
2 3 0.010 1.0 0.03 2600 488
0.16
0.08
3 2 0.04 1.0 0.08 2600 1300
0.16
52
Trip Distribution Matrix (Qij )
■ The data set, excluding the “Total” column and row,
constitutes the trip distribution matrix or the trip interchange
volumes between the production and attraction zones.
j
i 2 3 4 Total
1 875 260 365 1500
3 488 1300 812 2600
Total 1363 1560 1177 4100
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Calibration of the Gravity Model
54
• If the computed volumes are sufficiently close to the observed,
the current value of c is retained as the calibrated value
otherwise, an adjustment is made to the value of c and the
procedure repeated until convergence is achieved.
• In practice, adjustments to the c value are made through
adjusting the Fij values.
• At convergence, the friction factors last used become the desired
calibration values and these are used to establish the exact
relationship between Fij and Wij (see Eq. 2.9).
• When convergence is achieved, some discrepancies will still exist
between the values of the observed and model-estimated inter-
zonal base year volumes.
55
■ These are corrected by fine-tuning the model through the
introduction of a set of zone-to-zone socio-economic
adjustment factors Kij such that
(2.10)
where,
Xij=ratio of observed (base year) Qij to total trip productions
of zone i.
Zij=ratio of estimated to observed Qij.
56
Example
Find the value of c and Kij for the following base year trip data:
Zone P A Base year volumes
(Qij)
1 500 0
2 1000 0
3 0 2 Attraction Zone, j
4 0 3 Production
5 0 5 Zone, i 3 4 5
1 300 150 50
Inter-zonal impedances
(Wij)
j
i 3 4 5
1 5 10 15
2 10 5 15
57
Solution
■ Step 1
Draw up a trip-length frequency table showing the proportion (fo)
of the total trips that take place at a given impedance.
Q
W Qij fo
ij
Total trips
5 300+600=900 0.6
10 150+180=330 0.22
15 50+220=270 0.18
Total 1500 1.00
58
■ Step 2
Assume a value for c, say, c=2.0, and compute Fij values (see
Eq.2.9).
values
Zone j
Zone i 3 4 5
1 0.04 0.01 0.0044
2 0.01 0.04 0.0044
59
■ Step 3
• Assume Kij=1.0 and then apply the Gravity Model to obtain
estimates of the inter-zonal volumes along with the calculated
trip-length frequency table.
Model-estimated Qij
W
Zone j
Zone i 3 4 5 5 1044 0.70
10 237 0.16
1 303 114 83
15 219 0.14
2 123 741 136
Total 1500 1
60
■ Step 4
• Compare the f-values in Step 3 (fc) to those in Step1 (fo).
• If for all the impedance values the corresponding calculated and
estimated are equal or very nearly so, then convergence is
achieved. Otherwise the friction factor values in Step 2 are
replaced by adjusted values such that
(2.11)
• For example, the assumed Fij value corresponding to an impedance
value of 5 min is equal to 0.04. After the first iteration, the adjusted
value becomes 3
61
Similar adjustments to the other friction factor values will result in the
following new friction factor (adjusted) matrix.
matrix
Zone j
Zone i 3 4 5
1 0.0343 0.0138 0.0057
2 0.0138 0.0343 0.0057
62
■ Step 5
• When convergence is achieved, the friction factor values last
used provide the desired calibrated parameters. The relationship
between F and W is rewritten as
(2.12)
to obtain a straight line relationship between the logarithmic
values of the parameters or by other means using the
appropriate relationship between F and W.
■ Step 6
• The true socio-economic adjustment factors are determined
using Eqn. (9).
In the given example, the second iteration will produce the
following Qij and fc values;
63
Final estimated Qij
Attraction Zone, j
Prod. Zone, i 3 4 5
1 251 145 104
2 176 654 170
W
5 905 0.60
10 321 0.21
15 274 0.19
Total 1500 1
64
• Because of the close agreement between the fo and the fc
values obtained after the second iteration for each of the
impedance values, convergence is assumed to have occurred
so the process is terminated.
• Despite convergence, discrepancies would still exist between
the observed and model estimated Qij values.
• The discrepancies are removed by introducing socio-economic
adjustment factors using Eqn. (2.11). For example, applying
the equation, K13 can be computed as
65
• Applying Eqn. (2.11) to the example will result in the following
socio-economic adjustment factor matrix (Kij).
Kij matrix
Zone j
Zone i 3 4 5
1 1.7 1.0 0.5
2 1.0 0.8 1.4
66
c) Modal choice (Modal split)
■ This component of the sequential travel demand forecasting
predicts what mode of transport a trip maker will choose
when there are several competing modes.
■ The mode choices are aggregated to obtain the proportion or
percent of travellers that are expected or likely to use each of
the available transport modes.
■ This is done using a mode choice model.
67
■ In formulating a mode choice model, consideration is given to
the fact that a trip maker’s choice of travel mode depends on
the following factors:
• the characteristics (socio-economic status) of the trip
maker
• the characteristics of the trip
• the attributes of the available modes of travel.
68
■ To understand how trip makers make their choice of travel
mode, a way must be found to measure or assess the level of
satisfaction they derive from their choices.
■ Trip makers’ satisfaction with a particular transportation mode
may be assessed using a utility function.
■ A utility function is defined by mode choice attributes such as
the cost of travel, level of service, convenience associated with
the mode and the socio-economic status of the individual
making the choice.
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■ A calibrated utility function may be of the form
(2.13)
where,
Uk=utility of mode K
aK= the calibrated mode-specific constant which takes care of all
other factors affecting mode choice that could not be captured
by the independent variables (mode attributes)
ai =model constants and
Xi=mode attributes which have different weights for the different
modes.
70
■ Once the utilities of the available modes are known or have been
estimated, the aggregated mode choice of trip makers can then be
estimated.
■ The most popular model used in estimating the proportion of
travellers that will select a specific mode K is the multinomial logit
model which is mathematically stated as;
expu K
(2.14) p( K )
expu x
x
where,
p(K)= the proportion of travellers who select mode K.
71
■ In most transportation planning studies, particular attention is paid to
the improvement of the public transportation system in order to meet
the transportation needs of transport-disadvantaged groups.
■ This requires estimates of the total ridership of the public transportation
system.
■ Trip makers who use public transportation are of two categories:
Captive riders (also called Transit captives)
These do not have access to private transportation of their own and rely
almost exclusively on public transportation for their mobility. They
include the elderly, the poor, the very young and the second primary
person in a one-car household.
72
Choice riders
These have their private means of transportation but for
convenience or some other reason opt to use public
transportation.
■ The total ridership of any public transportation system is,
therefore, made up of captive riders and choice-riders.
■ Captive riders may be identified on a zonal basis as a percentage
of the trip generation but choice riders are estimated by applying
modal choice models to the category of trip makers who are not
captive riders.
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d) Network/Trip assignment
■ In this process, we attempt to predict the paths likely to be
selected by trip makers for their trips between any pair of zones
after having established the inter-zonal travel demand by mode.
■ Trips dealt with in network assignment are vehicle-trips because
the level of service that trip makers experience on a highway is
related to vehicular flow.
■ The essence of the assignment process is that knowing the
preferred travel path of travellers it becomes possible to predict
the resulting flows on the individual links that make up the
network of that mode.
74
■ Estimates of link utilization in turn makes it possible to assess
the likely level of service that will prevail on the link and to
anticipate potential capacity problems.
■ Link flows are estimated as the sum of all inter-zonal flows
that happen to include that link on their preferred path.
■ In the simplest network assignment procedure, the basic
assumption made in the assignment process is that all trip
makers between a pair of zones select the minimum path (the
path with the least impedance) after they have considered
the impedances of all the competing paths available to them.
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Minimum Path
■ The minimum path is determined by computing the minimum
tree (skim tree) which contains all the inter-zonal minimum
paths that emanate from a zone of origin.
■ A path’s impedance is the sum of the impedances of the links
that define it.
■ For the simple network shown below, it is very easy to
compute the corresponding minimum tree for trips originating
from a zone of origin A to all other zones (B, C, D and E) by
simple identification.
76
■ A network of roads connecting ■ Minimum tree (minimum path
several zones (A, B, C, D and E) network) for travel from Zone
showing impedances on the A to all other zones.
links.
B
5 5 B
A 1
1
3 A
E 3
D 6 E
4 D 6
2 4
C C
77
■ For large networks, determining the minimum path between
any pair of zones this way could be a daunting task unless very
efficient methods were used.
■ One such method is the minimum-tree algorithm.
■ The procedure computes the minimum tree that contains all
the inter-zonal minimum paths emanating from a node of
origin.
78
i) All-or-nothing Traffic Assignment
■ This assignment technique takes its name from the fact that it allocates all
the volume interchanging between pairs of zones to the minimum path
and none to any other path.
■ The assumption implicit in this approach is that all trip-makers between a
specific pair of zones will select the same path for their trip.
■ When all interchange volumes have been assigned, the flow on a
particular link is obtained by summing all inter-zonal flows that happen
to include that link on their minimum path.
■ This is illustrated by the following example.
79
Example
■ Assign the following inter-zonal vehicle trips from Zone 1 to zone J onto the
network below:
Zone
A B C D E F
J
Q1J 800 500 600 200 150 350
A
1 B
3
2 4
E
C F
80
Solution
■ Assign the vehicle trips onto the last links leading to the zones.
■ Work backwards to obtain the vehicle trips on the preceding links using
the following rule for each intermediate node (2, 3, and 4) of the network;
where,
V e ,i V d ,i
81
A
800
1 500
3 B
1300
2400
1100 150
200 2 4 E
600 350
D C F
82
ii) Multi-Path Traffic Assignment
■ The assumption that all trip-makers between any pair of zones will select
the path of least travel impedance and hence the same path is not
realistic.
■ In reality, all competing paths will get some allocation of the inter-zonal
volumes but in different proportions based on, for example, a disutility
factor such as travel impedance.
■ This approach to traffic assignment is close to reality and forms the basis
of multi-path traffic assignment.
■ One allocation rule uses impedance in an inverse-proportion function to
assign the inter-zonal volumes to each of a number of possible inter-zonal
routes (rx) between I and J in a proportion p(rx) given as;
83
1
wIJ ( rx)
p (rx )
1 1 1
(2.15) ......
w w w
IJ ( r 1) IJ ( r 2 ) IJ ( rn )
where,
p(rx) =proportion of traffic between zones I and J that will use
route x.
wIJ(rx) =impedance from I to J along route x.
■ Another possible approach to allocation is to determine p(rx) using
the multi-nomial logit model with dis-utilities based on path
impedances.
84
iii) Capacity-restrained Traffic Assignment
■ This assignment approach tries to resolve the problem of the increase in
free-flow link impedance when trips are assigned to the links in the
minimum path procedure.
■ Thus a minimum path prior to assignment may not be a minimum path
after assignment.
■ Capacity-restrained methods use iterative techniques to obtain
convergence between link impedances assumed prior to assignment
and link impedances implied by the resulting assignment.
■ It involves updating the free-flow link impedances of the links that make
up a minimum path by the link capacity function given as
85
■ (2.16)
where,
W=impedance of a given link at flow q
Wo=free flow impedance of the link
q=link flow
qmax=link capacity
86
■ The assignment procedure then becomes one of choosing an
interchange at random, determining the minimum path using
the free-flow impedances and assigning the entire volume to
this minimum path (all-or-nothing).
■ The impedances of the links that make up this path are then
updated according to the assigned flow and another
interchange is randomly chosen for similar treatment until all
interchanges have been considered.
■ This incremental updating of link impedances are expected to
result in some realistic estimates of the link equilibrium flows.
87