Transport Engineering

ADDIS ABABA UNIVERSITY
Institute Of Technology
2014/2015 A.Y- Semester I
School of Civil and

Environmental Engineering
Transport Planning Ceng 3301
Course Outline
Chapter 1: Introduction to Transport Engineering (1 week)
1.1 Overview
1.2 Historical Background and Future Trends of Transportation
1.3 Modes of Transport
Chapter 2: Transportation Planning and Modeling (3 weeks)
2.1 Transport Policy and Strategic Planning
2.2 Transport Modeling
2.3 Evaluation and Economic Appraisal of Transport Projects
Chapter 3: Traffic Engineering (2 weeks)
3.1 Behavioral analysis of users
3.2 Traffic Surveys
3.3 Traffic Flow Theory
3.4 Basic Queuing Theory
Chapter 4: Highway Capacity and Level of Service Analysis (2 weeks)
4.1 Concept of Level of Service
4.2 Determination of Level of Service
4.3 Basic Freeway Segments
4.4 Multilane Highways
4.5 Two-lane Highways
4.6 Design Traffic Volumes
Chapter 5: Traffic Management and Control (2 weeks)
5.1 Traffic Sign
5.2 Traffic Marking
5.3 Traffic Signal
Reference:- Listed at the end of each chapter on the lecture note
Assessment (Tentative)
Mid Exam
30%
Project and Assignments
20%
Final Exam
50%
Transportation Engineering (Ceng3301)
Chapter 1
Introduction to transportation Engineering
Overview
What is transportation?
Transportation is all about moving goods and people from one place to another
It is also Safe, efficient, reliable, and sustainable movement of persons and goods over time
and space
What is Transportation engineering?
Transportation engineering is a type of civil engineering which focuses on the infrastructure

of transportation: all the elements which support the movement of goods and people.
Transportation engineers design runways, build bridges, layout roads and plan docking
facilities. They look at traffic patterns, determine when new transport facilities are needed
and come up with better ways to get from point A to point B.
Also Application of technology and scientific principles to the planning, functional design,
operation, and management of facilities for any mode of transportation in order to provide
for the safe, rapid, comfortable, convenient, economical, and environmentally compatible
movement of people and goods
Mobility is a basic human need. From the times immemorial, everyone travels either for food or
leisure. A closely associated need is the transport of raw materials to a manufacturing unit or
finished goods for consumption. Transportation fulfils these basic needs of humanity.
Transportation plays a major role in the development of the human civilization. For instance, one
could easily observe the strong correlation between the evolution of human settlement and the
proximity of transport facilities. Also, there is a strong correlation between the quality of transport
facilities and standard of living, because of which society places a great expectation from
transportation facilities. In other words, the solution to transportation problems must be analytically
based, economically sound, socially credible, environmentally sensitive, and practically acceptable
and sustainable. Alternatively, the transportation solution should be safe, rapid, comfortable,
convenient, economical, and ecofriendly for both men and material.
AAIT, School of civil and Environmental Engineering
Page 1
The characteristics of transportation system

The characteristics of transportation system that makes it diverse and complex are listed below:
1. Multi-modal: Covering all modes of transport; air, land, and sea for both passenger and freight.
2. Multi-sector: Encompassing the problems and viewpoints of government, private industry, and
public.
3. Multi-problem: Ranging across a spectrum of issues that includes national and international
policy, planning of regional system, the location and design of specific facilities, carrier
management issues, regulatory, institutional and financial policies
4. Multi-objective: Aiming at national and regional economic development, urban development,
environment quality, and social quality, as well as service to users and financial and economic
feasibility.
5. Multi-disciplinary: Drawing on the theories and methods of engineering, economics, operations
research, political science, psychology, other natural, and social sciences, management and law.
The context in which transportation system is studied is also very diverse and are mentioned below:
1. Planning range: Urban transportation planning, producing long range plans for 5-25 years for
multimodal transportation systems in urban areas as well as short range programs of action for
less than five years.
2. Passenger transport: Regional passenger transportation, dealing with inter-city passenger transport by
air, rail, and highway and possible with new modes.
3. Freight transport: Routing and management, choice of different modes of rail and truck.
4. International transport: Issues such as containerization, inter-modal co-ordination
Therefore as we understand from above Transportation engineering is a very diverse and
multidisciplinary field, which deals with the planning, design, operation and maintenance of
transportation systems. Good transportation is that which provides safe, rapid, comfortable,
convenient, economical, and environmentally compatible movement of both goods and people. This
profession carries a distinct societal responsibility. Transportation planners and engineers recognize
the fact that transportation systems constitute a potent force in shaping the course of regional
development. Planning and development of transportation facilities generally raises living standards
and enhances the aggregate of community values.
Page 2
Generally a transportation system has three elements this are
Infrastructure: which includes Road, canal, rail, air Transfer points Supporting elements
(signs, signals, safety)
Vehicles: which includes Planes, trains, autos, buses, ships, trucks
Operators/Content : which includes Drivers, pilots, freight, passengers
History of transportation engineering

Long before cars, snowmobiles and airplanes, humans had migrated to all over the Earth powered
almost exclusively by their feet. Eventually, people got tired of walking around and carrying
everything they needed on their backs. They started to use domesticated animals to carry goods.
They also built machines and devices, like sleds and travois, to help them carry more. In some parts
of the world, they began using the wheel and axle to build carts and carriages. As people travelled
back and forth, establishing trading routes, well-used paths became more and more permanent.
These paths became the first roads. As time went on, people started to maintain the roads and look
at ways in which they could be made easier to travel, these people were the first transportation
engineers.
The strong interrelationship and the interaction between transportation and the rest of the society
especially in a rapidly changing world is significant to a transportation planner. Among them four
critical dimensions of change in transportation system can be identified; which form the background
to develop a right perspective.
1. Change in the demand: When the population, income, and land-use pattern changes, the pattern
of demand changes; both in the amount and spatial distribution of that demand.
2. Changes in the technology: As an example, earlier, only two alternatives (bus transit and rail
transit) were considered for urban transportation. But, now new systems like ITS ,LRT, MRTS,
etc over a variety of alternatives.
3. Change in operational policy: Variety of policy options designed to improve the efficiency,
such as incentive for car-pooling, bus fare, road tolls etc.
Page 3
4. Change in values of the public: Earlier all beneficiaries of a system was monolithically
considered as users. Now, not one system can be beneficial to all, instead one must identify the
target groups like rich, poor, young, work trip, leisure etc.
Major disciplines of transportation
Transportation engineering can be broadly consisting of the four major parts:
1. Transportation Planning
2. Geometric Design
3. Pavement Design
4. Traffic Engineering
Transportation planning
Transportation planning essentially involves the development of a transport model which will
accurately represent both the current as well as future transportation system.
Geometric design
Geometric design deals with physical proportioning of other transportation facilities, in contrast
with the structural design of the facilities. The topics include the cross-sectional features,
horizontal alignment, vertical alignment and intersections. Although there are several modes of
travel like road, rail, air, etc. The underlying principles are common to a great extent. Therefore
emphasis will be normally given for the geometric design of roads.
Pavement analysis and design
Pavement design deals with the structural design of roads, both (bituminous and concrete),
commonly known as (flexible pavements and rigid pavements) respectively. It deals with the
design of paving materials, determination of the layer thickness, and construction and
maintenance procedures. The design mainly covers structural aspects, functional aspects, drainage.
Structural design ensures the pavement has enough strength to withstand the impact of loads,
functional design emphasizes on the riding quality, and the drainage design protects the pavement
from damage due to water infiltration.
Traffic engineering
Traffic engineering covers a broad range of engineering applications with a focus on the safety of
the public, the efficient use of transportation resources, and the mobility of people and goods.
Page 4
Traffic engineering involves a variety of engineering and management skills, including design,
operation, and system optimization. In order to address the above requirement, the traffic
engineer must first understand the traffic flow behavior and characteristics by extensive collection
of traffic flow data and analysis. Based on this analysis, traffic flow is controlled so that the
transport infrastructure is used optimally as well as with good service quality. In short, the role of
traffic engineer is to protect the environment while providing mobility, to preserve scarce
resources while assuring economic activity, and to assure safety and security to people and
vehicles, through both acceptable practices and high-tech communications.
Other important disciplines
In addition to the four major disciplines of transportation, there are several other important
disciplines that are being evolved in the past few decades. Although it is difficult to categorize
them into separate well defined disciplines because of the significant overlap, it may be worth the
effort to highlight the importance given by the transportation community. They can be
enumerated as below:
1. Public transportation: Public transportation or mass transportation deals with study of the
transportation system that meets the travel need of several people by sharing a vehicle.
Generally this focuses on the urban travel by bus and rail transit. The major topics include
characteristics of various modes; planning, management and operations; and policies for
promoting public transportation.
2. Financial and economic analysis: Transportation facilities require large capital investments.
Therefore it is imperative that whoever invests money should get the returns. When
government invests in transportation, its objective is not often monetary returns; but social
benefits. The economic analysis of transportation project tries to quantify the economic
benefit which includes saving in travel time, fuel consumption, etc. This will help the planner
in evaluating various projects and to optimally allocate funds. On the contrary, private sector
investments require monetary profits from the projects. Financial evaluation tries to quantify
the return from a project.
3. Environmental impact assessment : The depletion of fossil fuels and the degradation of the
environment has been a severe concern of the planners in the past few decades.
Transportation; in spite of its benefits to the society is a major contributor to the above
Page 5
concern. The environmental impact assessment attempts in quantifying the environmental

impacts and tries to evolve strategies for the mitigation and reduction of the impact due to
both construction and operation. The primary impacts are fuel consumption, air pollution,
and noise pollution.
4.
Accident analysis and reduction: One of the silent killers of humanity is transportation. Several
statistics evaluates that more people are killed due to transportation than great wars and
natural disasters. This discipline of transportation looks at the causes of accidents, from the
perspective of human, road, and vehicle and formulate plans for the reduction.
5. Intelligent transport system: With advent to computers, communication, and vehicle technology,
it is possible in these days to operate transportation system much effectively with significant
reduction in the adverse impacts of transportation. Intelligent transportation system offers
better mobility, efficiency, and safety with the help of the state-of-the-art-technology.
In addition disciplines specific to various modes are also common. This includes railway engineering,
port and harbor engineering, and airport engineering.
Factors in Transportation Development

Transportation develops because of several and frequently overlapping factors. From the many, the
following are important:
Economic Factors
Almost all transport development is economic in origin. The chief preoccupation of the first human
was the procurement of food, shelter and sometimes clothing. As they become more highly
developed their needs increased, often beyond what their local economy could supply. Means of
transporting goods from distant places had to be devised, adding to the costs of the goods thereby
secured. The need for transporting individuals over wider areas also arose. Increasing transportation
productivity and lower unit costs have occurred over the years as the system of transportation
becomes more highly developed and complex.
Geographical Factor
Geography is closely related to economics. The geographical location of natural resources
determines the transport routes that gives access to those resources and create economic utility, that
Page 6
is, time and place utility, by taking them from a location where they have little values to processing
and consuming areas where their values is vastly increased.
Political Polices
Political polices frequently play a deciding role in transport development. Basically is in a way to
form integrated political system and control.
Military
The military might of a nation is primarily intended to support its political polices and to provide for
national defense. Consequently, often it has direct influence on transport development.
Technological Factor
Progress in direct and supporting technologies has played an obvious role in transportation, for
instance introduction of new economical transportation mode to the exist system calls for the
development of transportation
Competition
The competitive urges have given a powerful impetus to transport development. Railroads compete
with railroad also with trucks, barges, pipelines and airlines. Airlines have counted heavily on speed
but have also been forced to greater safety and dependability to meet ground transport competition.
No less real is the competition between products and industries tributary to transport. Bituminous
material competes with concrete as the road surface. Diesel won steam but may face competition
with electricity.
Urbanization
The rapid growth of urban areas by an even more rapidly expanding population is a phenomenon
that cannot be overlooked among transport development factors. Accessibility to land and the
intensity of land use are closely related to transport availability.
Role of transportation in society

Transportation is a non separable part of any society. It exhibits a very close relation to the style of
life, the range and location of activities and the goods and services which will be available for
consumption. Advances in transportation has made possible changes in the way of living and the
way in which societies are organized and therefore have a great influence in the development of
civilizations. This topic conveys an understanding of the importance of transportation in the modern
Page 7
society by presenting selected characteristics of existing transportation systems, their use and
relationships to other human activities.
Transportation is responsible for the development of civilizations from very old times by meeting
travel requirement of people and transport requirement of goods. Such movement has changed the
way people live and travel. In developed and developing nations, a large fraction of people travel
daily for work, shopping and social reasons. But transport also consumes a lot of resources like time,
fuel, materials and land.
Economic role of transportation

Economics involves production, distribution and consumption of goods and services. People
depend upon the natural resources to satisfy the needs of life but due to non uniform surface of
earth and due to difference in local resources, there is a lot of difference in standard of living in
different societies. So there is an immense requirement of transport of resources from one particular
society to other. These resources can range from material things to knowledge and skills like
movement of doctors and technicians to the places where there is need of them. Without the ability
to transport manufactured goods, raw materials, and technical know-how, a country is simply unable
to maximize the comparative advantage it may have in the form of natural or human resources.
Goods have little values unless given utility, that is, the capacity for being useful and satisfying wants.
Transportation contributes two kinds of utilities: place and time utility, economic terms that simply
mean having goods where they are wanted when they are needed, essential functions that can also be
applied to the movement of people. An example is given to evaluate the relationship between place,
time and cost of a particular commodity. If a commodity is produced at point A and wanted by
people of another community at any point B distant x from A, then the price of the commodity is
dependent on the distance between two centers and the system of transportation between two
points. With improved system the commodity will be made less costly at B.
In urban areas especially, transportation provides the connecting link between dwelling-units to
their corresponding activities.
Social role of transportation

Transportation has always played an important role in influencing the formation of urban societies.
Although other facilities like availability of food and water, played a major role, the contribution of
Page 8
transportation can be seen clearly from the formation, size and pattern, and the development of
societies, especially urban centers.
Formation of settlements: From the beginning of civilization, the man is living in settlements which
existed near banks of major river junctions, a port, or an intersection of trade routes.
Size and Pattern of Settlement: the initial settlements were relatively small developments but with due
course of time, they grew in population and developed into big cities and major trade centers. The
size of settlements is not only limited by the size of the area by which the settlement can obtain food
and other necessities, but also by considerations of personal travels especially the journey to and
from work. The increased speed of transport and reduction in the cost of transport has resulted in
variety of spatial patterns.
Growth of Urban Centers: When the cities grow beyond normal walking distance, then transportation
technology plays a role in the formation of the city. For example, many cities in the plains developed
as a circular city with radial routes, where as the cities beside a river developed linearly. The
development of automobiles and other factors like increase in personal income, and construction of
paved road network, the settlements were transformed into urban centers of intense travel activity.
Environmental role of transportation

The negative effects of transportation are more dominating than its useful aspects as far as
transportation is concerned. There are numerous categories into which the environmental effects
have been categorized. They are explained in the following sections.
Safety
Growth of transportation has a very unfortunate impact on the society in terms of accidents.
Worldwide death and injuries from road accidents have reached epidemic proportions. Present
indications are that about half a million killed and about 15 million injured on the road accidents
annually. Increased variation in the speeds and vehicle density resulted in a high exposure to
accidents. Accidents result in loss of life and permanent disability, injury, and damage to property.
Accidents also causes numerous non-quantifiable impacts like loss of time, grief to the near ones of
the victim, and inconvenience to the public. The loss of life and damage from natural disasters,
industrial accidents, or epidemic often receive significant attention from both government and
public. This is because their occurrence is concentrated but sparse. On the other hand, accidents
from transport sector are widespread and occurs with high frequency.
Page 9
Air Pollution
All transport modes consume energy and the most common source of energy is from the burning of
fossil fuels like coal, petrol, diesel, etc. The relation between air pollution and respiratory disease has
been demonstrated by various studies and the detrimental effects on the planet earth are widely
recognized recently. The combustion of the fuels releases several contaminants into the atmosphere,
including carbon monoxide, hydrocarbons, oxides of nitrogen, and other particulate matter.
Hydrocarbons are the result of incomplete combustion of fuels. Particulate matters are minute solid
or liquid particles that are suspended in the atmosphere. They include aerosols, smoke, and dust
particles. These air pollutants once emitted into the atmosphere, undergo mixing and disperse into
the surroundings.
Noise pollution
Sound is acoustical energy released into atmosphere by vibrating or moving bodies where as noise is
unwanted sound produced. Transportation is a major contributor of noise pollution, especially in
urban areas. Noise is generated during both construction and operation. During construction,
operation of large equipments causes considerable noise to the neighborhood. During the operation,
noise is generated by the engine and exhaust systems of vehicle, aerodynamic friction, and the
interaction between the vehicle and the support system (road-tire, rail-wheel).
Extended exposure to excessive sound has been shown to produce physical and psychological
damage. Further, because of its annoyance and disturbance, noise adds to mental stress and fatigue.
Energy consumption
The spectacular growths in industrial and economic growth during the past century have been
closely related to an abundant supply of inexpensive energy from fossil fuels. Transportation sector
is unbelieved to consume more than half of the petroleum products. The compact of the shortage of
fuel was experienced during major wars when strict rationing was imposed in many countries. The
impact of this had cascading effects on many factors of society, especially in the price escalation of
essential commodities. However, this has few positive impacts; a shift to public transport system, a
search for energy efficient engines, and alternate fuels. During the time of fuel shortage, people
shifted to cheaper public transport system. Policy makers and planners thereafter gave much
emphasis to the public transit which consumes less energy per person. The second impact was in the
Page 10
development of fuel-efficient engines and devices and operational and maintenance practices. A fast
depleting fossil fuel has accelerated the search for energy efficient and environment friendly alternate
energy source. The research is active in the development of bio-fuels, hydrogen fuels and solar
energy.
Other impacts
Transportation directly or indirectly affects many other areas of society and few of then are listed
below: Increased travel requirement also require additional land for transport facilities. A good
transportation system takes considerable amount of land from the society.
Aesthetics of a region is also affected by transportation. Road networks in quite country side are
visual intrusion. Similarly, the transportation facilities like fly-overs are again visual intrusion in
urban context.
The social life and social pattern of a community is severely affected after the introduction of some
transportation facilities. Construction of new transportation facilities often requires substantial
relocation of residents and employment opportunities.
Modes of Transportation
Transport modes are the means by which people and freight achieve mobility. They fall into one of
three basic types, depending on over what surface they travel land (road, rail and pipelines), water
(shipping), and air. Each mode is characterized by a set of technical, operational and commercial
characteristics.
Road transportation
Road infrastructures are large consumers of space with the lowest level of physical constraints
among transportation modes. However, physiographical constraints are significant in road
construction with substantial additional costs to overcome features such as rivers or rugged terrain.
Road transportation has an average operational flexibility as vehicles can serve several purposes but
are rarely able to move outside roads. Road transport systems have high maintenance costs, both for
the vehicles and infrastructures. They are mainly linked to light industries where rapid movements of
freight in small batches are the norm. Yet, with containerization, road transportation has become a
crucial link in freight distribution.
Page 11
Rail transportation
Railways are composed of traced paths on which are bound vehicles. They have an average level of
physical constrains linked to the types of locomotives and a low gradient is required, particularly for
freight. Heavy industries are traditionally linked with rail transport systems, although
containerization has improved the flexibility of rail transportation by linking it with road and
maritime modes. Rail is by far the land transportation mode offering the highest capacity with a
23,000 tons fully loaded coal unit train being the heaviest load ever carried.
Pipelines
Pipeline routes are practically unlimited as they can be laid on land or under water. The longest gas
pipeline links Alberta to Sarnia (Canada), which is 2,911 km in length. The longest oil pipeline is the
Transiberian, extending over 9,344 km from the Russian arctic oilfields in eastern Siberia to Western
Europe. Physical constraints are low and include the landscape and pergelisol in arctic or subarctic
environments. Pipeline construction costs vary according to the diameter and increase
proportionally with the distance and with the viscosity of fluids (from gas, low viscosity, to oil, high
viscosity).
Maritime transportation
Because of the physical properties of water conferring buoyancy and limited friction, maritime
transportation is the most effective mode to move large quantities of cargo over long distances.
Main maritime routes are composed of oceans, coasts, seas, lakes, rivers and channels. However, due
to the location of economic activities maritime circulation takes place on specific parts of the
maritime space, particularly over the North Atlantic and the North Pacific. The construction of
channels, locks and dredging are attempts to facilitate maritime circulation by reducing discontinuity.
Comprehensive inland waterway systems include Western Europe, the Volga / Don system, St.
Lawrence / Great Lakes system, the Mississippi and its tributaries, the Amazon, the Panama /
Paraguay and the interior of China. Maritime transportation has high terminal costs, since port
infrastructures are among the most expensive to build, maintain and improve. High inventory costs
also characterize maritime transportation. More than any other mode, maritime transportation is
linked to heavy industries, such as steel and petrochemical facilities adjacent to port sites.
Page 12
Air transportation
Air routes are practically unlimited, but they are denser over the North Atlantic, inside North
America and Europe and over the North Pacific. Air transport constraints are multidimensional and
include the site (a commercial plane needs about 3,300 meters of runway for landing and take off),
the climate, fog and aerial currents. Air activities are linked to the tertiary and quaternary sectors,
notably finance and tourism, which lean on the long distance mobility of people. More recently, air
transportation has been accommodating growing quantities of high value freight and is playing a
growing role in global logistics.
Intermodal transportation
Concerns a variety of modes used in combination so that the respective advantages of each mode
are better exploited. Although intermodal transportation applies for passenger movements, such as
the usage of the different, but interconnected modes of a public transit system, it is over freight
transportation that the most significant impacts have been observed. Containerization has been a
powerful vector of intermodal integration, enabling maritime and land transportation modes to
more effectively interconnect.
Page 13
CHAPTER 2
Transportation Planning and Modeling
Transportation can have significant effects on mobility, economic development, environmental
quality, government finance and the quality of life. Wise planning is, thus, needed to help create high
quality transportation facilities and services at a reasonable cost with minimal environmental impact
and to enhance economic activity. Failure to plan can lead to severe traffic congestion, dangerous
travel patterns, slow economic growth, adverse environmental impact and wasteful use of money
and resources.
Transportation planning is a process that develops information to help make decisions on the future
development and management of transportation systems, especially in urban areas. It involves the
determination of the need for transport facilities such as new highways, transit systems, freight
facilities, and transportation terminals. The planning process also allows determining the location,
capacity and management of these facilities.
Transportation planning is primarily focused on developing long range (15-30 years) transportation
plans that can be used to set priorities for project implementation in the future. Such plans should
ideally balance the need to build new roads and transit facilities (supply) with future travel demand
patterns with a minimum of environmental effect and within the funding capabilities of the
government agencies involved.
Problems addressed can range from broad issues of policy at the federal or state level to specific
programs and projects at a local level. Besides problems of congestion and travel growth, these
could include the following:
- Travel demand alternatives for congestion reduction
- Land use/transportation coordination
- Fuel reduction measures
- Air quality measures
- Safety measures
- Economic development/redevelopment activity
Page 14
The transportation planning process is direct application of problem solving via system analysis. It
provides a framework for the identification of transportation problems and the development of
alternative potential solutions. In its simplest form, it can be depicted by figure 2.1.
Problem
Definition
Solution
Generatio
Solution
Analysis
Evaluatio
n and
Implementatio
n and
Feedback to all steps

Figure 2.1-The Transportation Planning Process
The simplified planning process can be summarized as follows:
A problem is a deviation from expected or desired performance. Goals and objectives,

reflecting national or regional values, define the expected or desired performance.
Solution generation is a subjective process that reflects regional goals and objectives, the
nature of the identified problems, the nature of the existing transportation system and
regional preferences, as much as it reflects technical and economic functionality.
When the set of alternative solutions is identified, the process enters solution analysis where
each alternative is subject to formal technical analysis (such as transport models) to assess
resulting performance.
The estimated performance of each generated alternative is then evaluated using various
measures of performance (MOEs). These MOEs describe volumes, travel times or speed on
links and intersections, and the associated impacts (such as air quality or noise). The MOEs
must also be coupled with estimated cost and standard economic analysis techniques to
assess the relative overall performance and cost of each alternative.
The preferred alternative is selected for implementation, thus entering programming and
project planning processes. Once the selected option is implemented, the overall system
must be monitored to assess (a) real-world performance, (b) the degree that the problem has
been addressed, and (c) the emergence of additional performance problems.
Page 15
The transportation planning process is continuous- it is applied simultaneously at multiple levels,

including various spatial scales. It is also characterized by extensive feedback. The process may
iterate in defining alternatives and then estimating and assessing the associated performance. The
results might be that new alternatives must be found, or perhaps the problem needs to be re-defined.
Note that the planning process continues both during and after project construction to assess the
effectiveness of the selected alternative in addressing the identified problems.
2.1 Transport Policy and Strategic Planning
Policy, defined conservatively, is a guiding principle that influences how a system behaves. It is a
plan of action agreed on or chosen by a government, business entity etc. to satisfy the desires of a
society. In this broad sense, a transport policy is a guiding principle that influences how the
transport system should behave to achieve desired outcomes and avoid transport problems.
Examples of such policies may include road expansion plans, transit system priorities, fuel tax,
emission limits etc.
It is the task of politicians, and of the skilled professionals who advise them, to identify the most
appropriate solutions to today's and tomorrow's transport problems. These solutions form the basis
of a transport policy, which can be designed for a nation, a city, a town or a rural area. But it is
essential that professionals are clear on the reasons for such solutions: that is, that the objectives which
are to be achieved should be specified.
An objective is a statement of a desired end-state. However, that statement can range from the very
general, such as a successful urban economy or a high standard quality of life, to the very specific,
such as avoiding pollution levels above a specified threshold. Both are helpful, the first in providing
the context for the strategy, and a direction to it; the second in providing a basis for assessing
whether the objective is being met. Objectives in transport policy can be categorized into four
classes:
Statements of Vision: Broad indications of the type of area which politicians or the public
wish to see. These serve to identify long-term goals to which more detailed transport policy
objectives can contribute. These broad statements often say nothing about transport itself:
instead they raise the question: how best can transport help to realize this vision?.
Page 16
Higher level objectives: These higher level objectives, sometimes referred to as aims or
goals, identify attributes of transport system, or its side effects, which can be improved as a
means of realizing the vision. Typical among are to reduce congestions, protect the
environment, avoid accidents and improve accessibility. These broad objectives indicate the
directions in which strategies should be developed.
Quantified objectives: Quantified objectives may indicate a requirement, for example, to

avoid residents without cars being more than 30 minutes from the nearest bus station. They
provide a clear basis for assessing performance of the strategy, but they do require careful
definition if the specified thresholds are to be realistic. Once this is done, quantified
objectives provide a direct basis for identifying problems, for current or future conditions,
on the basis that a problem occurs wherever the quantified objective is not met.
Solution-specific objectives: It is important to avoid specifying solutions within the

objectives, since this constrains the search for solutions, and may lead to an overall strategy
which is less appropriate to the areas needs. Where politicians, or interest groups, wish to
introduce general objectives such as to impose physical restrictions on car use, it is
preferable to ask why this solution is being proposed and what it is designed to achieve.
Answer to such questions should lead to clearer specification of the true underlying
objectives.
The transport policy formulation process

There are in practice two different types of policy formulation approaches: objective-led and
problem oriented approaches.
1. Objective-led strategy formulation: broad (or more detailed) objectives are first specified.
These are then used to identify problems by assessing the extent to which current, or
predicted future conditions in the absence of new policy measures, fail to meet the
objectives. Possible solutions are then identified as ways of overcoming the problems which
have been identified. The potential solutions are then compared, often by means of
predictive model of transport systems, by appraising them against the objectives which they
are designed to meet. As the measures are implemented, their impact is assessed, through
Page 17
before and after studies, again in terms of achievement against objectives. On regular basis,
too, conditions are monitored and the current conditions and problems are reassessed, in
terms of overall objectives. Figure 2.2 presents a structure for strategy formulation in which
objectives are the starting point.
Figure
2.2 Objective-led policy formulation
This process may seem somewhat idealized and remote from standard practice, but it has
several virtues. First, it offers a logical basis for proposing solutions, and also for assessing
any proposals offered by others. Second, it ensures that the appraisal of alternatives is
conducted in a logical, consistent, and comprehensive way against the full set of objectives.
Third, assessing the performance of the implemented measures improves the ability to judge
the potential of similar measures elsewhere, and to predict their impact. Fourth, regular
Page 18
monitoring provides a means of checking not just on the scale of current problems, but also,
through attitude surveys, on the perception of those problems.
The main draw back with this approach is that many elected officials and the public are less
familiar with the abstract concept of objectives (such as improving accessibility) than they
are with concrete problems (such as the nearest job centre being 50 minutes away).
2. Problem oriented approach: The alternative problem-oriented approach is to start by
defining types of problem and to use data on current (or predicted future) conditions to
identify when and where these problems occur. This approach starts at the second box in
the flow chart in figure 2.2. The objectives are implicit in the specified problem, and may
never actually be stated.
It has the merit of being easily understood. However, it is critically dependent on developing
a full list of potential problems at the outset. If particular types of problem (like access to job
centers) are not identified because the underlying objective (accessibility) has not been
considered, the resulting strategy will be partial in its impact. It is thus probably still wise to
check with elected members and the public that the full set of problems has been identified.
As noted above, the problem-oriented approach to transport planning starts by identifying problems
and developing solutions to them. The objective-led approach defines problems in terms of
specified objectives. Both methods converge at the stage of problem identification and then use
these as a basis for identifying solutions and strategies (Figure 2.2). In either case it is essential to be
comprehensive in the list of types of problem. This may be difficult to achieve with the problemoriented planning approach in which there is no pre-defined set of objectives to prompt the
question 'how do we know that we have a problem?'
Policy Instruments/Measures
Transport planners have available to them, at least in principle, a wide range of instruments/
strategies of transport policy. These are the means by which the objectives described above can be
achieved, and problems overcome. These instruments can be categorized in several ways:
Page 19
1. Infrastructures- new or expansion of roads, new rail lines, parking, pedestrian walk ways
etc.
2. Management- traffic management, traffic calming, bus priorities, HOV lanes etc
3. Information- signs and markings, signals, real-time transit times etc.
4. Pricing- fuel taxes, bus fares, parking charges etc.
5. Land use- development densities, master plan, urban form etc
6. Attitudinal and behavioral measures
The key question with each of the measures is its ability to achieve one or more of the objectives.
(For more detail and exhaustive explanation of transport policy and strategies, please refer to OFlaherty 1997,
Chapters 3 and 6)
2.2 Transport modeling
Modeling principles
Models are a simplified representation of a part of reality. Their function is to give insight into
complex interrelationships in the real world and to enable statements about what (most probably)
will happen if changes occur or put in that (part of) reality.
Models are invaluable in offering a common ground for discussing policy and examining the
inevitable compromises required in practice with a minimum of objectivity. During their formulation,
calibration and use, planners can also learn much about the behavior and internal workings of the
system under scrutiny.
However, a model is only realistic from a particular perspective. Its appropriateness is highly
dependent on the context where it will be used i.e. its value is limited to a range of problems under
specific conditions. Therefore, extreme care should be taken when choosing and adapting models
for a particular context.
Transport models study of the behavior of individuals in making decisions regarding the provision
and use of transport. Models in transportation planning are abstract mathematical models, put into
the form of (systems of) mathematical equations in which the behavior of a dependent variable Y
(e.g. the number of daily bus passengers in the Addis Ababa) can be derived from one or more
Page 20
explaining or independent variables X (e.g. number of transit lines, bus fares, etc) and related
parameters a. Generally, they take the form;
Y = f (a, X)
where the parameters describe the sensitivity of Y to a unit change in X.
Model development starts from the formation of a hypothesis to explain the given phenomenon or
system from a particular point of view. These sets of hypotheses will form the theory. The
translation of such a theory into a quantitative model with quantifiable variables and associated
parameters we call a conceptual model. The Estimation/ Calibration process determines the
numerical values of the associated parameters from the given data. The model then needs further
testing and verification on another set of data that has not been used during the calibration process.
It is when the model is finally verified and approved that it can be applied to the transport system.
The process of the model development is shown in the figure below.
Figure 2.3 Model formulation process

The mathematical models have several purposes for transport planning, some of which are:
To gain a more structural analysis of the complex transport system
Page 21
To find out which factors play an important role, and how sensitive the transport system is
to changes in the different factors
To analyze the effect of alternative traffic projects and contribute towards their economic
appraisal
To help transport planners make reliable predictions and forecasts of future changes in usage
of traffic facilities for sake of facility design, control and operation.
To enable quantified calculations of expected effects in the transportation system when

changes (policy measures or interventions) are put in the system
To find design parameters that lead to an optimal performance of the modeled system
Thus, transport modeling contributes greatly to improved decision making and planning in the
transport field. However, transport modeling is only one element in transport planning:
administrative practices, an institutional framework, skilled professionals and good level of
communication with decision makers, the media and the public are some of the other requisites for
an effective planning system.
(For more detail on the basics of modeling, please refer OFlaherty 1997 chapter 5)
Prerequisite for transport modeling
Before embarking on the modeling of transport systems in the context of this chapter, the modeler
should be familiar with the basic terminologies, grasp the fundamental characteristics of transport
problems, gather the necessary data and understand basic regression analysis. These four
prerequisites are treated in more detail below:
Characteristics of transport problems
Both the demand for travel and the supply for transport facilities exhibit distinct characteristics that
the modeler should bear in mind. These characters include:
The demand for transport services is highly qualitative and differentiated. There is a whole
range of specific demands for transport which are differentiated by time of day, day of week,
journey purpose, type of cargo, and so on.
Page 22
The demand for transport is derived; it is not an end by itself. People travel in order to
satisfy a need (work, leisure, health) at their destination.
Transport demand takes place over space. It is the distribution of activities over space that
makes for transport demand.
Both transport demand and supply have very strong dynamic elements. A good deal of the
demand for transport is concentrated on a few hours of the day.
Transport is a service and not a good. Therefore, it is not possible to stock it.
The transport system requires fixed assets and the mobile units. It is often the case that the
infrastructure and the vehicles are not owned nor operated by the same entity.
Transport infrastructure is lumpy; one cannot provide half a runway or one-third of a railway
station. They take a long time to carry out and significant expenses.
Transport investment has an important political role.
Transport services come with side effects: accidents, pollution and environmental
degradation
Basic terms and definitions

Activity
An activity occurs at the end of every trip and reflects the trip purpose, that is, what
the trip maker did at the trip destination. Activities are categorized according to
schemes such as subsistence/maintenance/discretionary or work/shop/social/etc.
Calibration
Calibration is the fitting of a model to observed data, primarily by adjusting model

parameters. In travel forecasting, the terms estimation and calibration often have
been used interchangeably.
Centroid
A defined point within a TAZ from which all trips are assumed to start or end. It
should be located to reflect the center of activity in a TAZ and not necessarily the
geographic center.
Centroid
Abstract links that connect centroids to network nodes and represent general
Connector
access from a TAZ to the formal transportation network.
Page 23
Corridor
A linear study area along one or more transportation facilities for which estimates
of travel demand and system performance are desired.
Cordon Line
An abstract line defining the external boundary of a study area.
Estimation
Estimation, part of the model specification process, is the formal computation of

the parameters for a hypothesized model, to maximize the likelihood of fitting
observed data.
External
A "door" on the cordon line of a study area corresponding to major entry and exit
Station
points for external trips through, into, and out of the study area.
Home-based
A classification for trips that either begin and/or end at a trip maker's home
regardless
of
the origin and destination,
is always the production for
home-based
trips;
the
the
home
other
end
location
is
always
the attraction.
Home-based
A trip with one end at home and the other end at a non-work location.
Other
Home-based
A trip with one end at work and the other end at home.
Work
Household
A fundamental sampling unit for travel surveys, the household (HH) is a

behavioral unit of one or more individuals who share a dwelling unit, resources
(e.g., income, automobiles), and travel responsibilities. Interaction among HH
members influences travel and activity behavior.
Impedance
Impedance, a computed measure of the disincentive to travel due to spatial

separation, is a composite function of travel time (often split by access, in-vehicle,
and egress time), travel cost, and/or distance.
Incidence
An efficient means of storing network topology relationships, including node-link,
Matrix
link-path, and path-OD incidence matrices.
Page 24
External Trip
A trip with either its origin or its destination located outside of the study area. The
external trip end is assigned to an external station.
Internal Trip
A trip with both its origin and its destination located inside of the study area. If
both trip ends are outside the study area, it is a through trip.
Inter-zonal
A trip between two different analysis zones.
Trip
Intra-zonal
A trip with both origin and destination in the same zone. In trip assignment, intra-
Trip
zonal trips are not loaded on the network.
Land Use
The primary activity for which a parcel of land is used (residential, commercial,
industrial, open space, undeveloped, etc.).
Link
A fundamental element of a transportation network defined by a starting and an

ending node and having attributes such as length, travel time and/or speed, and
capacity.
Mode
A means of conveyance between origins and destinations, modes are motorized

(cars and other private vehicles, buses, rail transit) and non-motorized (walking,
bikes).
Network
A graphical and/or mathematical representation of a region's transportation

infrastructure and services, comprising links and nodes and their corresponding
characteristics.
Node
A point joining two or more links in a transportation network, and having

attributes such as spatial coordinates, turn penalties and prohibitions.
Non-Home-
A classification for trips which neither begin nor end at a trip maker's residence
Based
(home). The origin of a NHB trip is also the production; the destination of a NHB
trip is also the attraction.
Page 25
OD Matrix
A trip table in origin / destination format
Origin
The location or zone where a trip begins
Parameter
A constant describing a population property utilized in a model development

process.
Path
A sequence of links and nodes connecting an origin to a destination in a network.

Used interchangeably with route.
Peak Hour
For a transportation facility or network, the hour of the day during which the
maximum traffic volume occurs.
Person-Trip
A single trip by a single person. The output of trip generation is measured in

person-trips. On the other hand, a vehicle-trip is a single trip by a vehicle,
regardless of the number of occupants in the vehicle.
Prediction
A general term for the estimation of the value of a variable of interest in an

unknown situation.
Production
The location or zone responsible for a trip occurring but also used for
the produced trip itself: a zone is a production for N trip productions). Homebased trips, by definition, have their production in the zone containing the
household, regardless of the origin and destination of the trip. The productions for
non-home-based trips must be allocated to the NHB trip's origin zone.
Route
A path through a network; a series of links and nodes connecting an origin and a
destination. Used interchangeably with path.
Study Area
A defined region within which estimates of travel demand and system performance
are desired.
Traffic
A defined zone for travel forecasting and traffic simulation studies, represented in
Analysis Zone
the network by a centroid.
Page 26
Transportation The Transportation System constitutes the networks (modes, links, nodes, etc.)
System
connecting a region's Activity System.
Validation
An independent test of a calibrated model's predictive capabilities using data that

was not used in estimating or calibrating the model. The objective is to verify that
the model can replicate observed system performance.
(For exhaustive terminologies, visit http://www.its.uci.edu/~mcnally/tdf-glos.html#t courtesy of Professor M.G.

McNally)
Data requirements
Since transport models are applied to large systems, they require information about travelers of the
area influenced by the system. Here the data requirement is very high, and can be broadly
categorized into four:
Socio-economic data: Information regarding the socio-economic characteristics of the

study area. Important ones include income, vehicle ownership, family size, etc.
Travel surveys: Origin-destination travel survey at households and traffic data from cordon
lines. Former data include the number of trips made by each member of the household, the
direction of travel, destination, the cost of the travel, etc. The latter include the traffic flow,
speed, and travel time measurements.
Land use inventory: This includes data on the housing density at residential zones,
establishments at commercial and industrial zones.
Network data: This includes data on the transport network and existing inventories.
Transport network data includes road network, traffic signals, junctions etc. The service
inventories include data on public and private transport networks.
The data required for modeling is primarily collected through surveys. These surveys include:
Household survey
External cordon and Intercept surveys
Travel Diary
Page 27
O-D survey
Questionnaire
In-house and Roadside Interviews
Designing the data collection survey for the transportation projects requires considerable experience,
skill, and a sound understanding of the study area. It is also important to know the purpose of the
study and details of the modeling approaches. Further, many practical considerations like availability
of time and money also has a strong bearing on the survey design.
(For more on data collection and sampling, please refer chapter 3 of Ortuzar & Willumsen 2001)
Mathematical background
For this particular chapter, the modeling student needs to revise:
Multiple regression analysis
Elementary statistics
(For more on the basic mathematical requirements, please refer chapter 2 of Ortuzar and Willumsen 2001)
The Four step model
The most popular of the transport modeling approaches is the classic Four-Step Model (FSM). The
FSM aims to establish the spatial distribution of travel explicitly by means of an appropriate system
of zones. It is presented as a sequence of four mathematical sub models:
1. Trip generation- forecasts the number of trips that will be made.
2. Trip distribution- determines where the trips will go.
3. Mode usage- predicts how the trips will be divided among the available modes of travel.
4. Trip assignment- predicts the routes that the trips will take, resulting in traffic forecasts for
the highway system and rider-ship forecasts for the transit system.
In a nutshell, the FSM aims at explaining where the trips come from and where they go, and what
modes and which routes are used. The four sequential models result with the volume of traffic on
the road network, the level of service and travel attributes on each link, the split between the private
Page 28
vehicles and the public transit, etc. They can also project the level of traffic and the challenges to be
faced in the future.
1. Trip Generation
The objective of this first stage of the FSM process is to define the magnitude of total daily
travel in the model system, at the household and zonal level, for various trip purposes (activities).
This first stage also explicitly translates the FSM from activity-based to trip-based, and
simultaneously separates each trip into a production and an attraction. It aims at predicting the
total number of trips produced in the zone and attracted by it respectively for each TAZ of the
study area. It has two basic functions:
To develop a relationship between trip production or attraction and land use, and
To use the relationship developed to estimate the number of trips generated at some
future date under a new set of land-use conditions.
Trip generation (both production and attraction) depends on the nature and characteristics of
the activity system. In production models, estimates are primarily based on the demographics of
the population within a zone. For attraction models, the variables that have been found to have
the best explanatory power are those based on characteristics of the land use, such as office and
retail space or the employment levels of various sectors. Some factors which have been found to
have a considerable impact on the trip producing capacity of a TAZ are:
Income
Car ownership
Household structure
Family size
Value of land
Residential density
Accessibility
While the following factors are widely used with the affinity of a zone to attract trips:
employment
sales
Page 29
space available for industrial, commercial or other services
Trips can be modeled at the zonal, household, or personal level, with household level models
most common for trip productions and zonal level models most common for trip attractions.
Furthermore, it have been found in practice that better trip generation models can be obtained if
trips by different purposes are identified and modeled separately. In the case of home-based (HB)
trips, five categories have been usually employed:
trips to work
trips to school
shopping trips
social and recreational trips
other trips
It is also important to classify trips into peak and off-peak periods as the proportion of journeys
vary greatly with the time of the day. It is also wise to differentiate trips into personal and freight
as the two types have significant difference in nature and characteristics.
Several modeling approaches are available for trip generation including growth factor, regression,
discrete choice and category classification. In this course, only growth factor modeling and
regression analysis will be discussed.
Growth Factor Models
Growth factor model tries to predict the number of trips produced or attracted by a house hold
or a zone as a linear function of explanatory variables. The model has the following basic
equation:
where
zone and
is the number of future trips in the zone and
is the number of current trips in that
is the growth factor.
Page 30
The growth factor
depends on the explanatory variable such as population (P) of the zone,
average house hold income (I), average vehicle ownership (V). The simplest form of
is
represented as follows:
Where the subscript "d" denotes the design year and the subscript "c" denotes the current year.
The growth factor method delivers a simple and easy to understand formulation. However, the
method has usually resulted in an over-estimated number of trips (Check examples). Such an
error at the early stage of the FSM will be carried down to the subsequent stages and will grossly
mislead planners and decision makers.
Therefore, the growth factor method is only used in practice to predict the future number of
external trips to an area. This is because they are not too many in the first place (so errors cannot
be too large) and also because there are no simple ways to predict them.
Regression analysis models
Regression methods can be used to establish a statistical relationship between the number of
trips produced and the characteristics of the individuals, the zone, and the transportation
network.
The most common form of trip generation model is a linear multiple regression function of the
form:
Where
are explanatory variables such as income, car ownership, population etc. and
generated trip.
is
are parameters determined through calibration process.
Page 31
Model parameters and variables vary from one study area to another and are established by using
base-year information. Once the equations are calibrated, they are used to estimate future travel
for a target year. In developing regression equations the following is assumed:
1. All the independent variables are independent of each other.
2. All the independent variables are normally distributed.
3. The independent variables are continuous.
Two types of regression models are commonly used. The first uses data aggregated at the zonal
level, with average number of trips per household in the zone as the dependent variable and
average zonal characteristics as the independent (explanatory) variable. The second uses
disaggregated data at the household or individual level, with the number of trips made by a
household or individual as the dependent variable and the household and personal
characteristics as the independent variables.
The zonal-based regression is a premier method for modeling trip attractions where as the
household-based regression is primarily used with trip production.
(For more on trip generation models, refer chapter 4 of Ortuzar and Willumsen 2001 or chapter 4 of Bovy et.al
2006)
2. Trip Distribution
The trip-generation analysis provides the planner with the numbers of trip productions and trip
attraction that each zone will have. But where do the attractions in the zones come from and
where do the productions go? What are the zone-to-zone travel volumes?
Trip-distribution procedures determine where the trips produced in each zone will go- how they
will be divided among all other zones in the study area. The decision on where the trips go is
represented by comparing the relative attractiveness and accessibility of all zones in the area.
The major product of trip distribution models is an O-D matrix that shows the number of trips
originated in the study zone and where these trips are destined to. This is a two dimensional
array of cells where rows and columns represent each of the zones in the study area.
is the
Page 32
number of trips between origin and destination .

zone and
is the total number of trips originating in
is the total number of trips attracted to zone .
Two basic categories of aggregate trip distribution methods predominate in urban transportation
planning:
The Growth Factor methods- These involve scaling an existing matrix (called base
matrix) by applying multiplicative factors (often derived from predicted productions
and/or attractions) to matrix cells.
The Gravity Model- This explicitly relates flows between zones to inter-zonal
impedance to travel. For gravity models, typical inputs include one or more flow
matrices, an impedance matrix reflecting the distance, time, or cost of travel between
zones, and estimates of future levels of productions and attractions.
The Growth Factor Methods

In this approach a base year matrix is needed. Each cell of this matrix is multiplied by a growth
factor. Growth factors may be computed in a number of ways, e.g. as the output of an economic
model, a trend model, etc. However, in these course notes, we only discuss methods of
computing growth factors based on trip generation modeling.
The base year matrix contains an estimate of the trips being made in the base year. Depending
on these estimates, we may be able to use different growth-factor methods in our estimation of
future trip patterns.
Page 33
Uniform Growth Factor

If the only information available is about a general growth rate for the whole of the study area,
then we can only assume that it will apply to each cell in the matrix, which is a uniform growth
rate. The equation can be written as:
Where
is the uniform growth factor,
is the previous total number of trips and
is the
expected total number of trips.

Advantages are that they are simple to understand, and they are useful for short-term planning.
Limitation is that the same growth factor is assumed for all zones, where as in most cases
differential growth for different parts of the study area is expected.
Singly Constrained Growth-Factor
If information is available on the expected growth of either trips originating or trips attracted to
each zone, it will result in origin-specific
and destination-specific
growth factors
respectively. In this case, the expected number of trips between origin-destination pairs is
written as:
for origin-specific factors
for destination-specific factors
Doubly Constrained Growth Factor
When information is available on the growth in the number of trips originating and terminating
in each zone, we know that there will be different growth rates for trips in and out of each zone
and consequently having two sets of growth factors for each zone. This implies that there are
two constraints for that model and such a model is called doubly constrained growth factor
model. Historically a number of iterative methods have been proposed to obtain an estimated
trip matrix which satisfies both sets of trip-end constraints, or the two sets of growth factors.
Page 34
The best known of these methods is due to Furness (1965), who introduced balancing factors
and
as follows:
Or incorporating the growth rates into new variables
With
and
and
The factors
and
1. Set
must be calculated so that the constraints are satisfied. The procedure is:
=1
2. With
3. With
= 1, solve for
solve for
to satisfy trip generation constraint (

to satisfy trip attraction constraint (
.
.
4. Update matrix and check for errors.

5. Repeat steps 2 and 3 till convergence.
The advantages of Growth Factor method are:
1. Simple to understand.
2. Preserve observed trip pattern.
3. Useful in short term-planning.
The limitations are:
1. Depends heavily on the observed trip pattern.
2. It cannot explain unobserved trips.
3. Do not consider changes in travel cost.
4. Not suitable for policy studies like introduction of a mode.
The Gravity model
The gravity model derives its base from Newtons law of gravity, which states that the attractive
force between any two bodies is directly related to their masses and inversely related to the
Page 35
distance between them. Similarly, in the gravity model, the number of trips between two zones is
directly related to activities in the two zones, and inversely related to the separation between the
zones as a function of the generalized cost. A more general term used to represent the
generalized cost (for the separation between zones) is impedance or deterrence function.
In its simplest formulation, the model has the following functional form:
Where
is the proportionality factor and
is a generalized function of the travel costs with
one or more parameters for calibration.

The need to satisfy the constraints (
proportionality factor
by two sets of balancing factors
requires replacing the single

and
as in the Furness model,
yielding:
In the case of the doubly constrained model, the values of the balancing factors are:
The calculation of
and
, thus, requires an iterative process analogous to Furnesss as shown
in the Growth Factor modeling.

The deterrence function
is the essence of the gravity model. It takes several forms based
on the decision of the modeler such as (the last one being empirical and more common):
Page 36
The Gravity model is a synthetic model as opposed to the growth factor model. It estimates trips
for each cell of the O-D matrix without directly using observed trip pattern i.e. it doesnt require
a base year matrix to forecast future trip patterns.
(For more on trip generation models, refer chapter 5 of Ortuzar and Willumsen 2001 or chapter 5 of Bovy et.al
2006)
3. Modal Choice
In this phase of travel-demand forecasting, we analyze peoples decisions regarding mode of
travel; auto, bus, train, and so on. Before we can predict how travel will be split among the
modes available to the travelers, we must analyze the factors that affect the choices that people
make. Three broad categories of factors are considered in mode usage:
1. The characteristics of the trip maker (e.g. family income, number of autos available,
family size, residential density)
2. The characteristics of the trip (e.g. trip distance, time of day)
3. The characteristics of the transportation system (e.g. riding time, excess time)
Mode usage analysis can be done at various points in the forecasting process. Mode usage
analyses are sometimes done within trip-generation analyses. However, the most common point
is after trip distribution, because the information on where trips are going allows the mode usage
relationship to compare the alternative transportation services competing for users. Mode choice
models can also be done on both aggregate (Zonal) and disaggregate (Household or individual)
levels. In this course, we will concentrate on aggregate post-distribution models.
The most common of these aggregate post-distribution models is the family of the logit models
(binary logit, multinomial logit, nested logit etc.). A logit model is choice model that assumes an
individual maximizes utility in choosing between available alternatives. The logit model's utility
Page 37
function comprises a deterministic component (which is a function of measurable characteristics

of the individual and of the alternatives in the individual's choice set) and a stochastic
component (or error term) assumed to have an extreme value distribution
The functional form of the logit model for k number of alternative modes is:
Where
is the proportion of trips travelling from to via mode 1.
of mode 1 and
is the generalized cost
is a calibrated parameter. The logit function results in an S-shaped curve.
Figure 2.4- S-shaped logit mode choice curve

One alternation of the logit models is the Nested or Hierarchical logit model. Here the options
which have common elements are taken together in a primary split (for example, public
transport and auto-travel). After they have been separated from the uncorrelated option, they are
subdivided in a secondary split (for example, train and bus). This will avoid the error committed
in splitting modes with common properties (check the red bus/blue bus paradox).
4. Trip Assignment
Traffic assignment is the step in traffic analysis in which inter-zonal trips are assigned to the
network. The traffic demand, as described in the origin-destination (OD) tables per trip purpose
and per travel mode (and sometimes per period), is confronted with the infrastructure supply,
Page 38
which is a network of links and nodes having characteristics as capacity, maximum travel speed,
one-way streets, tolls and other factors of resistance.
Traffic assignment involves computing one or more optimal (usually shortest) routes between
each origin and destination and distributing travel demand over these routes. The sum of all trips
along these routes over all OD pairs results in a traffic load on all links and nodes. Usually, there
is a separate assignment for each mode, since the networks for each of the modes is very
different. For the sake of simplicity, we restrict ourselves to assignments of individual road
traffic (car, bike); the more complex assignments on public transportation networks will not be
discussed here.
The major aims of traffic assignment procedures are:
To estimate the volume of traffic on the links of the network and obtain aggregate
network measures.
To analyze the travel pattern of each origin to destination (O-D) pair.
To identify congested links and to collect traffic data useful for the design of future
junctions
Necessary input for the assignment:
an OD table of trips between the zones, usually all trip purposes combined;
a (computer)representation of the network;
characteristics of the network elements (links and nodes);
a route choice model.
Direct output of the assignment computation:
the routes (consecutive series of adjacent links and nodes);
the route characteristics (travel times, distances, costs);
route loads: the number of trips per route;
link and node loads: the number of trips per unit time (flow) on each link and each turn
at junctions.
Page 39
Technically, there are two broad assignment models: the minimum path assignment and the
congested assignment. The minimum path assignment models assume that the capacity and
travel cost of the links is unaffected by the volume of traffic and all the traffic will choose to
travel on the shortest path. Whereas, the congested assignment models address the fact that the
travel time and cost on a link increases as the volume of traffic on the link increases.
The all-or-nothing (AON) assignment is the basic form of the minimum path assignment
models while incremental assignment, capacity restraint assignment, user equilibrium assignment
(UE), stochastic user equilibrium assignment (SUE), system optimum assignment (SO), etc are
some forms of the congested assignment models.
All-or-Nothing Assignment
In an All-Or-Nothing (AON) assignment, all traffic between an O-D pair is assigned to just one
path (usually the shortest path) connecting the origin and destination. This model is unrealistic in
that only one path between every O-D pair is utilized even if there is another path with the same
or nearly the same travel time. Also, traffic is assigned to links without consideration of whether
or not there is adequate capacity or heavy congestion; travel time is taken as a fixed input and
does not vary depending on the congestion on a link.
However, this model may be reasonable in sparse and uncongested networks where there are
few alternative routes and they have a large difference in travel cost. This model may also be
used to identify the desired path: the path which the drivers would like to travel in the absence
of congestion. In fact, this model's most important practical application is that it acts as a
building block for other types of assignment techniques. It has a limitation that it ignores the
fact that link travel time is a function of link volume and when there is congestion or that
multiple paths are used to carry traffic.
One form of the AON is the shortest path all-or-nothing assignment. This is an assignment in which
for each OD pair the corresponding flow is assigned to a single path that, according to a fixed
set of link costs, has minimum path costs (congestion effects are not taken into account).
Page 40
Finding the minimum path in the transportation network is an optimization problem. Several
numerical formulations such as Moores and Dijkstas are available to solve this minimum path
problem. But this is outside the scope of this course.
User Equilibrium Assignment
The user equilibrium assignment is based on Wardrop's first principle, which states that:
Under equilibrium conditions traffic arranges itself in congested networks in such a way that no individual
trip maker can reduce his path costs by switching routes.
This means, in the congested network, all the used routes between an O-D pair have equal and
minimum costs while all unused routes have greater or equal costs.
The user equilibrium assignment assumes that:
The user has perfect knowledge of the path cost.
Travel time on a given link is a function of the flow on that link only.
Travel time functions are positive and increasing.
System Optimum Assignment (SO)

The system optimum assignment is based on Wardrop's second principle, which states that:
Under social equilibrium conditions, traffic should be arranged in congested networks in such a way that
the average (or total) travel cost is minimized.
This assignment can be thought of as a model in which congestion is minimised when drivers
are told which routes to use. Obviously, this is not a behaviourally realistic model, but it can be
useful to transport planners and engineers, trying to manage the traffic to minimise travel costs
and therefore achieve an optimum social equilibrium.
Page 41
In general the flows resulting from the two principles are not the same but one can only expect, in
practice, to arrange itself following an approximation to Wardrops first principle, i.e. selfish or
users equilibrium.
(For detail explanation of traffic assignment models, please refer to Ortuzar and Willumsen Chapter 10)
2.3 Evaluation and Economic Appraisal of transport projects
Assessing whether an alternative solution is worthwhile clearly involves forecasting the effect it will
have on policy indicators and weighing them up to decide whether overall the proposal is beneficial.
This process is known as appraisal. Techniques of project appraisal generally rest, wholly or partly,
on the concept of economic efficiency. An economically efficient allocation of resources is achieved
when it is possible to make one person or group in society better off without making another group
worse off. In other words, if projects could be found and undertaken which would make everyone
better off, those projects would serve to promote economic efficiency.
A project is economically efficient if the benefits measured in money terms exceed the costs; the
most efficient project is that for which the difference is greatest. A method is also required for
dealing with the fact that costs and benefits of transport projects are spread over many years.
Conventionally this is handled by the technique of discounting for time.
But some other indicators cannot be expressed in money terms and readily aggregated into a single
measure of the net benefit of the project. These may arise for two reasons: first, the difficulty of
finding satisfactory methodologies for valuing some benefits and costs in money terms, and second,
that decision-takers may wish to look at a broader range of criteria than economic efficiency. In
particular, equity, and the distribution of costs and benefits, is an objective that cannot be viewed
simply as a part of the search for economic efficiency.
Valuing Transport Costs and Benefits
Many of the transport project expenditures can be readily valued using monitory terms. Costs such
as capital and maintenance can be computed using the market price of the nation. Operating cost
usually takes the form:
Page 42
Where
is the generalized cost,
is the monitory cost,
is the journey time and
is the value of
time.
But many costs of transport projects- pain and grief resulting from accidents, environmental effectsdo not have a market price. In this case, a variety of methods have been used to try to establish what
those affected would be willing to pay for the benefits or would require in compensation for the
costs.
Turning to accidents, the costs may be divided into those that are readily valued in money terms, and
those that are not. The former include damage to property and vehicles, health service, ambulance
and police costs, and loss of production due to victims being unable to work (this again is typically
valued at the gross wage). What is more difficult is to place a money value on the pain, grief and
suffering caused by death or injury in an accident.
Transport projects have many important environmental effects, both at the local and global level. At
the local level, they lead to property demolition, noise nuisance, visual intrusion and air pollution.
They may add to the consumption of scarce and non-renewable resources such as oil. Property
demolitions can be calculated using monitory terms while it is difficult to put a price on noise and air
pollution.
But these projects result in a lot of benefits too. They result in the reduction of congestion and
travel time, provision of accessibility, enhancement of environment and so on.
The time saving can be generally indicated by the change in the operating cost after the opening of
the transport project. In the case of time savings, there is a distinction to be made between time
spent travelling during working hours (which includes bus and lorry drivers as well as business
travelers), and time spent travelling during one's own time. In the former case, it is usual to value the
time at the wage rate of the employee concerned plus a markup to allow for overhead costs of
employing labor (such as social insurance charges). This assumes that the time saved can be gainfully
employed, and that the gross wage represents the value of the marginal product of labor in its
alternative use.
Page 43
Where
is the saving in operating cost,
is the initial cost before the project and
is the
current cost after the construction of the project.

The time saving should also consider the newly generated traffic. From basic economics, the
demand for transport will increase when the operating cost decreases. Therefore, the transport
project does not only benefit the existing traffic but also the latent demand that will be generated.
Therefore, the total saving in operating cost is given by (Check OFlaherty 1997 for derivation):
Where
and
are the initial and final volume of traffic,
is the mode and is the link.
In the case of public transport, usually a fare is charged for the journey, and often the fares and
service decisions are left up to the operator, acting on a commercial basis.
Transport projects can also improve the safety of the society. At the same time, by taking traffic off
other, perhaps more environmentally sensitive roads, projects may offer environmental benefits.
Valuing such benefits in monitory terms requires advanced studies. Stated preference or revealed
preference surveys are usually adopted to understand the value the society puts on these
environmental and safety benefits.
Cost-Benefit Analysis: the Appraisal Process
The cost-benefit analysis mainly involves financial and social appraisal of the projects. Financial
appraisal of a project involves measuring all the effects of the project on the cash flow of the agent
undertaking it. These are then 'discounted' back to the present to find its Net Present Value (NPV)
in financial terms. On the other hand, in a social appraisal, one is not just concerned with cash and
not just concerned with the agent undertaking the project: the objective is to measure the benefits
and costs whoever receives them and whatever form they take.
Page 44
In order to undertake an appraisal, it is necessary to identify:
The base case (i.e. what will happen without the project)
The option (what will happen with it)
For a financial appraisal, one simply seeks to identify the change in cash flow between the above two
cases. However, in considering cash flows it is necessary to allow for the fact that one would rather
have cash now than in the future, because of the interest they could have earned if they had the
money immediately. With an interest rate of , one birr now is worth
after 2 years and
after one year,
after years. Simply reversing the procedure, it may be said that
the present value of one birr in one years time, two years time and t years time is given by:
One year
Two years
T years
This, therefore, is the basis of the method known as discounting for time to calculate the Net
Present Value (NPV) of the project.
The NPV is simply the difference between the sum of the discounted costs and the discounted
benefits. Note that the costs and benefits arising in each year of the life of the project are simply
multiplied by the discount factor which converts them into present values. It is given by:
A number of decision rules have been proposed for appraisal, but the simplest to use is to undertake
all projects for which the net present value is positive. This is only valid, however, when there is no
shortage of funds to undertake all the projects in question. If a number of projects are competing
for scarce resources, a simple value for money index can then be derived by dividing the net present
Page 45
value of the benefits minus costs of the project by the net present value of the financial requirement,
and then ranking the projects in order of this indicator.
The Net Present Value compares different alternatives satisfactorily when all costs and benefits can
be valued in money terms. But in practice, many items are not valued in money terms, whether
because of practical difficulties in ascertaining appropriate valuations or because of the inclusion of
objectives other than economic efficiency. In this situation, some sort of 'framework' layout of costs
and benefits by incidence group is the most popular approach to appraisal, whether or not it is
accompanied by a formal multi-criteria weighting system.
Multi-criteria approaches require three stages:
1. Definition of a set of objectives, which may for instance relate to accessibility, the
environment, safety, economy and equity
2. Measurement of the extent to which each project contributes towards the desired objective;
3. Weighting of the measures in order to aggregate them and produce a ranking of projects.
It appears then that, as currently practiced, multi-criteria decision-making techniques are essentially
concerned with aiding and ensuring consistency in the latter stage of weighting by the decision-taker.
But what is clear is that it must be provided in a sufficiently disaggregate form for the decision-taker
to apply, explicitly or implicitly, his or her own weights.
(For more on cost-benefit analysis, please refer to OFlaherty 1997 chapter 4)
References
C.A. OFlaherty et.al, Transport Planning and Traffic Engineering, Elsevier, 1997
C. J. Khisty and B.K. Lall, Transportation Engineering: An Introduction, 3rd Edition, Prentice Hall
of India, 2006
J.D. Ortuzar & L.G. Willumsen, Modeling Transport, 3rd edition, Wiley, 2001
P.H.L Bovy, M.C.J Blemier & R. van Nes, Transportation Modeling: CT4801 Course Notes, Delft
University of Technology, Faculty of Civil Engineering, 2
Page 46
CHAPTER 3
TRANSPORTATION SYSTEM ANALYSIS

Topics covered under this chapter are:
3.1.
Traffic engineering studies

3.1.1. Spot speed studies
3.1.2. Volume studies
3.1.3. Travel time and delay studies
3.1.4. Parking studies
3.2.
Fundamental principles of traffic flow

3.2.1. Traffic flow elements
3.2.2. Flow-density relationships
3.2.3. Fundamental diagram of traffic flow
3.2.4. Mathematical relationships describing traffic flow
3.2.5. Shock waves in traffic streams
3.2.6. Gap and gap acceptance
3.3.
Queuing Analysis
3.3.1. Queuing Patterns
3.3.2. Queuing models
3.1.
Traffic Engineering Studies
The availability of highway transportation has provided several advantages that contribute to a high
standard of living. However, several problems related to the highway mode of transportation exist.
These problems include highway-related accidents, parking difficulties, congestion, and delay. To
reduce the negative impact of highways, it is necessary to adequately collect information that
describes the extent of the problems and identifies their locations. Such information is usually
collected by organizing and conducting traffic surveys and studies.
Page 47
3.2.
Spot speed studies
Spot speed studies are conducted to estimate the distribution of speeds of vehicles in a stream of
traffic at a particular location on a highway. A spot speed study is carried out by recording the
speeds of a sample of vehicles at a specified location. Speed characteristics identified by such a study
will be valid only for the traffic and environmental conditions that exist at the time of the study.
Speed characteristics determined from a spot speed study may be used to Establish speed zones,
Determine whether complaints about speeding are valid, Establish passing and no-passing zones,
Design geometric alignment, Analyze accident data, Evaluate the effects of physical improvements,
Determine the effects of speed enforcement programs and speed control measures, to determine
speed trends and so forth.
Locations for Spot Speed Studies
The locations for spot speed studies depend on the anticipated use of the results. For example, it
may be for basic data collection or speed trend analyses. Any location may be used for the solution
of a specific traffic engineering problem. When spot speed studies are being conducted, it is
important that unbiased data be obtained. This requires that drivers be unaware that such a study is
being conducted. Equipment used should therefore be concealed from the driver, and observers
conducting the study should be inconspicuous.
Time of Day and Duration of Spot Speed Studies
The time of day for conducting a speed study depends on the purpose of the study. In general, when
the purpose of the study is to establish posted speed limits, to observe speed trends, or to collect
basic data, it is recommended that the study be conducted when traffic is free-flowing, usually
during off-peak hours. However, when a speed study is conducted in response to citizen complaints,
it is useful if the time period selected for the study reflects the nature of the complaints.
The duration of the study should be such that the minimum number of vehicle speeds required for
statistical analysis is recorded. Typically, the duration is at least 1 hour and the sample size is at least
30 vehicles.
Definitions of values that are used to describe speed characteristics:
Average speed is the arithmetic mean of all observed vehicle speeds (which is the sum of all spot
speeds divided by the number of recorded speeds). It is given as
Page 48
u=
fu
f
i i
or ; u =
Where: u = arithmetic mean; f i = number of observations in each speed group; u i = mid value
for the ith speed group; n = number of observed values
Median speed is the speed at the middle value in a series of spot speeds that are arranged in
ascending order. Fifty percent of the speed values will be greater than the median; 50 percent
will be less than the median.
Modal speed is the speed value that occurs most frequently in a sample of spot speeds.
The ith-percentile spot speed is the spot speed value below which i percent of the vehicles
travel; for example, 85th-percentile spot speed is the speed below which 85 percent of the
vehicles travel and above which 15 percent of the vehicles travel.
Pace is the range of speed- usually taken at 10-mph intervals- that has the greatest number of
observations.
Standard deviation of speeds is a measure of the spread of the individual speeds. It is

estimated as
S=
(u
u)2
N 1
Where: S = standard deviation; u = arithmetic mean; u j =
jth observation; N = number of observations

However, speed data are frequently presented in classes where each class consists of all
range of speeds. The standard deviation is computed for such cases as
S=
( f u
i
2
i
( f i u i ) 2 / f i
Where: u i = midvalue of speed class i, f i = frequency of speed class i

Sample Size for Spot Speed Studies
The calculated mean (or average) speed is used to represent the true mean value of all vehicle speeds
at that location. The accuracy of this assumption depends on the number of vehicles in the sample.
The larger the sample size, the greater the probability that the estimated mean is not significantly
different from the true mean. It is therefore necessary to select a sample size that will give an
estimated mean within acceptable error limits. Statistical procedures are used to determine this
Page 49
minimum sample size.

The minimum sample size depends on the precision level desired. The precision level is defined as
the degree of confidence that the sampling error of a produced estimate will fall within a desired
fixed range. Thus, for a precision level of 90-10, there is a 90 percent probability (confidence level)
that the error of an estimate will not be greater than 10 percent of its true value. The confidence
level is commonly given in terms of the level of significance ( ), where = (100 - confidence
level). The commonly used confidence level for speed counts is 95 percent.
The properties of the normal distribution have been used to develop an equation relating the sample
size to the number of standard variations corresponding to a particular confidence level, the limits of
tolerable error, and the standard deviation.
Z
The formula is N =
Where: N= minimum sample size; Z = number of standard deviations
d
2
corresponding to the required confidence level 1.96 for 95 percent confidence level; = standard
deviation (mph); d = limit of acceptable error in the speed estimate (mph). The standard deviation
can be estimated from previous data, or a small sample size can first be used.
Methods for Conducting Spot Speed Studies
The methods used for conducting spot speed studies can generally be divided into two main
categories: manual and automatic. Several automatic devices that can be used to obtain the
instantaneous speeds of vehicles at a location on a highway are now available on the market. These
automatic devices can be grouped into three main categories:
(1) Those that use road detectors,
(2) Those that use Doppler principle meters (radar type), and
(3) Those that use the principles of electronics.
Road Detectors
Road detectors can be classified into two general categories: pneumatic road tubes and induction
loops. These devices can be used to collect data on speeds at the same time as volume data are being
collected. When road detectors are used to measure speed, they should be laid such that the
probability of a passing vehicle closing the connection of the meter during a speed measurement is
reduced to a minimum. This is achieved by separating the road detectors by a distance of 3 to 15 ft.
The advantage of the detector meters is that human errors are considerably reduced. The
Page 50
disadvantages are that (1) these devices tend to be rather expensive, and (2) when pneumatic tubes
are used, they are rather conspicuous and may, therefore, affect driver behavior, resulting in a
distortion of the speed distribution.
Doppler-Principle Meters
Doppler meters work on the principle that when a signal is transmitted onto a moving vehicle, the
change in frequency between the transmitted signal and the reflected signal is proportional to the
speed of the moving vehicle. The difference between the frequency of the transmitted signal and
that of the reflected signal is measured by the equipment, and then converted to speed in mph. In
setting up the equipment, care must be taken to reduce the angle between the direction of the
moving vehicle and the line joining the center of the transmitter and the vehicle. The value of the
speed recorded depends on that angle. If the angle is not zero, an error related to the cosine of that
angle is introduced, resulting in a lower speed than that which would have been recorded if the angle
had been zero. However, this error is not very large, because the cosines of small angles are not
much less than 1.
The advantage of this method is that because pneumatic tubes are not used, if the equipment can be
located at an inconspicuous position, the influence on driver behavior is considerably reduced.
Electronic-Principle Detectors
In this method, the presence of vehicles is detected through electronic means, and information on
these vehicles is obtained, from which traffic characteristics such as speed, volume, queues, and
headways are computed. The great advantage of this method over the use of road detectors is that it
is not necessary to physically install loops or any other type of detector on the road. The most
promising technology using electronics is video image processing, sometimes referred to as a
machine-vision system. This system consists of an electronic camera overlooking a large section of
the roadway and a microprocessor. The electronic camera receives the images from the road; the
microprocessor determines the vehicle's presence or passage. This information is then used to
determine the traffic characteristics in real time. One such system is the auto scope.
3.3.
Volume studies
Traffic volume studies are conducted to collect data on the number of vehicles and/or pedestrians
that pass a point on a highway facility during a specified time period. This time period varies from as
little as 15 min to as much as a year, depending on the anticipated use of the data. The data collected
Page 51
may also be put into subclasses which may include directional movement, occupancy rates, vehicle
classification, and pedestrian age. Traffic volume studies are usually conducted when certain volume
characteristics are needed, some of which are:
1. Average Annual Daily Traffic (AADT) is the average of 24-hr counts collected every day in
the year. AADTs are used in several traffic and transportation analyses for
a.
Estimation of highway user revenues
b.
Computation of accident rates in terms of accidents per 100 million vehicles per miles
c.
Establishment of traffic volume trends
d.
Evaluation of the economic feasibility of highway projects
e.
Development of freeway and major arterial street systems
f.
Development of improvement and maintenance programs
2. Average Daily Traffic (ADT) is the average of 24-hour counts collected over a number of days
greater than 1 but less than a year. ADTs may be used for Planning of highway activities,
Measurement of current demand, Evaluation of existing traffic flow and so forth.
3. Peak Hour Volume (PHV) is the maximum number of vehicles that pass a point on a highway
during a period of 60 consecutive minutes. The peak hour volumes PHVs are used for,
Functional classification of highways, Design of the geometric characteristics of a highway, for
example, number of lanes, intersection signalization, or channelization, For capacity analysis,
Development of programs related to traffic operations, for example street systems or traffic
routing and Development of parking regulations and etc.
4. Vehicle Classification (VC) records Volume with respect to the type of vehicles, for example,
passenger cars, two-axle trucks, or three-axle trucks. VC is used in
a. Design of geometric characteristics, with particular reference to turning radii requirements,
maximum grades, and lane widths, and so forth
b. Capacity analyses, with respect to passenger-car equivalents of trucks
c. Adjustment of traffic counts obtained by machines
d. Structural design of highway pavements, bridges, and so forth
5. Vehicle Miles of Travel (VMT) is a measure of travel along a section of road. It is the product
of the traffic volume (that is, average weekday volume or ADT) and the length of roadway in
miles to which the volume is applicable. VMTs are used mainly as a base for allocating resources
Page 52
for maintenance and improvement of highways.

Methods of Conducting Volume Counts
Traffic volume counts are conducted using two basic methods: manual and automatic.
I.
Manual Method
Manual counting involves one or more persons recording observed vehicles using a counter. The
main disadvantages of the manual count method are that (1) it is labor-intensive and can therefore
be expensive, (2) it is subject to the limitations of human factors, and (3) it cannot be used for long
periods of counting.
II.
Automatic Method
The automatic counting method involves the laying of surface detectors (such as pneumatic road
tubes) or subsurface detectors (such as magnetic or electric contact devices) on the road. These
detect the passing vehicle and transmit the information to a recorder, which is connected to the
detector at the side of the road.
Traffic Volume Data Presentation
The data collected from traffic volume counts may be presented in one of several ways, depending
on the type of count conducted and the primary use of the data. Some of the conventional data
presentation techniques are:
Traffic Flow Maps
Intersection Summary Sheets
Time-Based Distribution Charts
Summary Tables
Traffic Volume Characteristics

A continuous count of traffic at a section of a road will show that traffic volume varies from hour to
hour, from day to day, and from month to month. However, the regular observation of traffic
volumes over the years has identified certain characteristics showing that although traffic volume at
a section of a road varies from time to time this variation is repetitive and rhythmic. These
characteristics of traffic volumes are taken in to consideration when traffic counts are being planned
so that volumes collected at a particular time or place can be related to volumes collected at other
times and places. Knowledge of these characteristics can also be used to estimate the accuracy of
Page 53
traffic counts.
Sample Size and Adjustment of Periodic Counts
The impracticality of collecting data continuously every day of the year at all counting stations makes
it necessary to collect sample data from each class of highway and to estimate annual traffic volumes
from periodic counts. This involves the determination of the minimum sample size (number of
count stations) for a required level of accuracy and the determination of daily, monthly, and/or
seasonal expansion factors for each class of highway.
Determination of Number of Count Stations
The minimum sample size depends on the precision level desired. The commonly used precision
level for volume counts is 95-10. When the sample size is less than 30 and the selection of counting
stations is random, a distribution known as the student's t distribution may be used to determine the
sample size for each class of highway links. The student's t distribution is unbounded, with a mean
of zero, and has a variance that depends on the scale parameter, commonly referred to as the
degrees of freedom ( ). The degrees of freedom ( ) is a function of the sample size; = N -1 for
the student's t distribution. The variance of the student's t distribution is /( - 2), which indicates
that as approaches infinity, the variance approaches 1.
Assuming that the sampling locations are randomly selected, the minimum sample number is given
as
n=
t2 / 2, N 1 ( S 2 / d 2 )
1 + (1 / N )(t2 / 2, N 1 )( S 2 / d 2 )
Where: n = minimum number of count locations required; t = value of the student's t distribution
with (1 - /2) confidence level (N - 1 degrees of freedom); N = total number of links (population)
from which a sample is to be selected = significance level; S = estimate of the spatial standard
deviation of the link volumes; d= allowable range of error
To use the above equation, estimates of the mean and standard deviation of the link volumes are
required. These estimates can be obtained by taking volume counts at a few links or by using known
values for other, similar highways.
Page 54
Adjustment of Periodic Counts

Expansion factors, used to adjust periodic counts, are determined either from continuous count
stations or from control count stations.
Expansion Factors from Continuous Count Stations- Hourly, daily, and monthly expansion
factors can be determined using data obtained at continuous count stations.
Hourly expansion factors (HEFs) are determined by the formula
HEF =
total..volume.. for..24 hr.. period

volume.. for.. particular..hour
These factors are used to expand counts of durations shorter than 24 hr to 24-hr volumes by
multiplying the hourly volume for each hour during the count period by the HEF for that hour and
finding the mean of these products.
Daily expansion factors (DEFs) are computed as
DEF =
average..total..volume.. for..the..week
average..volume.. for.. particular..day
These factors are used to determine weekly volumes from counts of 24-hr duration multiplying the
24-hr volume by the DEF.
Monthly expansion factors (MEFs) are computed as
MEF =
AADT
ADT .. for.. particular..month
The AADT for a given year may be obtained from the ADT for a given month multiplying this
volume by the MEF.
3.3.1. Travel time and delay studies
A travel time study determines the amount of time required to travel from one point to another on a
given route. In conducting such a study, information may also be collected on the locations,
durations, and causes of delays. When this is done, the study is known as a travel time and delay
study. Data obtained from travel time and delay studies give a good indication of the level of service
on the study section. These data also aid the traffic engineer in identifying problem locations, which
may require special attention in order to improve the overall flow of traffic on the route.
Page 55
Applications of Travel Time and Delay Data

The data obtained from travel time and delay studies may be used in any one of the following traffic
engineering tasks:
Determination of the efficiency of a route with respect to its ability to carry traffic
Identification of locations with relatively high delays and the causes for those delays
Performance of before-and-after studies to evaluate the effectiveness of traffic operation

improvements
Determination of relative efficiency of a route by developing sufficiency ratings or

congestion indices
Determination of travel times on specific links for use in trip assignment models
Compilation of travel time data that may be used in trend studies to evaluate the changes in
efficiency and level of service with time
Performance of economic studies in the evaluation of traffic operation alternatives that

reduce travel time.
Definition of Terms Related to Time and Delay Studies

1. Travel time is the time taken by a vehicle to traverse a given section of a highway
2. Running time is the time a vehicle is actually in motion while traversing a give section of a
highway.
3. Delay is the time lost by a vehicle due to causes beyond the control of the driver.
4. Operational delay is that part of the delay caused by the impedance of other traffic This
impedance can occur either as side friction, where the stream flow is interfered with by other
traffic (for example, parking or un parking vehicles), or as internal friction, where the
interference is within the traffic stream (for example, reduction in capacity of the highway).
5. Stopped-time delay is that part of the delay during which the vehicle is at rest
6. Fixed delay is that part of the delay caused by control devices such as traffic signals. This
delay occurs regardless of the traffic volume or the impedance that may exist.
7. Travel-time delay is the difference between the actual travel time and the time that will be
obtained by assuming that a vehicle traverses the study section at an average speed equal to
Page 56
that for an uncontested traffic flow on the section being studied.
Methods for Conducting Travel Time and Delay Studies

Several methods have been used to conduct travel time and delay studies. These methods can be
grouped into two general categories:
(1) Those using a test vehicle and
(2) Those not requiring a test vehicle.
Methods Requiring a Test Vehicle
This category involves three possible techniques:
Floating-car,
Average-speed and
Moving-vehicle techniques.
Floating-Car Technique. In this method, the test car is driven by an observer along the
test section so that the test car "floats" with the traffic. The driver of the test vehicle
attempts to pass as many vehicles as those that pass his test vehicle. The time taken to
traverse the study section is recorded. This is repeated, and the average time is as the travel
time. The minimum number of test runs can be determined using values of the Tdistribution. The equation is
t .
N = -- d
2
eq4.8
Where: N = sample size (minimum number of test runs), s = standard deviation (mph), d = limit of
acceptable error in the speed estimate (mph), t = value of the student's t distribution with (1 - a/2)
confidence level and (N - 1) degrees of freedom, a = significance level
The limit of acceptable error used depends on the purpose of the Study. The following limits are
commonly used:
Before-and-after studies: 1.0 to 3.0 mph
Traffic operation, economic evaluations, and trend analyses: 2.0 to 4.0
Highway needs and transportation planning studies: 3.0 to 5.0 mph
Page 57
Average-Speed Technique. This technique involves driving the test car along the length of
the test section at a speed that, in the opinion of the driver, is the average speed of traffic
stream. The time required to traverse the test section is noted. The test run is repeated for
the minimum number of times, determined from Eq. 4.8, and the avenge time is recorded as
the travel time.
Moving-Vehicle Technique. In this technique, the observer makes a round trip on a test
section like the one shown in Figure 4.15, where it is assumed that the road runs east-west.
The observer starts collecting the relevant data at section X-X, drives the car eastward to
section Y-Y, and then turns the vehicle around and drives westward to section X-X again.
The following data are collected as the test vehicle makes the round trip:
The time it takes to travel from X-X to Y-Y (Te), in minutes
The time it takes to travel from Y-Y to X-X (Tw), in minutes
The number of vehicles traveling west in the opposite lane while the test car is traveling
east (Ne)
The number of vehicles that overtake the test car while it is traveling from Y-Y to X-X,
that is, traveling in the westbound direction (Ow)
The number of vehicles that the test car passes while it is traveling from Y-Y to X-X,
that is, traveling in the westbound direction (Pw)
The volume (Vw) in the westbound direction can then be obtained from the expression
Vw =
( N e + Ow Pw ) * 60
-----------4.9
Te + Tw
Where, (Ne+ Ow - Pw) is the number of vehicles traveling westward that cross the line X-X during
the time (Te-Tw). Note that when the test vehicle starts at X-X, traveling eastward, all vehicles
traveling westward should get to XX before the test vehicle, except those that are passed by the test
vehicle when it is traveling westward. Similarly, all vehicles that pass the test vehicle when it is
traveling westward will get to X-X before the test vehicle. The test vehicle will also get to X-X
before all vehicles it passes while traveling westward. These vehicles have, however, been counted as
part of Ne or Ow and should therefore be subtracted from the sum of Ne and Ow to determine the
number of westbound vehicles that cross X-X during the time the test vehicle travels from X-X to
Page 58
Y-Y and back to X-X.

Similarly, the average travel time Tw in the westbound direction is obtained from
Tw Tw Ow Pw
=
Vw
60 60
60 * (Ow Pw )
Tw = Tw
Vw
----------4.10
If the test car is traveling at the average speed of all vehicles, it will most likely pass the same number
of vehicles as the number of vehicles that overtake it. Since it is probable that the test car will not be
traveling at the average speed, the second term of Eq. 4.10 corrects for the difference between the
number of vehicles that overtake the test car and the number of vehicles that are overtaken by the
test car.
Methods Not Requiring a Test Vehicle
This category includes the
License-plate method and
The interview method
License-Plate Observations. The license-plate method requires that observers be positioned at the beginning and end of the test section. Observers can also be positioned at other
locations if elapsed times to those locations are required. Each observer records the last
three or four digits of the license plate of each car that passes, together with the time at
which the car passes. The reduction of the data is accomplished in the office by matching
the times of arrival at the beginning and end of the test section for each license plate
recorded. The difference between these times is the traveling time of each vehicle. The
average of these is the average traveling time on the test section. It has been suggested that a
sample size of 50 matched license plates will give reasonably accurate results.
Interviews. The interviewing method is carried out by obtaining information from people
who drive on the study site regarding their travel times, their experience of delays, and so
forth. This method facilitates the collection of a large amount of data in a relatively short
time. However, it requires the cooperation of the people contacted, since the result depends
entirely on the information given by them.
Page 59
3.3.2. Parking studies

Types of Parking Facilities
Parking facilities can be divided into two main groups:
On-street and
Off-street.
On-Street Parking Facilities

These are also known as curb facilities. Parking bays are provided alongside the curb on one or both
sides of the street. These bays can be unrestricted parking facilities if the duration of parking is
unlimited and parking is free, or they can be restricted parking facilities if parking is limited to
specific times of the day for a maximum duration. Parking at restricted facilities may or may not be
free. Restricted facilities may also be provided for specific purposes, such as to provide handicapped
parking or as bus stops or loading bays.
Off-Street Parking Facilities
These facilities may be privately or publicly owned; they include surface lots and garages. Selfparking garages require that drivers park their own automobiles; attendant-parking garages maintain
personnel to park the automobiles.
Definitions of Parking Terms
1. A space-hour is a unit of parking that defines the use of a single parking space for a period of 1
hr.
2. Parking volume is the total number of vehicles that park in a study area during a specific length
of time, usually a day.
3. Parking accumulation is the number of parked vehicles in a study area at any specified time.
These data can be plotted as a curve of parking accumulation against time, which shows the
variation of the parking accumulation during the day.
4. The parking load is the area under the accumulation curve between two specific times. It is
usually given as the number of space-hours used during the specified period of time.
5. Parking duration is the length of time a vehicle is parked at a parking bay. When the parking
duration is given as an average, it gives an indication of how frequently a parking space becomes
available.
6. Parking turnover is the rate of use of a parking space. It is obtained by dividing the parking
Page 60
volume for a specified period by the number of parking spaces.

Methods of Parking Studies
A comprehensive parking study usually involves
(1) Inventory of existing parking facilities,
(2) Collection of data on parking accumulation, parking turnover, and parking duration,
(3) Identification of parking generators, and
(4) Collection of information on parking demand.
(5) Information on related factors, such as financial, legal, and administrative matters, may also
be collected.
Analysis of Parking Data
Analysis of parking data includes summarizing, coding, and interpreting the data so
that the relevant information required for decision-making can be obtained. The relevant
information includes
Number and duration for vehicles legally parked
Number and duration for vehicles illegally parked
Space-hours of demand for parking
Supply of parking facilities
The analysis required to obtain information on the first two items is straightforward; it usually
involves simple arithmetical and statistical calculations. Data obtained from these items are then
used to determine parking space-hours.
The space-hours of demand for parking are obtained from the expression
N
D = ( ni t i )
i =1
Where: D= space vehicle-hours demand for a specific period of time; N = number of classes of
parking duration ranges; ti = mid parking duration of the ith class; ni= number of vehicles parked
for the ith duration range
The space-hours of supply are obtained from the expression
N
S = f (t i )
i =1
Where: S = practical number of space-hours of supply for a specific period of time; N = number of
Page 61
parking spaces available; ti = total length of time in hours when the ith space can be legally parked
on during the specific period; f= efficiency factor
The efficiency factor is used to correct for time lost in each turnover. It is determined on the basis
of the best performance a parking facility is expected to produce. Efficiency factors should therefore
be determined for different types of parking facilities for example, surface lots, curb parking, and
garages. Efficiency factors for curb parking, during highest demand, vary from 78 percent to 96
percent; for surface lots and garages, from 75 percent to 92 percent. Average values of f are 90
percent for curb parking, 80 percent for garages, and 85 percent for surface lots.
3.4. Fundamental Principles of Traffic Flow

Traffic flow theory involves the development of mathematical relationships among the primary
elements of a traffic stream: flow, density, and speed. These relationships help the traffic engineer in
planning, designing, and evaluating the effectiveness of implementing traffic engineering measures
on a highway system. Traffic flow theory is used in design to determine adequate lane lengths for
storing left-turn vehicles on separate left-turn lanes, the average delay at intersections and freeway
ramp merging areas, and changes in the level of freeway performance due to the installation of
improved vehicular control devices on ramps. Another important application of traffic flow theory
is simulation, where mathematical algorithms are used to study the complex interrelationships that
exist among the elements of a traffic stream or network and to estimate the effect of changes in
traffic flow on factors such as accidents, travel time, air pollution, and gasoline consumption.
3.4.1. Traffic flow elements
Let us first define the elements of traffic flow before discussing the relationships among them.
Before we do that, though, we will describe the time-space diagram, which serves as a useful device
for defining the elements of traffic flow.
Page 62
The time-space diagram is a graph that describes the relationship between the location of vehicles in
a traffic stream and the time as the vehicles progress along the highway. Figure 6.1 shows a timespace diagram for six vehicles, with distance plotted on the vertical axis and time on the horizontal
axis, At time zero, vehicles 1, 2, 3, and 4 are at respective distances d1, d2, d3, and d4 from a
reference point, whereas vehicles 5 and 6, cross the reference point later at times t5 and t6
respectively.
The primary elements of traffic flow are flow, density, and speed. Another element associated with
density, is the gap or headway between two vehicles in a traffic
The definitions of these elements follow.
Flow (q) is the equivalent hourly rate at which vehicles pass a point on a highway during a time
period less than 1 hr. It can be determined by
q=
n * 3600
vph
T
Where: n = the number of vehicles passing a point in the roadway in T secs; q = the equivalent
hourly flow.
Density (k), sometimes referred to as concentration, is the number of vehicles traveling over a
unit length of highway at an instant in time. The unit length is usually 1 mile thereby making vehicles
per mile (vpm) the unit of density.
Speed (u) is the distance traveled by a vehicle during a unit of time. It can be expressed in miles per
hour (mph), kilometers per hour (km/h), or feet per second (ft/sec). The speed of a vehicle at any
time t is the slope of the time-space diagram for that vehicle at time t. Vehicles 1 and 2 in Figure 6.1,
Page 63
for example, are moving at a constant speed because the slopes of the associated graphs are constant.
Vehicle 3 moves at a constant speed between time zero and time t3, then stops for the period t3 to
t3(the slope of the graph equals zero), and then accelerates and eventually moves at a constant
speed.
There are two types of mean speeds: time mean speed and space mean speed.
Time mean speed ( u t ) is the arithmetic mean of the speeds of vehicles passing a point on a
highway during an interval of time. The time mean speed is found by
ut =
1 n
ui
n i =1
Where: n =number of vehicles passing a point on the highway; ui = speed of the ith vehicle (ft/sec)
Space mean speed ( u s ) is the harmonic mean of the speeds of vehicles passing a point in a
highway during an interval of time. It is obtained by dividing the total distance traveled by two or
more vehicles on a section of highway by the total time required by these vehicles to travel that
distance. This is the speed that is involved in flow-density relationships. The space mean speed is
found by
ut =
n
n
(1/ ui )
i =1
nL
n
t
i =1
Where: u s = space mean speed (ft/sec); n = number of vehicles; ti = the time it takes the ith vehicle
to travel across a section of highway (see); Ui =speed of the ith vehicle (ft/sec); L = length of
section of highway (ft)
Time headway (h) is the difference between the time the front of a vehicle arrives at a point on the
highway and the time the front of the next vehicle arrives at that same point. Time headway is
usually expressed in seconds. For example, in the time-space diagram (Figure 6.1), the time headway
between vehicles 3 and 4 at d1 is h3-4.
Space headway (d) is the distance between the front of a vehicle and the front of the following
vehicle. It is usually expressed in feet. The space headway between vehicles 3 and 4 at time t5 is d3-4
(see Figure 6.1).
Page 64
3.4.2.
Flow-density relationships
The general equation relating flow, density, and space mean speed is given as
Flow = (density) x (space mean speed)
q = k * u s --------------3.5
Each of the variables in Eq. 6.5 also depends on several other factors, including the characteristics
of the roadway, the characteristics of the vehicle, the characteristics of the driver, and environmental
factors such as the weather.
Other relationships that exist among the traffic flow variables are given below.
Space mean speed = (flow) x (space headway)

us = q * d
Where: d = (1/ k) = average space headway
Density = (flow) x (travel time for unit distance)

k = q *t
Where: t is the average time for unit distance.

Average space headway = (space mean speed) x (average time headway)
d = us * h
Average time headway = (average travel time for unit distance) x (average space headway)
h = t *d
3.4.3. Fundamental diagram of traffic flow

The relationship between the density (vpm) and the corresponding flow of traffic on a highway
generally is referred to as the fundamental diagram of traffic flow. The fol1owing theory has been
postulated with respect to the shape of the curve depicting this relationship.
1. When the density on the highway is zero, the flow is also zero because there are no vehicles
on the highway.
2. As the density increases, the flow also increases.
3. However, when the density reaches its maximum, generally referred to as the jam density (kj),
the flow must be zero because vehicles will tend to line up end to end.
4. It follows that as density increases from zero, the flow will also initially increase from zero to
Page 65
a maximum value. Further continuous increase in density will result in continuous reduction
of the flow, which will eventually be zero when the density is equal to the jam density. The
shape of the curve therefore takes the form in Figure 6.3a.
A similar argument can be postulated for the general relationship between the space mean speed and
the f1ow. When the flow is very low, there is little interaction between individual vehicles. Drivers
are therefore free to travel at the maximum possible speed. The absolute maximum speed is
obtained as the flow tends to zero, and it is known as the mean free speed (Uf). Continuous increase
in flow will result in a continuous decrease in speed. A point will be reached, however, when further
addition of vehicles will result in the reduction of the actual number of vehicles that pass a point on
the highway (that is, reduction of flow). This result in congestion, and eventually both the speed and
the flow become zero. Figure 6.3c shows this general relationship. Figure 6.3b shows the direct
relationship between speed and density.
From Eq. 6.5, we know that space mean speed is flow divided by density, which makes the slopes of
lines OB, OC, and OE in Figure 6.3a represents the space mean speeds at densities kb, kc, and ke,
respectively. The slope of line OA is the speed as the density tends to zero and little interaction
exists between vehicles. The slope of this line is therefore the mean free speed (Uf); it is the
maximum speed that can be attained on the highway. The slope of line OE is the space mean speed
for maximum flow. This maximum flow is the capacity of the highway. Thus it can be seen that it is
desirable for highways to operate at densities not greater than that required for maximum flow.
Page 66
3.4.4. Mathematical relationships describing traffic flow

Mathematical relationships describing traffic flow can be classified into two general Categories macroscopic and microscopic- depending on the approach used in the development of these
relationships. The macroscopic approach considers flow density relationships, whereas the
microscopic approach considers spacing between and speed of individual vehicles.
Macroscopic Approach
The macroscopic approach considers traffic streams and develops algorithms that relate the flow to
the density and space mean speeds. The two most commonly used macroscopic models are the
Green shields and Greenberg models.
Green shields Model. Green shields carried out one of the earliest recorded works, in which he
studied the relationship between speed and density. He hypothesized that a linear relationship
existed between speed and density, which he expressed as
us = u f
uf
kj
* k ------3.11
Corresponding relationships for flow and density and for flow and speed can be developed. Since
q = u s k substituting q / u s , for k in Eq. 3.11 gives
Page 67
u s = u f .u s
2
uf
kj
* q ------3.12
Also substituting q / k for u s , in Eq. 6.11 gives

q = u f .k
uf
kj
* k 2 -------3.13
Equations 6.12 and 6.13 indicate that if a linear relationship in the form of Eq. 6.11 is assumed for
speed and density, then parabolic relationships are obtained between flow and density and between
flow and speed. The shape of the curve shown in Figure 6.3a will therefore be a parabola. Also, Eqs.
6.12 and 6.13 can be used to determine the corresponding speed and the corresponding density for
maximum flow.
Consider Eq. 6.12.
u s = u f .u s
2
uf
kj
*q
Differentiating q with respect to u s we obtain

2u s = u f
u f dq
k j du s
That is,
kj
kj
kj
dq
= uf
2u s
= k j 2u s
uf
uf
du s
uf
For maximum flow,
uf
kj
dq
=> u o =
-----3.14
= 0 => k j = 2u s
2
uf
du s
Thus, the space mean speed u o , at which the volume is maximum, is equal to half the free mean
speed.
Consider Eg. 3.13.
q = u f .k
uf
kj
*k2
Page 68
Differentiating q with respect to k, we obtain

uf
dq
= u f 2k
dk
kj
For maximum flow,
kj
uf
dq
=> k o =
-----3.15
= 0 => u f = 2k
2
kj
dk
Thus, at the maximum flow, the density k. is half the jam density. The maximum flow for the
Greenshields relationship can therefore be obtained from Eqs. 6.5, 6.14, and 6.15, as shown in Eq.
6.16.
k ju f
q max =
----------3.16
Greenberg Model. Several researchers have used the analogy of fluid flow to develop macroscopic
relationships for traffic flow. One of the major contributions using the fluid-flow analogy was
developed by Greenberg in the form
u s = c ln
kj
q = ck ln
kj
-------3.17
-------3.18
Differentiating q with respect to k, we obtain
kj
dq
= c ln c
dk
k
For maximum flow,
kj
dq
=1
= 0 , ln
k
dk
Giving ln k j = 1 + ln k o -----3.19
That is, ln
kj
ko
= 1 and Substituting 1 for ln
kj
ko
in eq 3.17 gives u o = c
Thus, the value of c is the speed at maximum flow.
Page 69
Model Application
Use of these macroscopic models depends on whether they satisfy the boundary criteria of the
fundamental diagram of traffic flow at the region that describes the traffic conditions. For example,
the Green shields model satisfies the boundary conditions when the density k is approaching zero as
well as when the density is approaching the jam density kj. The Greenshields model therefore can be
used for light or dense traffic. The Greenberg model, on the other hand, satisfies the boundary
conditions when the density is approaching the jam density, but it does not satisfy the boundary
conditions when k is approaching zero. The Greenberg model is therefore useful only for dense
traffic conditions.
Calibration of Macroscopic Traffic Flow ModelsThe traffic models discussed thus far can be used to determine specific characteristics such as the
speed and density at which maximum flow occurs and the jam density of a facility. This usually
involves collecting appropriate data on the particular facility of interest and fitting the data points
obtained to a suitable model. The most common method of approach is regression analysis. This is
done by minimizing the squares of the differences between the observed and the expected values of
a dependent variable. When the dependent variable is linearly related to the independent variable,
the process is known as linear regression analysis, and when the relationship is with two or more
independent variables, the process is known as multiple linear regression analysis.
If a dependent variable y and an independent variable x are related by an estimated regression
function, then
y = a + bx ------3.20
The constants a and b could be determined from

a=
1 n
b n
y
xi = y bx ------------3.21
i n
n i =1
i =1
And
n
b=
xi y i
i =1
1 n
n
xi y i
n i =1 i =1 ----------3.22
xi2
i =1
1 n
xi
n i =1
Page 70
Where: n = number of sets of observations; xi = ith observation for x; yi = ith observation for y
A measure commonly used to determine the suitability of an estimated regression function is the
coefficient of determination (or square of the estimated correlation coefficient) R 2 , which is given
by
n
R =
2
(Y
y) 2
(y
y)
i =1
n
i =1
---------3.23
Where: Yi is the value of the dependent variable as computed from the regression equations.
The closer R 2 is to 1, the better the regression fit.
Microscopic Approach
The microscopic approach, which is sometimes referred to as the car-following theory or the followthe-leader theory, considers spacing between and speeds of individual vehicles. Consider two
consecutive vehicles, A and B, on a single lane of a highway, as shown in Figure 6.6. If the leading
vehicle is considered to be the nth vehicle and the following vehicle is considered the (n + 1)th
vehicle, then the distances of these vehicles from a fixed section at any time t can be taken as x n
and x n +1 respectively.
If the driver of vehicle B maintains an additional separation distance P above the separation distance
at rest S such that P is proportional to the speed of vehicle B, then
p = .x n +1 ---------3.25
Where: = factor of proportionality with units of time; x n +1 = speed of the (n + l)th vehicle
Page 71
We can write
x n x n +1 = .x n +1 + S -----3.26
Where S is the distance between front bumpers of vehicles at rest
Differentiating Eq. 6.26 gives
xn +1 =
( x n x n +1 ) ----3.27
Equation 6.27 is the basic equation of the microscopic models, and it describes the stimulus
response of the models. Researchers have shown that a time lag exists for a driver to respond to any
stimulus that is induced by the vehicle just ahead, and Eq. 6.27 can therefore be written as
xn +1 (t + T ) = [ x n (t ) x n +1 (t )] ------3.28
Where: T = time lag of response to the stimulus; = (1 / ) (sometimes called the sensitivity)
A general expression for is given in the form
=a
x nm+1 (t + T )
--------3.29
[ x n (t ) x n +1 (t )]l
The general expression for the microscopic models can then be written as
xn +1 (t + T ) = a
x nm+1 (t + T )
[ x n (t ) x n +1 (t )] -------3.30
[ x n (t ) x n +1 (t )]l
Where a, l, and m are constants.

The microscopic model (Eq. 6.30) can be used to determine the velocity, flow, and density of a
traffic stream when the traffic stream is moving in a steady state. The direct analytical solution of
either Eq. 6.28 or Eq. 6.30 is not easy. It can be shown, however, that the macroscopic models
discussed earlier can all be obtained from Eq. 6.30.
For example, if m = 0 and l = 1, the acceleration of the (n+ 1)th vehicle is given as
xn +1 (t + T ) = a
x n (t ) x n +1 (t )
[ x n (t ) x n +1 (t )]
Integrating the above expression, we find that the velocity of the (n + 1)th vehicle is
x n +1 (t + T ) = a ln[ x n (t ) x n +1 (t + 1)] + C
Since we are considering the steady state condition,
Page 72
x n (t + T ) = x n (t ) = u
u = a ln[ x n x n +1 ] + C
Also,
x n x n +1 = Average space headway =

u = a ln
1
k
1
+C
k
Using the boundary condition,
u = 0 When k = k j
1
0 = a ln + C
k
j
1
C = a ln
k
j
Substituting for C in the equation for u, we obtain
1
1
u = a ln a ln
k
k
j
kj
u = a ln
k
Which is the Greenberg model given in eq. 3.17. Similarly, if m s allowed to be 0 and l =2, we obtain
the Greenshilds model.
3.4.5. Shock waves in traffic streams
The fundamental diagram of traffic flow for two adjacent sections of a highway with different
capacities (maximum flows) is shown in Figure 6.7. This figure describes the phenomenon of
backups and queuing on a highway due to a sudden reduction of the capacity of the highway (known
as a bottle neck condition). The sudden reduction in capacity could be due to accidents, reduction in
the number of lanes, restricted bridge sizes, work zones, a signal turning red, and so forth, creating a
situation where the capacity on the highway suddenly changes from C1 to a lower value of C2, with
a corresponding change in optimum density from k oa to a value of k o .
b
Page 73
When such a condition exists and the normal flow and density on the highway are relatively large,
the speeds of the vehicles will have to be reduced while passing the bottleneck. The point at which
the speed reduction takes place can be approximately noted by the turning on of the brake lights of
the vehicles. An observer will see that this point moves upstream as traffic continues to approach
the vicinity of the bottleneck, indicating an upstream movement of the point at which flow and
density change. This phenomenon is usually referred to as a shockwave in the traffic stream.
Let us consider two different densities of traffic, k1 and k 2, along a straight highway as shown in
Figure 6.8, where k 1 > k 2. Let us also assume that these densities are separated by the line w,
representing the shock wave moving at a speed Uw. If the line w moves in the direction of the arrow
(that is, in the direction of the traffic flow), Uw is positive.
Page 74
With U1 equal to the space mean speed of vehicles in the area with density kl (section P), the speed
of the vehicle in this area relative to the line w is
u r1 = (u1 u w )
The number of vehicles crossing line w from area P during a time period t is
N 1 = u r 1 k1t
Similarly, the speed of vehicles in the area with density k2 (section Q) relative to w is
u r 2 = (u 2 u w )
And the number of vehicles crossing line w during a time period t is
N 2 = ur 2 k 2t
Since the net change is zero
N1 = N 2
(u1 u w )k1t = (u 2 u w )k 2 t
u 2 k 2 u1 k1 = u w (k 2 k1 ) -----6.31
If the flow rates in sections P and Q are ql and q2, respectively, then
q 2 = u 2 k 2 , q1 = u1 k1
Substituting ql and q2 for k1u1 and k2u2 in Eg. 6.31 gives
q 2 q1 = u w (k 2 k1 )
That is,
uw =
q 2 q1
k 2 k1
Which is also the slope of the line CD shown in Figure 6.7. This indicates that the velocity of the
shock wave created by a sudden change of density from kl to k2 on a traffic stream is the slope of
the chord joining the points associated with kl and k2 on the volume density curve for that traffic
stream.
Special Cases of Shock Wave Propagation
The shock wave phenomenon can also be explained by considering a continuous change of flow and
density in the traffic stream. If the change in flow and the change in density are very small, we can
write
Page 75
q 2 q1 = q
k 2 k1 = k
The wave velocity can then be written as
uw =
q dq
-------3.33
=
k dk
Since q = ku s , Substituting ku s for q in eq 6.33 gives
uw =
d (ku s )
-----3.34
dk
uw = us k
du s
dk
When such a continuous change of volume occurs in a vehicular flow, a phenomenon similar to that
of fluid flow exists, in which the waves created in the traffic stream transport the continuous
changes of flow and density. The speed of these waves is dq/dk and is given by Eq.6.34.
We have already seen that as density increases, the space mean speed decreases (see Eq. 6.5), giving a
negative value for du/dk. This shows that at any point on the fundamental diagram, the speed of the
wave is theoretically less than the space mean speed of the traffic stream. Thus, the wave moves in
the opposite direction relative to that of that of the traffic stream.
The actual direction and speed of the wave will depend on the point at which we are on the curve
(that is, the flow and density on the highway), and the resultant effect on the traffic downstream will
depend on the capacity of the restricted area (bottleneck).
1. When both the flow and the density of the traffic stream are very low, that is, approaching
zero, the flow is much lower than the capacity of the restricted area and there is very little
interaction between the vehicles. The differential of u s with respect to k (du s / dk ) then
tends to zero, and the wave velocity approximately equals the space mean speed. The wave
therefore moves forward with respect to the road, and no backups result.
2. As the flow of the traffic stream increases to a value much higher than zero but still less than
the capacity of the restricted area (say, q3 in Figure 6.7), the wave velocity is still less than
the space mean speed of the traffic stream, and the wave moves forward relative to the road.
This results in a reduction in speed and an increase in the density from k3 to k3b as vehicles
Page 76
enter the bottleneck but no backups occur.

3. When the volume on the highway is equal to the capacity of the restricted area (C2 in Figure
6.7), the speed of the wave is zero and the wave does not move. This result in a much slower
speed and a greater increase in the density to k ob as the vehicles enter the restricted area.
Again, delay occurs but there are no backups.
4. However, when the flow on the highway is greater than the capacity of the restricted area,
not only is the speed of the wave less than the space mean speed of the vehicle stream, but it
moves backward relative to the road. As vehicles enter the restricted area, a complex queuing
condition arises, resulting In an immediate increase in the density from k1to k2 in the
upstream section of the road and a considerable decrease in speed. The movement of the
wave toward the upstream section of the traffic stream creates a shock wave in the traffic
stream, eventually resulting in backups, which gradually moves upstream of the traffic stream.
The expressions developed for the speed of the shock wave, Eqs. 3.32 and 3.34, can be applied to
any of the specific models described earlier. For example, the Greenshields model can be written as
k
u si = u f 1 i
k
j
k
u si = u f (1 ) where i = i
k
j
(normalized density)
If the Greenshields model fits the flow density relationship for a particular traffic stream, Eq.3.32
can be used to determine the speed of a shock wave as
k
k
k 2 u f 1 2 k1u f 1 1
k
k
j
j
uw =
k 2 k1
u f (k 2 k1 )
=
uf
kj
u f (k 2 k1 )
(k 22 k12 )
k 2 k1
= k 2 u f (1 2 ) k1u f (1 1 ) = u f (k 2 k1 ) k 2 u f ( 2 ) + k1u f (1 )
k 2 k1
k 2 k1
==
uf
kj
(k 2 k1 )(k 2 + k1 )
k 2 k1
= u f [1 (1 2 )]
The speed of a shock wave for the Green shields model is therefore given as
= u f [1 (1 2 )] ------3.36
Page 77
Density Nearly Equal

When there is only a small difference between kl and k2 (that is, 1 2 ), (neglecting the small
change in 1 )
u w = u f [1 (1 2 )] = u f [1 21 ]
Stopping Waves
Equation 6.36 can also be used to determine the velocity of the shock wave due to the change from green to
red of a signal at an intersection approach if the Greenshields model is applicable. During the green phase,
the normalized density is 1 .When the traffic signal changes to red, the traffic at the stop line of the
approach comes to a halt, which results in a density equal to the jam density. The value of 2 is then equal to
1. The speed of the shock wave, which in this case is a stopping wave, can be obtained by
u w = u f [1 (1 + 1)]
u w = u f 1
-----6.37
Equation 6.37 indicates that in this case the shock wave travels upstream of the traffic with a
velocity of u f 1 . If the length of the red phase is t sec, then the length of the line of cars upstream at
the stop line is u f 1t .
Starting Waves
At the instant when the signal again changes from red to green, 1 equals 1. Vehicles will then move
forward at a speed of u s 2 , resulting in a density of 2 .The speed of the shock wave, which in this
case is a starting wave, is obtained by
u w = u f [1 (1 + 2 )]
u w = u f 2
-------6.38
Equation 6.35, u s 2 = u f (1 2 ) , gives 2 = 1
us2
uf
The velocity of the shock wave is then obtained as

u w = u f + u s 2
Since the starting velocity u s 2 just after the signal changes to green is usually small, velocity of the
starting shock wave approximately equals u f .
Page 78
3.4.6. Gap and gap acceptance

Thus far we have been considering the theory of traffic flow as it relates to the flow of vehicles in a
single stream. Another important aspect of traffic flow is the interaction of vehicles as they join,
leave, or cross a traffic stream. Examples of these include ramp vehicles merging onto an
expressway stream, freeway vehicles leaving the freeway onto frontage roads, and the changing of
lanes by vehicles on a multilane highway. The most important factor a driver considers in making
anyone of these maneuvers is the availability of a gap between two vehicles that, in the driver's
judgment, is adequate for him or her to complete the maneuver. The evaluation of available gaps
and the decision to carry out a specific maneuver within a particular gap are inherent in the concept
of gap acceptance.
Following are the important measures that involve the concept of gap acceptance.
Merging is the process by which a vehicle in one traffic stream joins another traffic stream moving
in the same direction, such as a ramp vehicle joining a freeway stream.
Diverging is the process by which a vehicle in a traffic stream leaves that traffic stream, such as a
vehicle leaving the outside lane of an expressway.
Weaving is the process by which a vehicle first merges into a stream of traffic, obliquely crosses that
stream, and then merges into a second stream moving in the same direction; for example, the
maneuver required for a ramp vehicle to join the far side stream of flow on an expressway.
Gap is the headway in a major stream, which is evaluated by a vehicle driver in a minor stream who
wishes to merge into the major stream. It is expressed either in units of time (time gap) or in units of
distance (space gap).
Time lag is the difference between the time a vehicle that merges into a main traffic stream reaches
a point on the highway in the area of merge and the time a vehicle in the main stream reaches the
same point.
Space lag is the difference, at an instant of time, between the distance a merging vehicle is away
from a reference point in the area of merge and the distance a vehicle in the main stream is away
from the same point.
Figure 6.9 depicts the time-distance relationships for a vehicle at a stop sign waiting to merge and
for vehicles on the near lane of the main traffic stream.
Page 79
A driver who intends to merge must first evaluate the gaps that become available to determine
which gap (if any) is large enough to accept the vehicle, in his or her opinion. In accepting that gap,
the driver feels that he or she will be able to complete the merging maneuver and safely join the
main stream within the length of the gap. This phenomenon generally is referred to as gap
acceptance. It is of importance when engineers are considering the delay of vehicles on minor
roads wishing to join a major-road traffic stream at un-signalized intersections, and also the delay of
ramp vehicles wishing to join expressways. It can also be used in timing the release of vehicles at an
on-ramp of an expressway, such that the probability of the released vehicle finding an acceptable gap
in arriving at the freeway shoulder lane is maximum.
3.3.
Queuing Analysis
One of the major issues in the analysis of any traffic system is the analysis of delay. Delay is a more
subtle concept. It may be defined as the difference between the actual travel time on a given
segment and some ideal travel time of that segment. This raises the question as to what is the ideal
travel time. In practice, the ideal travel time chosen will depend on the situation; in general, however,
there are two particular travel times that seem best suited as benchmarks for comparison with the
actual performance of the system. These are the travel time under free flow conditions and
travel
time
at capacity. Most recent research has found that for highway systems, there is
comparatively little difference between these two speeds. That being the case, the analysis of delay
normally focuses on delay that results when demand exceeds its capacity; such delay is known as
queuing delay, and may be studied by means of queuing theory. This theory involves the analysis of
what is known as a queuing system, which is composed of a server; a stream of customers, who
Page 80
demand service; and a queue, or line of customers waiting to be served. The F i g . 1 s h o w s a

schematic diagram illustrating the concept of a queuing system.
Figure: Components of a basic queuing system

For the analysis of a queuing system the input parameters are discussed in the following section.
Input parameters
Mean arrival rate ()
Mean service rate ()
The number of servers (N)
Queue discipline
Mean arrival rate is rate at which customers arrive at a service facility. It is expressed in flow
(customers/hr or vehicles/hour) or time headway (seconds/customer or seconds/vehicle). If inter
arrival time that is time headway (h) is known, the arrival rate can be found out from the equation:
where
is in veh/hr
Mean arrival rate can be specified as a deterministic distribution or probabilistic distribution and
sometimes demand or input are substituted for arrival.
Mean service rate is the rate at which customers (vehicles depart from a transportation facility. It
is expressed in flow (customers/hr or vehicles/hour) or time headway (seconds/customer or
seconds/veh. If inter service time that is time headway (h) is known, the service rate can be
found out from the equation:
where
is in veh/hr
The number of servers that are being utilized should be specified and in the manner they work
that is they work as parallel servers or series servers has to be specified.
Page 81
Queue discipline is a parameter that explains how the customers arrive at a service facility. The
various types of queue disciplines are
First in first out (FIFO) If the customers are served in the order of their arrival, then
this is known as the first-come, first- served (FCFS) service discipline. Prepaid taxi queue at
airports where a taxi is engaged on a first-come, first-served basis is an example of this discipline.
First in last out (FILO) Sometimes, the customers are serviced in the reverse order of their
entry so that the ones who join the last are served first. For example, the people who join an
elevator first are the last ones to leave it.
Served in random order (SIRO) under this rule customers are selected for service at
random, irrespective of their arrivals in the service system. In this every customer in the queue
is equally likely to be selected. The time of arrival of the customers is, therefore, of no relevance
in such a case.
Priority scheduling under this rule customers are grouped in priority classes on the basis of
some attributes such as service time or urgency or according to some identifiable characteristic,
and FIFO rule is used within each class to provide service. Treatment of VIPs in preference to
other patients in a hospitalis an example of priority service.
3.3.1. Queuing Patterns
A variety of queuing patterns can be encountered and a classification of these patterns is
proposed in this section. The classification scheme is based on how the arrival and service rates vary
over time. In the following figures the top two graphs are drawn taking time as
independent variable and volume of vehicles as dependent variable and the bottom two graphs
are drawn taking time as independent variable and cumulative volume of vehicles as dependent
variable.
Page 82
Constant arrival and constant service rates
Figure : Constant arrival and service rates ( l = arrival rate and m = service rate)
In the left hand part of the above Fig. arrival rate is less than service rate so no queuing is encountered
and in the right hand part of the figure the arrival rate is higher than service rate, the queue has a never
ending growth with a queue length equal to the product of time and the difference between the arrival
and service rates.
Constant arrival rate and varying service rate
Figure: Constant arrival rate and varying service rate (= arrival rate, = service rate)
In the left hand of the above Fig. the arrival rate is constant over time while the service rates vary
over time. It should be noted that the service rate must be less than the arrival rate for some
periods of time but greater than the arrival rate for other periods of time. One of the examples
of the left hand part of the figure is a signalized intersection and that of the right hand side part of
the figure is an incident or an accident on the roads which causes a reduction in the service rate.
Page 83
Varying arrival rate and constant service rate
Figure: Varying arrival rate and constant service rate

In the left part of t h e Fig. the arrival rate vary over time but service rate is constant. Both the
left and right parts are examples of traffic variation over a day on a facility but the left hand
side one is an approximation to make formulations and calculations simpler and the right
hand side one considers all the transition periods during changes in arrival rates.
Varying arrival and service rates
Figure: Varying arrival and service rates

In the Fig. the arrival rate follows a square wave type and service rate follows inverted square wave
type. The diagrams on the right side are an extension of the first one with transitional periods
during changes in the arrival and service rates. These are more complex to analyzed using analytical
Page 84
methods so simulation is often employed particularly when sensitivity parameter is to be

investigated.
3.3.2. Queuing models
There are various kinds of queuing models. These queuing models have a set of defined
characteristics like some arrival and service distribution, queue discipline, etc. The queuing models
are represented by using a notation which is discussed in the following section of queue notation.
Queue Notation
The generally used notation for describing queue is given by X / Y/ N where in place of X the
arrival distribution type should be used, in place of Y the service distribution type should be used,
N represents the number of servers. Some of the most general notations are D/D/1, D/D/N,
M/D/N, M/M/N, M/G/N where D stands for deterministic, M stands Markovian, G stands
for Generalized.
The analysis of these models is classified as deterministic analysis and stochastic analysis. If
either the arrival distribution and/or the service distribution are probabilistic, the exact arrival
and/or service time of each vehicle is unknown, and stochastic queuing analysis must be selected.
On the other hand, if both the arrival and service distributions are deterministic, the arrival and
service times of each vehicle are known and deterministic queuing analysis is selected. In the
following sections some of the most commonly used models like M/M/1, M/M/N, etc. with their
formulae for calculations of delays are discussed.
M/M/1 model
In this model the arrival times and service rates follow markovian distribution or exponential
distribution which are probabilistic distributions, so this is an example of stochastic process. In this
model there is only one server. Some of the assumptions we make in this model are given below.
Assumptions
1. Customers are assumed to be patient.
2. System is assumed to have unlimited capacity.
3. Users arrive from an unlimited source.
Page 85
4. The queue discipline is assumed to be first in first out.

The various parameters that are to be evaluated in a queuing model and their formulae for this
model are given below.
The following formulae are valid only if arrival rate is less than service rate.
x = 0,1,2.....the number of customers at any instant. With this formula we can find out what
percentage x number of customers are in the system. If x is taken as zero the formula yields the
percentage of time the server is idle. The average number of customers at any time in the system
The average number of customers in the queue at any time is
Expected time a customer spends in the system
Expected time a customer spends in the queue
Page 86
Numerical Example 1
The Vehicles arrive at a toll booth at an average rate of 300 per hour. Average waiting time at the
toll booth is 10s per vehicle. If both arrivals and departures are exponentially distributed, what is the
average number of vehicles in the system, average queue length, the average delay per vehicle,
the average time a vehicle is in the system?
Solution
= 300 veh/hr
vehicles/hr
Utilization factor = traffic intensity =

The
percent
of
time
the
toll
booth
will
be
idle
(0)
P(X=0)
=8.34 min.
The average number of vehicles in the system =

The average number of vehicles in the queue =
The average a vehicle spend in the system =
=4.98
= 4.01
= 0.016 hr = 0.96 min = 57.6 sec
The average time a vehicle spends in the queue
M/M/N model
The difference between the earlier model and this model is the number of servers. This is a multi server model with N number of servers whereas the earlier one was single server model. The
assumptions stated in M/M/1 model are also assumed here.
Page 87
Figure: Multi-server model

Here
is the average service rate for N identical service counters in parallel. For x=0
The probability of x number of customers in the system is given by P(x) for 1
For X
The average number of customers in the system is
Page 88
The average queue length
The expected time in the system
The expected time in the queue
Numerical Example 2
Consider the earlier problem as a multi-server problem with two servers in parallel.
Solution
=300 veh/hr
The average number of vehicles in the system

The average time a vehicle spend in the system =
T h e a v e r ag e t i m e a v e h i c l e s pe n d i n g i n t h e q u e u e
= 0.387
= 0.004 hr = 14 sec
= 0.00129hr = 4.64sec
Page 89
Multiple single servers' model

In this model there are N numbers of identical independent parallel servers
which
receive
customers from a same source but in different parallel queues (Compare to M/M/N model. It
has only one queue) each one receiving customers at a rate of
. Fig. shows how a typical
multiple single servers' model looks like.
Figure: Multiple single servers

Numerical Example 3
Consider the problem 1 as a multiple single server's model with two servers which work
independently with each one receiving half the arrival rate that is 150 veh/hr.
Solution
=150 veh/hr
Page 90
The percent of time the toll booth will be idle P(X=0)

35.04 min
P (0) =
The average number of vehicles in the system =
= 0.712
= 0.296
The average a vehicle spend in the system =
=0.0047 hr = 0.285 min = 17.14 sec
The average time a vehicle spends in the queue =
=0.0022hr =0.13 min = 8.05 sec
Comparison of the results obtained using three models

Table: Comparison of the results obtained using three models
M/M/1
M/M/2
Multiple
model
model
sever model
single
Idle time of toll

booths (minutes)
8.34
55.2
35.04
4.98
1.22
0.712
4.01
0.387
0.296
57.6
14
17.14
50
4.64
8.05
Number of vehicles
in the system (unit)
Number of vehicles
in the queue (unit)
Average waiting time
in system (seconds)
Average waiting time
in queue (seconds)
Page 91
From the Table by providing 2 servers the queue length reduced from 4.01 to 0.387 and the
average waiting time of the vehicles came down from 50 sec to 4.64 sec, but at the expense of
having either one or both of the toll booths idle 92% of the time as compared to 13.9% of the time
for the single-server situation. Thus there exists a trade-off between the customers'
convenience and the cost of running the system.
D/D/N model
In this model the arrival and service rates are deterministic that is the arrival and service times of
each vehicle are known. Assumptions
1. Customers are assumed to be patient.
2. System is assumed to have unlimited capacity.
3. Users arrive from an unlimited source.
4. The queue discipline is assumed to be first in first out.
Numerical Example 4
Morning peak traffic upstream of a toll booth is given in the table below. The toll plaza consists of
three booths, each of which can handle an average of one vehicle every 8 seconds. Determine
the maximum queue, the longest delay to an individual vehicle.
Time period
10 minVolume
7.00 - 7.10
200
7.10 - 7.20
400
7.20 - 7.30
500
7.30 - 7.40
250
7.40 - 7.50
200
7.50 - 8.00
150
Page 92
Solution: The arrival volume is given in the table 2. Service rate is given as 8 seconds per vehicle.
This implies for 10 min, 75 vehicles can be served by each server. It is given there are 3 servers.
Hence 225 vehicles can be served by 3 servers in 10 min. In the first 10 min only 200 vehicles
arrive which are served so the service rate for rest 50 min is 225 veh/10 min as there is a
queue for the rest period. The solution to the problem is showed in the table 3 following.
The cumulative arrivals and services are calculated in columns 3 and 5. Queue length at the end of
any 10 min interval is got by simply subtracting column 5 from column 3 and is recorded in
column 6. Maximum of the column 6 is maximum queue length for the study period which
is 300 vehicles. The service rate has been found out as 225 vehicles per hour. From
proportioning we get the time required for each queue length to be served and as 475 vehicles
is the max queue length, the max delay is corresponding to this queue. Therefore max delay is 21.11
min.
Time
period
10 min Cumulative
Cumulative
volume
volume rate
Service service
Queue
Delay
7.00 - 7.10
200
200
200
200
0.00
7.10 - 7.20
400
600
225
425
175
7.78
7.20 - 7.30
500
1100
225
650
450
20.00
7.30 - 7.40
250
1350
225
875
475
21.11
7.40 - 7.50
200
1550
225
1100
450
20.00
7.50 - 8.00
150
1700
225
1325
375
16.67
The queuing models often assume infinite numbers of customers, infinite queue capacity, or no
bounds on inter-arrival or service times, when it is quite apparent that these bounds must exist in
reality. Often, although the bounds do exist, they can be safely ignored because the differences
between the real-world and theory is not statistically significant, as the probability that such
boundary situations might occur is remote compared to the expected normal situation. Furthermore,
Page 93
several studies show the robustness of queuing models outside their assumptions. In other cases the
theoretical solution may either prove intractable or insufficiently informative to be useful.
Alternative means of analysis have thus been devised in order to provide some insight into problems
that do not fall under the scope of queuing theory, although they are often scenario-specific because
they generally consist of computer simulations or analysis of experimental data.
References
1. Traffic engineering third edition by Roess & Prasas, 2004

2. Highway Engineering , Martin rogers
3. Traffic and Highway Engineering, Nicholas J. Garber
Page 94
CHAPTER 4
Highway Capacity and Level of Service Concepts
Topics covered under this chapter are:
4.1. Introduction
4.2. Factors affecting level of service
4.3. Determining the capacity and LOS of a highway
4.3.1. Analysis Methodologies for Basic Freeway Sections and Multilane Highways
4.3.2. Analysis method of Two-Lane Rural Highways Capacity
4.1.
Introduction
One of the most critical needs in traffic engineering is a clear understanding of how much traffic a
given facility can accommodate and under what operating conditions. These important issues are
addressed in highway capacity and level-of-service analysis. The basis for all capacity and level-ofservice analysis is a set of analytic procedures that relate demand or existing flow levels, geometric
characteristics, and controls to measures of the resulting quality of operations.
Highway Capacity
The capacity of a facility defined as the maximum hourly flow rate at which the maximum number
of vehicles, passengers, or the like, per unit time, which can be accommodated under prevailing
roadway, traffic and control conditions with a reasonable expectation of occurrence. For most cases,
to analyze the capacity we used the peak 15 minutes of the peak hour.
Capacity is independent of the demand. It speaks about the physical amount of vehicles and
passengers that a road can afford. It does not depend on the total number of vehicles demanding
service. Generally the highway capacity depends on certain conditions as listed below;
1. Road way characteristics: This are associated with the geometric characteristics and design
elements of the facility, which include type of facility, number of lanes, lane width, shoulder
width, horizontal and vertical alignments, lateral clearance, design speed, and availability of
queuing space at intersections. For example, a curved road has lesser capacity compared to a
straight road.
Page 95
2. Traffic conditions: Capacity is expressed in terms of units of some specific thing (car, people,
etc.), so it also does depend on the traffic conditions. The traffic conditions are associated with
the characteristics of the traffic stream on the segment of the highway. These include the
distribution of the different types of vehicles in the traffic stream or traffic composition such as
the mix of cars, trucks, buses etc. and the directional and lane distribution of the traffic volume
on the highway segment. Furthermore it includes peaking characteristics, proportions of turning
movements at intersections etc.
3. Control conditions: This primarily applies to surface facilities and includes the types of traffic
control devices in operation, signal phasing, allocation of green time, cycle length, and the
relationship with adjacent control measures.
Level of Service
The level-of-service concept was introduced in the 1965 HCM as a convenient way to describe the
general quality of operations on a facility with defined traffic, roadway, and control conditions.
Using a letter scale from A to F, a terminology for operational quality was created that has become
an important tool in communicating complex issues to decision-makers and the general public. The
HCM 2000 defines level of service as follows: "Level of service (LOS) is a quality measure
describing operational conditions within a traffic stream, generally in terms of such service measures
as speed and travel time, freedom to maneuver, traffic interruptions, and comfort and convenience."
A term level-of-service closely related to capacity and often confused with it is service volume.
When capacity gives a quantitative measure of traffic, level of service or LOS tries to give a
qualitative measure. Service volume is the maximum number of vehicles, passengers, or the like,
which can be accommodated by a given facility or system under given conditions at a given level of
service.
Level of service (LOS) qualitatively measures both the operating conditions within a traffic system
and how these conditions are perceived by drivers and passengers. It is related with the physical
characteristics of the highway and the different operating characteristics that can occur when the
highway carries different traffic volumes. Speed-flow-density relationships are the principal factor
affecting the level of service of a highway segment under ideal conditions.
Page 96
For a given road or facility, capacity could be constant. But actual flow will be different for different
days and different times in a day itself. The intention of LOS is to relate the traffic service quality to
a given flow rate of traffic. It is a term that designates a range of operating conditions on a particular
type of facility. Highway capacity manual (HCM) provides some procedure to determine level of
service. It divides the quality of traffic into six levels ranging from level A to level F. Level A
represents the best quality of traffic where the driver has the freedom to drive with free flow speed
and level F represents the worst quality of traffic.
Service
A:
This
represents
free-flow
conditions where traffic flow is virtually zero.

Only the geometric design features of the
highway may limit the speed of the car.
Level of service A
Comfort and convenience levels for road

users are very high as vehicles have almost
complete freedom to maneuver.
Service B: Represents reasonable free-flow

conditions. Comfort and convenience levels for
road users are still relatively high as vehicles have
only slightly reduced freedom to maneuver.
Minor accidents are accommodated with ease
although local deterioration in traffic flow
conditions would be more discernible than in
service A.
Level of service B
Service C: Delivers stable flow conditions.
lane. While minor incidents can still be
Flows are at a level where small increases will
absorbed, major incidents will result in the
cause a considerable reduction
the
formation of queues. The speed chosen by the
performance or service of the highway.
driver is substantially affected by that of the
There are marked restrictions in the ability to
other
in
vehicles.
Driver
comfort
and
maneuver and care is required when changing

Page 97
convenience have decreased perceptibly at
Level of service C
this level
Service D: The highway is operating at highdensity levels but stable flow still prevails.
Small increases in flow levels will result in
significant operational difficulties on the
highway. There are severe restrictions on a
drivers ability to maneuver, with poor levels
Level of service D
of comfort and convenience.
Service E: Represents the level at which the

capacity of the highway has been reached.
Traffic flow conditions are best described as
unstable with any traffic incident causing
extensive queuing and even breakdown.
Levels of Basic Elements of comfort and
convenience are very poor and all speeds are
low if relatively uniform.
Level of service E
Service F: Describes a state of breakdown or
with constant queuing and traffic moving on a
forced flow with flows exceeding capacity.
stop-go basis.
The operating conditions are highly unstable

Page 98
Level of service F
4.2.
Factors affecting level of service
One can derive from a road under different operating characteristics and traffic volumes. The
factors affecting level of service (LOS) can be listed as follows:
1. Speed and travel time
2. Traffic interruptions/restrictions
3. Freedom to travel with desired speed
4. Driver comfort and convenience
5. Operating cost.
Factors such as lane width, lateral obstruction, traffic composition, grade and driver population also
affect the maximum flow on a given highway segment. The effect of each of these factors on flow is
discussed.
Lane Width. Traffic flow tends to be restricted when lane widths are narrower than 12 ft
(3.65m). This is because vehicles have to travel closer together in the lateral direction, and
motorists tend to compensate for this by driving more cautiously and by increasing the spacing
between vehicles, thus reducing the maximum flow on the highway.
Lateral Obstruction. In general, when roadside or median objects are located too close to the
edge of the pavement, motorists in lanes adjacent to the object tend to shy away from the object,
resulting in reduced lateral distances between vehicles. This lateral reduction in space also results
in longer spacings between vehicles and a reduction in the maximum flow on the highway. This
effect is eliminated if the object is located at least 6ft (1.8m) from the edge of the roadway. Note,
however, that lateral clearances are based mainly on safety considerations and not on flow
consideration.
Page 99
Traffic Composition. The presence of vehicles other than passenger cars-such as trucks, buses, and
recreational vehicles-in a traffic stream reduces the maximum flow on the highway because of their
size, operating characteristics, and interaction with other vehicles.
Grade. The effect of a grade depends on both the length and the slope of the grade. Traffic
operations are significantly affected when grades of 3 percent or greater are longer than 1/4 mi
(400m) and when grades are less than 3 percent and longer than l/2 mi (800m). The effect of heavy
vehicles on such grades is much greater than that for passenger vehicles.
Speeds, Space mean speed, are also used in level-of-service analysis because flow has a significant
effect on speed.
Driver Population. Under ideal conditions, a driver population consisting primarily of weekday
commuters is assumed. However, it is known that other driver populations do not exhibit the same
behavior.
Because these factors affect traffic operations on the highway, it is essential that they be considered in
any LOS analysis. Highway Capacity Manual (HCM) used travel speed and volume by capacity ratio (v/c
ratio) to distinguish between various levels of service. The value of v/c ratio can vary between 0 and 1.
Depending upon the travel speed and v/c ratio, HCM has defined six levels of service as shown in the
figure 1.
These operating conditions can be expressed

graphically with reference to the basic speedflow relationship. At the level of service A,
speed is near its maximum value, restricted
only by the geometry of the road, and flows
are low relative to the capacity of the highway,
given the small number of vehicles present. At
the level of service D, flows are maximized,
with speed at approximately 50% of its
maximum value. Level of service F denotes
the breakdown condition at which both
Figure 4.1 Linkage between level of service

(LOS), speed and flow/capacity.
speeds and flow levels tend towards zero.
Page 100
4.3.
Determining the capacity and LOS of a highway
Level of service describes in a qualitative way the operational conditions for traffic from the
viewpoint of the road user. It gauges the level of congestion on a highway in terms of variables such
as travel time and traffic speed.
In order to determine a roads level of service, a comprehension of the relationship between hourly
volume, peak hour factor and service flow is vital:
Hourly volume (V) The highest hourly volume within a 24-hour period
Peak-hour factor (PHF) The ratio of the hourly volume to the peak 15 minute flow (V 15 ) enlarged
to an hourly value
PHF = V V 15 4 .. (4.1)
Service flow (SF) The peak 15 minute flow (V 15 ) enlarged to an hourly value
SF = V 15 4 (4.2)
4.3.1. Analysis Methodologies for Basic Freeway Sections and Multilane Highways
The characteristics and criteria described for freeways and multilane highways in the previous
section apply to facilities with base traffic and roadway conditions.
In most cases, base conditions do not exist, and a methodology is required to address the impact of
prevailing conditions on these characteristics and criteria.
Analysis methodologies are provided that account for the impact of a variety of prevailing
conditions, including:
Lane widths
Lateral clearances
Number of lanes (freeways)
Type of median (multilane highways)
Frequency of interchanges (freeways) or access points (multilane highways)
Presence of heavy vehicles in the traffic stream
Driver populations dominated by occasional or unfamiliar users of a facility
Page 101
Some of these factors affect the free-flow speed of the facility, while others affect the equivalent
demand flow rate on the facility.
Speed-Flow Characteristics
Capacity analysis procedures for freeways and multilane highways are based on calibrated speed-flow
curves for sections with various free-flow speeds operating under base conditions. Base conditions
for freeways and multilane highways indicated above.
Figures 4.2 and 4.3 show the standard curves calibrated for use in the capacity analysis of basic
freeway sections and multilane highways. These exhibits also show the density lines that define levels
of service for uninterrupted flow facilities. Modem drivers maintain high average speeds at relatively
high rates of flow on freeways and multilane highways.
This is clearly indicated in Figures 4.2 and 4.3. For freeways, the free-flow speed is maintained until
flows reach 1,300 to 1,750 pc/hr/ln. Multilane highway characteristics are similar. Thus, on most
uninterrupted flow facilities, the transition from stable to unstable flow occurs very quickly and with
relatively small increments in flow.
Levels of Service
For freeways and multilane highways, the measure of effectiveness used to define levels of service is
density. The use of density, rather than speed, is based primarily on the shape of the speed-flow
relationships depicted in Figures 4.2 and 4.3. Because average speed remains constant through most
of the range of flows and because the total difference between free-flow speed and the speed at
capacity is relatively small, defining five level-of-service boundaries based on this parameter would
be very difficult.
Page 102
Fig 4.2 Speed-Flow Curves for Basic Freeway Sections
Fig 4.3 Speed-Flow Curves for Multilane Highway Sections
Page 103
Types of Analysis
There are three types of analysis that can be conducted for basic freeway sections and multilane
highways:
Operational analysis
Service flow rate and service volume analysis
Design analysis
All forms of analysis require the determination of the free-flow speed of the facility in question.
Field measurement and estimation techniques for making this determination are discussed in a later
section.
1. Operational Analysis
The most common form of analysis is operational analysis. In this form of analysis, all traffic,
roadway, and control conditions are defined for an existing or projected highway section, and the
expected level of service and operating parameters are determined.
The basic approach is to convert the existing or forecast demand volumes to an equivalent flow rate
under ideal conditions:
.4.1
Where:
V P = demand flow rate under equivalent ideal conditions, pc/h/ln
PHF = peak-hour factor
N = number of lanes (in one direction) on the facility
f Hv = adjustment factor for presence of heavy vehicles
f P = adjustment factor for presence of occasional or non-familiar users of a facility
Page 104
This result is used to enter either the standard speed-flow curves of Figure 4.2 (freeways) or 4.3
(multilane highways). Using the appropriate free-flow speed, the curves may be entered on the x-axis
with the demand flow rate, V P , to determine the level of service and the expected average speed.
Service Flow Rate and Service Volume Analysis

It is often useful to determine the service flow rates and service volumes for the various levels of
service under prevailing conditions. The service flow rate for level of service i is the maximum flow
rate that can be maintained under prevailing condition. Prevailing conditions are usually not the
same as the ideal conditions, and therefore the service flow rate must be obtained by adjusting the
maximum service flow MSF i to reflect the number of lanes and the prevailing conditions. The
maximum service flow rate at level of service i (MSF i ) is the maximum flow that a section of the
freeway can maintain at level of service i under ideal conditions. Ideal conditions are defined as
follows:
1. Lanes are 12ft (3.65m) or wider.
2. Lateral obstructions are no closer than 6 ft (1.83m)to the edge of the travel lane.
3. Only passenger cars are in the traffic stream.
4. Driver population is dominated by regular and familiar users of the facility.
The maximum service flow rate is determined as the product of the capacity under ideal conditions
and the maximum volume-to-capacity ratio for the level of service i. as shown in eqn 4.2.
..4.2
Where
MSF i = maximum service flow rate per hour per lane (pc/hr/ln) under ideal conditions for level of
service i
(V/C) i = maximum volume-to-capacity ratio for level of service i
C j = capacity under ideal conditions for the freeway segment having design speed j (2200 pc/hr/ln
for four-lane freeway segments and 2300 pc/hr/ln for six or more lane freeway segments)
Page 105
The MSF i is multiplied by adjustment factors that reflect deviations from ideal conditions. And so
that the service flow rate is calculated as shown in Eq. 4.3
SF i = MSF i (N) (f W )(f HV ) (f p ) .. 4.3
Substituting for MSF i using Eq. 9.1,
SF i = C j (v/c) i (N) (f W )(f HV ) (f p ) .4.4
Where SF i = service flow rate for level of service i under prevailing traffic and roadway conditions
for N lanes in one direction (vph)
MSF i = maximum service flow rate per hour per lane under ideal conditions for level of service i
f W = factor to adjust for the effect of restricted lane widths and/or lateral clearance
f HV = factor to adjust for the combined effect of heavy vehicles in the traffic stream.
fp = factor to adjust for the effect of recreational or unfamiliar driver populations
N = number of lanes in one direction of the freeway
The adjusted service flow rate obtained from either Eq. 4.3 or Eq. 4.4 will be achieved only if good
pavement and weather conditions exist and there are no incidents on the freeway segments. If these
conditions do not exist, the actual service flow that will be achieved may be less.
Table 4.2 (for freeways) and Table 4.3 (for multilane highways) give maximum service flow rates,
maximum density and minimum speed for different free-flow speeds at levels of service A-E. Since
operating at level of service E is the same as operating at capacity the maximum service flow rate at
level of service E equals the capacity of the freeway segments.
Page 106
Table 4.1: Level-of-Service Criteria for Basic
Table 4.2: Level of Service Criteria for Multilane
Freeway Sections
Highways
Service flow rates are stated in terms of peak flows within the peak hour, usually for a 15-minute
analysis period. It is often convenient to convert service flow rates to service volumes over the full
peak hour. This is done using the peak-hour factor:
.4.5
Where: SV i = Service volume over a full peak hour for level of service "i"
SF i , PHF as previously defined
Page 107
Adjustments to Maximum Service Flow Rate

Restricted Lane Width and Lateral Clearance Factor, (f w )
This factor is used to adjust for lane widths less than 12 ft and/or lateral clearance less than 6 ft.
Table 4.3 gives the appropriate values for this factor for different lane widths and lateral clearances.
Table 4.3 Adjustment Factor for Restricted Lane Width and Lateral Clearance
Heavy Vehicle Adjustment Factor; f HV

The heavy-vehicle adjustment factor is based upon the concept of passenger-car equivalents. A
passenger-car equivalent is the number of passenger cars displaced by one truck, bus, or RV in a
given traffic stream under prevailing conditions. Given that two categories of heavy vehicle are used,
two passenger car equivalent values are defined:
E T = passenger car equivalent for trucks and buses in the traffic stream under prevailing conditions
E R = passenger car equivalent for RV's in the traffic stream under prevailing conditions
The relationship between these equivalents and the heavy-vehicle adjustment factor is best illustrated
by example:
Consider a traffic stream of 1,000 veh/h, containing 10% trucks and 2% RVs. Field studies indicate
that for this particular traffic stream, each truck displaces 2.5 passenger cars (E T ) from the traffic
stream, and each RV displaces 2.0 passenger cars (E R ) from the traffic stream. What is the total
number of equivalent passenger cars/h in the traffic stream?
Page 108
Note that from the passenger car equivalent values, it is known that: 1 truck = 2.5 passenger cars
and 1 RV = 2.0 passenger cars.
The number of equivalent passenger cars in the traffic stream is found by multiplying the number of
each class of vehicle by its passenger-car equivalent, noting that the passenger-car equivalent of a
passenger car is 1.0 by definition. Passenger-car equivalents are computed for each class of vehicle:
Trucks: 1,000*0.10*2.5 = 250 pce/h
RVs: 1,000*0.02*2.0 = 40 pce/h
Cars: 1,000 * 0.88 * 1.0 = 880 pce/h
TOTAL: 1,170pce/h
Thus, the prevailing traffic stream of 1,000 veh/h operates as if it contained 1,170 passenger cars per
hour.
By definition, the heavy-vehicle adjustment factor,fHV converts veh/h to pc/h when divided into
the flow rate in veh/h. Thus:
..4.6
Where: Vpce = flow rate, pce/h Vvph = flow rate, veh/h
In the case of the illustrative computation:
In the example, the number of equivalent passenger cars per hour for each vehicle type was
computed by multiplying the total volume by the proportion of the vehicle type in the traffic stream
and by the passenger-car equivalent for the appropriate vehicle type. The number of passenger-car
equivalents in the traffic stream may be expressed as:
Page 109
.4.7
Where: P T = proportion of trucks and buses in the traffic stream, P R = proportion of RV s in the
traffic stream E T = passenger car equivalent for trucks and buses, E R = passenger car equivalent for
RV s
The heavy-vehicle factor may now be stated as:
4.8
Passenger-Car Equivalents for Extended Freeway and Multilane Highway Sections
A long section of roadway may be considered as a single extended section if no one grade of 3% or
greater is longer than 0.25 miles, and if no grade of less than 3% is longer than 0.5 miles. Such
general terrain sections are designated in one of three general terrain categories i.e level, rolling or
Mountainous.
Table 4.4: Passenger-Car Equivalents for Trucks,
Buses, and RVs on Extended General Terrain
Sections of Freeways or Multilane Highways
Passenger-Car Equivalents for Specific Grades on Freeways and Multilane Highways
Any grade of less than 3% that is longer than 0.50 miles and any grade of 3% or steeper that is
longer than 0.25 miles must be considered as a specific grade. This is because a long grade may have
a significant impact on both heavy-vehicle operation and the characteristics of the entire traffic
stream.
The passenger car equivalent for RVs on downgrade sections is taken to be the same as that for level
terrain sections, or 1.2.
Page 110
Table 4.5: Passenger-Car Equivalents for Trucks Table 4.6: Passenger-Car Equivalents for RVs
and Buses on Upgrades
on Upgrades
Table 4.7: Passenger-Car Equivalents for Trucks

and Buses on Downgrades
Composite Grades
The passenger-car equivalents given in Tables 4.5 through 4.7 are based on a constant grade of
known length. In most situations, however, highway alignment leads to composite grades (i.e., a
series of upgrades and/ or downgrades of varying steepness). In such cases, an equivalent uniform
grade must be used to determine the appropriate passenger car equivalent values. One approach to
this problem is to find the average grade over the length of the composite grade. This involves
finding the total rise in the composite profile and divides it by the total length.
Page 111
Example (finding f HV )
Consider the following situation: A volume of 2,500 veh/h traverses a section of freeway and
contains 15% trucks and 5% RVs. The section in question is on a 5% upgrade, 0.75miles in length.
What is the equivalent volume in passenger car equivalents?
Solution:
The solution is started by finding the passenger car equivalent of trucks and RVs on the freeway
section described (5% upgrade, 0.75 miles). These are found in Tables 4.4 and 4.5, respectively:
E T = 2.5 (Table 12.14, 15% trucks, >4-5%, >0.50-0.75 mi) and E R = 3.0 (Table 12.15, 5% RV's, >45%, >0.50 mi)
In entering values from these tables, care must be taken to observe the boundary conditions. The
heavy-vehicle adjustment factor may now be computed as:
= 0.7547 and the passenger-car equivalent volume may be estimated as:
The solution can also be found by applying the passenger car equivalents directly:
Truck pces: 2,500 * 0.15 * 2.5 = 938
RV pces: 2,500*0.05*3.0= 375
Pass Cars: 2,500 * 0.80 * 1.0 = 2,000
TOTAL pees: 3,313
Driver Population Adjustment Factor; f p
The base procedures for freeways and multilane highways assume a driver population of commuters
or drivers familiar with the roadway and its characteristics. Since the "ideal" conditions discussed
earlier include weekday commuter traffic, it is necessary to correct for the case when non commuter
drivers are prevalent in the traffic stream. On some recreational routes, the majority of drivers may
Page 112
not be familiar with the route. This can have a significant impact on operations. This adjustment
factor is not well defined and is dependent upon local conditions. In general, the factor ranges
between values of 1.00 (for commuter traffic streams) to 0.85 as a lower limit for other driver
populations. Unless specific evidence for a lower value is available, a value of 1.00 is generally used
in analysis. The adjustment factors f p for the characteristics of the driver population are given in
Table 4.9.
Table 4.9: Adjustment Factor for Driver Population
2. Design Analysis
There are two types of problems that are solved by capacity analysis. They are:
Type I: Given the highway volume and the number of lanes, determine the maximum service
flow rate and the level of service
Type II: Given the highway volume and the level of service, determine the number of highway
lanes required.
To solve these problems, it is necessary to convert the given highway volume to equivalent 15minute peak-hour volume, which is computed
..4.9
Where
V C = equivalent 15-min peak-hour volume (vph); V = actual hourly volume (vph)
PHF = actual hourly volume divided by 4 times the peak 15-min volume (range: 0.25-1)
Thus the above equation Eq. 4.9 can be written
Page 113
and
..4.9 (1)
In design analysis, an existing or forecast demand volume is used to determine the number of lanes
needed to provide for a specified level of service. The number of lanes may be computed as:
.4.10
Where:
N i = number of lanes (in one direction) required to provide level of service "i"
V or DDHV = directional design hour volume, veh/h
MSF i , f Hv , f p as previously defined
Design analysis for freeways, however, becomes an iterative process. Values of MSF i depend upon
the free-flow speed of the facility. For freeways, as will be seen, the free-flow speed is dependent
upon the number of lanes provided. Thus, a number must be assumed, then computed, continuing
to iterate until the assumed and computed values agree.
When such iteration is required, it is often more convenient to compute the service flow rate and
service volume for the desired level of service for a range of reasonable values of N (usually 2, 3, 4,
and possibly 5 lanes). Then the demand volume or flow rate can be compared to the results for a
simpler determination of the required number of lanes.
Determining the Free-Flow Speed
The free-flow speed of a facility is best determined by field measurement. Given the shape of speedflow relationships for freeways and multilane highways, an average speed measured when flow is less
than or equal to 1,000 veh/h/ln may be taken to represent the free-flow speed.
It is not always possible, however, to measure the free-flow speed. When new facilities or redesigned
facilities are under consideration, it is not possible to measure free-flow speeds. Even for existing
facilities, the time and cost of conducting field studies may not be warranted.
Freeways
Page 114
The free-flow speed of a freeway can be estimated as:

4.11
Where: FFS = free-flow speed of the freeway, mi/h; BFFS = base free-flow speed of the freeway
(70 mi/h for urban and suburban freeways, 75 mi/h for rural freeways); f LW = adjustment for lane
width, mi/h; f LC = adjustment for lateral clearance, mi/h; f N = adjustment for number of lanes,
mi/h; f ID = adjustment for interchange density, mi/h
Lane Width Adjustment (f LW ): The base condition for lane width is an average width of 12 ft
(3.65m) or greater. For narrower lanes, the base free-flow speed is reduced by the factors shown in
Table 4.10.
Table 4.10: Adjustment to Free-Flow Speed
for Lane Width on a Freeway
Lateral Clearance Adjustment Base lateral clearance is 6 ft (1.83m) or greater on the right side and
2 ft (0.60m) or greater on the median or left side of the basic freeway section. Adjustments for rightside lateral clearances less than 6 ft (1.83m) are given in Table 4.11. There are no adjustments
provided for median clearances less than 2 ft (0.6m), as such conditions are considered rare.
Care should be taken in assessing whether an "obstruction" exists on the right side of the freeway.
Obstructions may be continuous, such as a guardrail or retaining wall, or they may be periodic, such
as light supports and bridge abutments. In some cases, drivers may become accustomed to some
obstructions, and the impact of these on free-flow speeds may be minimal.
Page 115
Table 4.11: Adjustment to Free-Flow Speed

for Lateral Clearance on a Freeway
Right-side obstructions primarily influence driver behavior in the right lane. Drivers "shy away"
from such obstructions, moving further to the left in the lane. Drivers in adjacent lanes may also
shift somewhat to the left in response to vehicle placements in the right lane.
The overall affect is to cause vehicles to travel closer to each other laterally than would normally be
the case, thus making flow less efficient. This is the same effect as for narrow lanes. Since the
primary impact is on the right lane, the total impact on free-flow speed declines as the number of
lanes increases.
Adjustment for Number of Lanes The base condition for number of lanes in one direction on a
freeway is five or more lanes. The use of this size freeway as a base has been questioned, as it is a
relatively rare occurrence. The adjustment for number of lanes is given in Table 4.12.
Table 4.12: Adjustment to Free-Flow Speed for
Number of Lanes on a Freeway
Interchange Density Adjustment Perhaps the most significant impact on freeway free-flow speed
is the number and spacing of interchanges. Interchange density is defined as the average number of
interchanges per mile over a six-mile section of the facility, taken as three miles upstream and three
miles downstream of the point or section under consideration. Note that the interchange density is
not based on the number of ramps. An interchange may consist of several ramp connections. A
Page 116
typical diamond interchange has four ramps, while a full cloverleaf interchange has eight. To qualify
as an interchange, there must be at least one on-ramp. Thus, a junction with only off-ramps would
not qualify as an interchange. The base condition for interchange density is 0.50 interchanges/mile,
which implies an average interchange spacing of two miles. Adjustments for interchange density are
shown in Table 4.13.
Interchange Density on a Freeway
Multilane Highways
The free-flow speed for a multilane highway may be estimated as:
4.12
Where: FFS = free-flow speed of the multilane highway, mi/h; BFFS =base free-flow speed; f LW =
adjustment for lane width, mi/h; f LC = adjustment for lateral clearance, mi/h; f M = adjustment for
type of median, mi/h; f A = adjustment for access points, mi/h
A base free-flow speed of 60 mi/h may be used for rural and suburban multilane highways, if no
field data is available. It may also be estimated using the posted speed limit. The base free-flow
speed is approximately 7 mi/h higher than the posted speed limit, for speed limits of 40 and 45
mi/h. and for speed limits of 50 and 55 mi/h, the base free-flow speed is approximately 5 mi/h
higher than the limit.
Lane Width Adjustment The base lane width for multilane highways is 12 ft, as was the case for
freeways. For narrower lanes, the free-flow speed is reduced by the values shown in Table 4.14.
Page 117

Lane Width on a Multilane Highway
Lateral Clearance Adjustment For multilane highways, this adjustment is based on the total lateral
clearance, which is the sum of the lateral clearances on the right side of the roadway and on the left
(median) side of the roadway. While this seems like a simple concept, there are some details that
must be observed:
Table
4.15:
Adjustment
to
Total
Lateral
Clearance on a Multilane Highway
Median-Type Adjustment The median-type adjustment is shown in Table 4.16. A reduction of 1.6
mi/h is made for undivided configurations, while divided multilane highways, or multilane highways
with two-way left-turn lanes, represent base conditions.
Median Type on Multilane Highways
Access-Point Density Adjustment A critical adjustment to base free-flow speed is related to

access-point density. Access-point density is the average number of unsignalized driveways or
roadways per mile that provide access to the multilane highway on the right side of the roadway (for
the subject direction of traffic).
Page 118
Driveways or other entrances with little traffic, or that, for other reasons, do not affect driver
behavior, should not be included in the access-point density. Adjustments are shown in Table 4.17.
Access-Point Density on a Multilane Highway
4.3.2.
Analysis method of Two-Lane Rural Highways Capacity
The capacity of a two-lane highway under base conditions is now established as 3200 pc/h in both
directions, with a maximum of 1700 pc/h in one direction. The base conditions for which this
capacity is defined include:
12-foot (or greater) lanes
6-foot (or greater) usable shoulders
Level terrain
50/50 directional split of traffic
No heavy vehicles
No traffic interruptions
100% passing sight distance available

(no "No Passing" zones)
Level of Service
Level of service for two-lane rural highways is defined in terms of two measures of effectiveness:
Average travel speed (ATS)
Percent time spent following (PTSF)
Average travel speed is the average speed of all vehicles traversing the defined analysis segment for
the specified time period, which is usually the peak 15-minutes of a peak hour. When analysis of
both directions is used, the average travel speed includes vehicles in both directions. When analysis
of single direction is used, the average travel speed includes those vehicles in the analysis direction
only.
Percent time spent following is similar to "percent time delay,. It is the aggregate percentage of
time that all drivers spend in queues, unable to pass, with the speed restricted by the queue leader. A
Page 119
surrogate measure for PTSF is the percentage of vehicles following others at headways of 3.0 s or
less.
Level of service criteria for two-lane rural highways is shown in Table 4.18. The criteria vary for
Class I and Class II highways. Class II highways, where mobility is not a principal function; use only
the PTSF criteria for determination of level of service. For Class I highways, the LOS is determined
by the measure yielding the poorest result.
Table 4.18: Level-of-Service Criteria for Two-Lane
Rural Highways
Figure 4.4 illustrates the relationships between ATS, PTSF, and two-way flow rate on a two-lane
highway with base conditions. Figure 4.4 (b) clearly illustrates the unique nature of operations on a
two-lane highway. For multilane highways and freeways, operational deterioration does not occur
until v/c ratios are quite high. Drivers on such facilities maintain high speeds in the vicinity of freeflow speed for v/c ratios in excess of 0.75. On a two-lane highway, however, operational
deterioration, particularly with respect to PTSF, occurs at relatively low v/c ratios.
Fig 4.4 (a) Average Travel Speed versus Two- Fig 4.4 (b) Percent Time Spent Following versus
Way Flow
Two-Way Flow
Page 120
As illustrated in Figure 4.4 (b), at a demand flow of 1,500 pc/h (a v/c ratio of 1500/3200 = 0.47),
PTSF is already at 64%. This is for a highway with base, or nearly ideal, conditions. As the analysis
methodology makes clear, the value would be considerably higher where conditions are worse than
those defined for the base.
Types of Analysis
Generally two-direction and single-direction analysis with three distinct methodologies are provided
to analyses two lane two way rural roads
Two-directional analysis of general extended sections ( 2.0 mi) in level or rolling terrain
Single-directional analysis of general extended sections (2.0 mi) in level or rolling terrain
Single-direction analysis of specific grades
For specific grades, only single-direction analysis of the upgrade and downgrade is permitted, as
these tend to differ significantly. In what is usually referred to as "mountainous" terrain, all analysis
is on the basis of specific grades comprising that terrain. Any grade of 3% or more and at least 0.6
mi long must be addressed using specific grade procedures.
Free-Flow Speed
As was the case for multilane highways and freeways, the free-flow speed of a two-lane highway is a
significant variable used in estimating expected operating conditions.
Field Measurement of Free-Flow Speed

The free-flow speed of a two-lane rural highway may be measured directly in the field. The speed
study should be conducted at a representative site within the study section. Free-flow speeds may be
directly measured as follows:
A representative speed sample of 100 or more vehicles should be obtained.
Total two-way traffic flow should be 200 pc/h or less.
All vehicle speeds should be observed during the study period, or a systematic sampling (such as
1 vehicle out of every 10) should be applied.
When two-direction analysis is contemplated, the speed sample should be selected from both
directions of flow; when a one-direction analysis is contemplated, the speed sample should be
selected only from the direction under study.
Page 121
If field measurements must be made at total flow levels higher than 200 pc/h, the free-flow speed
may be estimated as:
..4.13
Where: FFS = free-flow speed for the facility, mi/h; S m = mean speed of the measured sample
(Where total flow> 200 pc/h), mi/h; V f = observed flow rate for the period of the speed sample,
veh/h and f HV = heavy vehicle adjustment factor.
Estimating Free-Flow Speeds
If field observation of free-flow speed is not practical, free-flow speed on a two-way rural highway
may be estimated as follows:
FFS = BFFS- f LS - f A (4.14)
Where: FFS = free-flow speed for the facility, mi/h, BFFS =base free-flow speed for the facility,
mi/h; f LS = adjustment for lane and shoulder width, mi/h and f A = adjustment for access point
density, mi/h
Most of the time BFFS is limited to a range of 45-65 mi/h, with Class I highways usually in the 5565 mi/h range and Class II highways usually in the 45-50 mi/h range. Sometimes the design speed,
which represents the maximum safe speed for the horizontal and vertical alignment of the highway,
is a reasonable surrogate for the BFFS.
Adjustment factors for lane and shoulder width are shown in Table 4.19; adjustment factors for
access point density are shown in Table 4.20. Access point density is computed by dividing the total
number of driveways and intersections on both sides of the highway by the total length of the
segment in miles.
Table 4.19: Free-Flow Speed Adjustments for
Lane and Shoulder Width
Page 122
Table 4.20: Free-Flow Speed Adjustments for

Access Point Density
Estimating Demand Flow Rate

As for most HCM 2000 methodologies, a critical computational step is the determination of a
demand flow rate reflecting the base conditions for the facility type being analyzed. This requires
that an hourly volume reflecting prevailing conditions be adjusted to reflect peak flow rates within
the hour and base conditions. For two-lane rural highways, this adjustment is made as follows:
4.15
Where: v = demand flow rate pc/h; V = hourly demand volume under prevailing conditions veh/h;
PHF = peak hour factor; f HV = adjustment for heavy vehicle presence f G = adjustment for grades.
Determining Grade Adjustment Factors
For every computation, two grade adjustment factors will be required: one for the ATS
determination and one for the PTSF determination. Selection of appropriate adjustment factors also
depends upon the type of analysis being conducted. Grade adjustment factors are found as follows:
Two-direction analysis of general terrain segments for both ATS and PTSF
determinations: Table 4.21.
One-direction analysis of general terrain segments for both ATS and PTSF
determinations: Table 4.21.
One-direction analysis of specific upgrades for ATS determination: Table 4.22.
One-direction analysis of specific upgrades for PTSF determination: Table 4.23.
One-direction analysis of specific downgrades for both ATS and PTSF determination:
Table 4.21.
Page 123
Table 4.21: Grade Adjustment Factor (f G ) for General Terrain Segments and Specific Downgrades
(ATS
and
PTSF
Determinations)
Table 4.22: Grade Adjustment Factor (f G ) Table 4.23: Grade Adjustment Factor (f G ) for
for Specific Upgrades: ATS Determinations
Specific Upgrades: PTSF Determinations
Page 124
Determining the Heavy-Vehicle Adjustment Factor

The heavy-vehicle adjustment factors for ATS and PTSF determinations are found from passengercar equivalents as follows:
4.16
Where: f HV = heavy-vehicle adjustment factor; P T = proportion of trucks and buses in the traffic
stream; P R = proportion of recreational vehicles in the traffic stream E T = passenger-car equivalent
for trucks and buses E R = passenger-car equivalent for recreational vehicles
As in multilane methodologies, the passenger-car equivalent is the number of passenger cars
displaced by one truck (or RV) under the prevailing conditions on the analysis segment.
As in the determination of the grade-adjustment factor, values of E T and E R depend upon initial
estimates of the demand flow rate and are therefore iterative.
Iteration rules are the same as described for the grade-adjustment factor. Passenger-car equivalents also
depend upon which measure of effectiveness is being predicted (ATS or PTSF), and the type of analysis
being applied. Passenger-car equivalents are found from the following tables:
Table 4.24: Passenger-Car Equivalents for General Terrain Segments: ATS and PTSF Determinations
Page 125
Table 4.25: Passenger-Car Equivalents of Trucks
Table 4.26: Passenger-Car Equivalents of RVs for
for Specific Upgrades: ATS Determination
Specific
Upgrades:
Determination
Page 126
ATS
Table 4.27: Passenger-Car Equivalents for Trucks and RV's on Specific Upgrades: PTSF Determination
Some specific downgrades are steep enough to require some trucks to shift into low gear and travel at crawl
speeds to avoid loss of control. In such situations, the effect of trucks traveling at crawl speed may be taken into
account by replacing Equation 14-22 with the following when computing the heavy vehicle adjustment factor,
f Hv , for ATS determination:
...4.17
Where: P TC = proportion of heavy vehicles forced to travel at crawl speeds; E TC = passenger care equivalents for
trucks at crawl speed Table 14.14.
In applying Equation 14-23, note that P TC is stated as a proportion of the truck population, not of the entire
traffic stream. Thus, a P TC of 0.50 means that 50% of the trucks are operating down the grade at crawl speeds.
Note that for two-lane highways; all composite grades are treated using the average grade of the analysis section.
The average grade for any segment is the total change in elevation (ft) divided by the length of the segment (ft).
Page 127
Table 4.28: Passenger-Car Equivalents for Trucks

Operating at Crawl Speeds on Specific Downgrades:
ATS Determination
Estimating Average Travel Speed

Once the appropriate demand flow rate(s) are computed, the average travel speed in the section is estimated
using Equation 14-10 for two-direction analysis and Equation 14-11 for single-direction analysis:
ATS = FFS - 0.00776V - f np .. (4.18)
ATS d = FFS d - 0.00776( v d + V 0 ) - f np (4.19)
Where: ATS = average travel speed, both directions, mi/h, ATS d = average travel speed in the direction of
analysis, mi/h., FFS = free-flow speed, both directions, mi/h; FFS d = free-flow speed in the direction of analysis,
mi/h; v = demand flow rate, both directions, pc/h; V d = demand flow rate in the direction of analysis, pc/h; V o
= demand flow rate in the opposing direction, pc/h; f np = adjustment for the existence of "No Passing" zones in
the study segment
Values of the adjustment factor, f np are given in Table 4.29 for two-direction analyses and in Table 4.30 for
single-direction analyses. The adjustment is based on flow rates, the percentage of the analyses segment for
which passing is prohibited, and (for single-direction analyses) the free-flow speed of the facility.
Page 128
Table 4.29: Adjustment for Effect of "No Passing" Zones f np ) on ATS: Two-Direction Segments
Page 129
Table 4.30: Adjustment for Effect of "No Passing"

Zones fnp) on ATS Single-Direction Segments
Determining Percent Time Spent Following

For two-direction analyses, and single-direction analyses Percent time spent following (PTSF) is determined
using the following equation:
PTSF = BPTSF + fd/np
BPTSF = 100(1 - e-o.ooo879v) (4.20)
PTSF d = BPTSF d + f np
.(4.21)
Page 130
Where: PTSF = percent time spent following, two directions, %

PTSFd = percent time spent following, single direction, %
BPTSF = base percent time spent following, two directions,%
v = demand flow rate, pc/h, both directions
Vd = demand flow rate in analysis direction, pc/h
f d/np = adjustment to PTSF for the combined effect of directional distribution and percent "No Passing" zones
on two way analysis segments, %
f np = adjustment to PTSF for the effect of percent "No Passing" zones on single-direction analysis segments,%
a, b = calibration constants based on opposing flow rate in single direction analysis
Adjustnient factor fd/np is found in Table 4.30. Adjustment factor fnp is found in Table 4.31 and calibration
constants "a" and "b" are found in Table 4.32.
Table 4.31: Adjustment f np ) to PTSF for Percent
"No Passing" Zones in Single-Direction Segments
Page 131
.
Table 4.32: Coefficients "a" and "b"
References
4. Traffic engineering third edition by Roess & Prasas, 2004
5. Highway Engineering , Martin rogers
6. Traffic and Highway Engineering, Nicholas J. Garber
School of Civil and Environmental Engineering, AAiT
Page 132
.
Chapter Five
Traffic Controls
Traffic control devices are the media by which traffic engineers communicate with drivers.
Virtually every traffic law, regulation, or operating instruction must be communicated through
the use of devices that fall into three broad categories:
Traffic markings
Traffic signs
Traffic signals
The effective communication between traffic engineer and driver is a critical link if safe and
efficient traffic operations are to prevail. Traffic engineers have no direct control over any
individual driver or group of drivers. If a motorman violated a RED signal while conducting a
subway train, an automated braking system would force the train to stop anyway. If a driver
violates a RED signal, only the hazards of conflicting vehicular and/or pedestrian flows would
impede the maneuver. Thus, it is imperative that traffic engineers design traffic control devices
that communicate uncomplicated messages clearly, in a way that encourages proper observance.
The driver is accustomed to receiving a certain message in a clear and standard fashion, often
with redundancy. A number of mechanisms are used to convey messages. These mechanisms
make use of recognized human limitations, particularly with respect to eyesight. Messages are
conveyed through the use of:
Color. Color is the most easily visible characteristic of a device. Color is recognizable
long before a general shape may be perceived and considerably before a specific legend
can be read and understood. The principal colors used in traffic control devices are red,
yellow, green, orange, black, blue, and brown. These are used to code certain types of
devices and to reinforce specific messages whenever possible.
Shape. After color, the shape of the device is the next element to be discerned by
the driver. Particularly in signing, shape is an important element of the message, either
identifying a particular type of information that the sign is conveying or conveying a
unique message of its own.
Page 133
.
Pattern. Pattern is used in the application of traffic markings. In general, double solid,
solid, dashed, and broken lines are used. Each conveys a type of meaning with which
drivers become familiar. The frequent and consistent use of similar patterns in similar
applications contributes greatly to their effectiveness and to the instant recognition of
their meaning.
Legend. The last element of a device that the driver comprehends is its specific
legend. Signals and markings, for example, convey their entire message through use of
color, shape, and pattern. Signs, however, often use specific leg end to transmit the
details of the message being transmitted. Legend must be kept simple and short, so
that drivers do not divert their attention from the driving task, yet are able to see and
understand the specific message being given.
This chapter introduces some of the basic principles involved in the design and placement of
traffic controls with reference of MUTCD [Manual on Uniform Traffic Control Devices] standards.
5.1 Traffic Markings
Traffic markings are the most plentiful traffic devices in use. They serve a variety of purposes
and functions and fall into three broad categories:
Longitudinal markings
Transverse markings
Object markers and delineators
Longitudinal and transverse markings are applied to the roadway surface using a variety of
materials, the most common of which are paint and thermoplastic. Reflectorization for better
night vision is achieved by mixing tiny glass beads in the paint or by applying a thin
layer of glass beads over the wet pavement marking as it is placed. The latter provides high
initial reflectorization, but the top layer of glass beads is more quickly worn. When glass
beads are mixed into the paint before application, some level of reflectorization is preserved
as the marking wears.
Page 134
.
5.1.1
Longitudinal Markings
Longitudinal markings are those markings placed parallel to the direction of travel. The vast
majority of longitudinal markings involve centerlines, lane lines, and pavement edge lines.
Longitudinal markings provide guidance for the placement of vehicles on the traveled way
cross-section and basic trajectory guidance for vehicles traveling along the facility. The best
example of the importance of longitudinal markings is the difficulty in traversing a newly
paved highway segment on which lane markings have not yet been repainted. Drivers do not
automatically form neat lanes without the guidance of longitudinal markings; rather, they tend
to place themselves somewhat randomly on the cross-section, encountering many difficulties.
Longitudinal markings provide for organized flow and optimal use of the pavement width.
Centerlines
Centre line separates the opposing streams of traffic and facilitates their movements. Usually
no centre line is provided for roads having width less than 5 m and for roads having more
than four lanes. The centre line may be marked with either single broken line, single solid line,
double broken line, or double solid line depending upon the road and traffic requirements. On
urban roads with less than four lanes, the centre line may be single broken line segments of 3 m
long and 150 mm wide. The broken lines are placed with 4.5 m gaps (figure 5.1).
Figure 5.1: Centre line marking for a two lane road

On two-lane, two-way rural highways, centerline markings supplemented by signs are used to
regulate passing maneuvers. A double-solid yellow center marking indicates that passing is not
permitted in either direction. A solid yellow line with a dashed yellow line indicates that passing is
permitted from the dashed side only. Where: passing is permissible in both directions, a single
dashed yellow centerline is used.
Page 135
.
Lane Markings
The typical lane marking is a single white dashed line separating lanes of traffic in the same
direction. MUTCD standards require the use of lane markings on all free ways and Interstate
highways and recommend their use on all highways with two or more adjacent traffic lanes in a
single direction. The dashed lane line indicates that lane changing is permitted. A single solid
white lane line is used to indicate that lane-changing is discouraged but not illegal. Where lanechanging is to be prohibited, a double-white solid lane line is used.
Figure 5.2: Centre line and lane marking for a four lane road
Figure 5.3: Double solid line for a two lane road

Edge Markings
Edge lines indicate edges of rural roads which have no curbs to delineate the limits up to
which the driver can safely venture. They should be at least 150 mm from the actual edge
of the pavement. They are painted in yellow or white.
All the lines should be preferably light reflective, so that they will be visible during night also.
Improved night visibility may also be obtained by the use of minute glass beads embedded
in the pavement marking materials to produce a retroreflective surface.
Page 136
.
Warning lines
Warning lines warn the drivers about the obstruction approaches. They are marked on
horizontal and vertical curves where the visibility is greater than prohibitory criteria
specified for no overtaking zones. They are broken lines with 6 m length and 3 m gap. A
minimum of seven line segments should be provided. A typical example is shown in figure
5.4.
Figure 5.4: Warning line marking for a two lane road

5.1.2 Transverse Markings
Transverse markings, as their name implies, include any and all markings with a
component that cuts across a portion or all of the traveled way. When used, all transverse
markings are white. May be added to provide greater focus in areas with heavy pedestrian
flows. The use of parallel transverse markings to identify the crosswalk is another option
used at locations with heavy pedestrian flows.
Crosswalk Markings
While not mandated by the MUTCD, it is recommend that crosswalks be marked at all
intersections with "substantial" conflict between
vehicles and pedestrian exists. They
should also be used at points of pedestrian may be added to provide greater focus in areas
with heavy pedestrian flows. The use of parallel transverse markings to identify the crosswalk is
another option used at locations with heavy pedestrian flows. The manual also contains a special
pedestrian crosswalk marking for signalized intersections where a full pedestrian phase is
included.
Page 137
.
Figure 5.5: Pedestrian marking near an intersection
Parking Space Markings

Parking space markings are not purely transverse, as they contain both longitudinal and
transverse elements. They are officially categorized as transverse markings, however, in the
MUTCD. They are always optional and are used to encourage efficient use of parking
spaces. Such markings can also help prevent encroachment of parked vehicles into fire hydrant
zones, loading zones, taxi stands and bus stops, and other specific locations at which parking is
prohibited. They are also useful on arterials with curb parking, as they also clearly demark
the parking lane, separating it from travel lanes. Figure 5.6 illustrates typical parking lane
markings.
Figure 5.6: Typical Parking Space Markings

Page 138
.
Directional arrows
In addition to the warning lines on approaching lanes, directional arrows should be used to guide
the drivers in advance over the correct lane to be taken while approaching busy intersections.
Because of the low angle at which the markings are viewed by the drivers, the arrows should be
elongated in the direction of traffic for adequate visibility. The dimensions of these arrows are also
very important.
Figure 5.7 A typical example of a directional arrow
Word and Symbol Markings

The MUTCD prescribes a number of word and symbol markings that may be used, often in
conjunction with signs and/or signals. These include arrow markings indicating lane-use
restrictions. Such arrows (with accompanying signs) are mandatory where a through lane becomes
a left- or right-turn-only lane approaching an intersection.
Word markings include "ONLY" used in conjunction with lane use arrows, and "STOP" which
can be used only in conjunction with a STOP line and a STOP sign. "SCHOOL" markings are
often used in conjunction with signs to demark school and school-crossing zones. The MUTCD
contains a listing of all authorized word markings and allows for discretionary use of
unique messages where needed.
5.1.3 Object Markers

Object markers are used to denote obstructions either or adjacent to the traveled
way. There are three types of object markers used, as illustrated in Figure below. Obstructions
within the roadway must be marked using a Type 1 or Type 3 marker. The Type 3 marker, when
used, must have the alternating yellow and black stripes sloped downward at a 45 angle towards
the side on which traffic is to pass the obstruction. When used to mark a roadside obstruction, the
inside edge. of the marker must be in line with the inner edge of the obstruction.
Page 139
.
Typical Type 1 Object Markers
Nine yellow retroreflectors with 3-in minimum diameter on a yellow or black diamond panel of 18 in
or more on a side; or an all-yellow retroreflective diamond panel of the same size.
Three yellow retroreflectors with 3-in minimum diameter arranged horizontally or vertically on
white panel of at least 6 X 12 in; or an all yellow retroreflective panel of the same size.
A striped marker measuring 12 X 36 in with alternating black and yellow stripes sloping
downward at an angle of 45 toward the side of the obstruction on which traffic is to pass.
5.2 Traffic Signs
In general, traffic signs fall into one of three major categories:
Regulatory signs.
Warning signs.
Guide signs.
Page 140
.
5.2.1. Regulatory Signs

Regulatory signs shall be used to inform road users of selected traffic laws or regulations and
indicate the applicability of the legal requirements. Regulatory signs convey information concerning
specific traffic regulations. Regulations may relate to right-of-way, speed limits, lane usage, parking,
or a variety of other functions.
Regulatory signs shall be installed at or near where the regulations apply. The signs shall clearly
indicate the requirements imposed by the regulations and shall be designed and installed to provide
adequate visibility and legibility in order to obtain compliance.
Drivers are expected to be aware of many general traffic regulations, such as the basic right-of-way
rule at intersections and the state speed limit. Signs, however, should be used in all cases where
the driver cannot be expected to know the applicable regulation.
Except for some special signs, such as the STOP and YIELD sign, most regulatory signs are
rectangular, with the long dimension vertical. Some regulatory signs are square. These are primarily
signs using symbols instead of legend to impart information. The
background
color
of
regulatory signs, with a few exceptions, is white, while legend or symbols are black. In symbol
signs, a red circle with a bar through it signifies a prohibition of the movement indicated by
the symbol.
Right of way series: These include two unique signs that assign the right of way to the
selected approaches of an intersection. They are the STOP sign and GIVE WAY sign For example,
when one minor road and major road meets at an intersection, preference should be given to
the vehicles passing through the major road. Hence the give way sign board will be placed on the
minor road to inform the driver on the minor road that he should give way for the vehicles on
the major road. In case two major roads are meeting, then the traffic engineer decides based on
the traffic on which approach the sign board has to be placed. Stop sign is another example
of regulatory signs that comes in right of way series which requires the driver to stop the vehicle
at the stop line.
Speed series: Number of speed signs may be used to limit the speed of the vehicle on the road.
They include typical speed limit signs, truck speed, minimum speed signs etc. Speed limit signs are
placed to limit the speed of the vehicle to a particular speed for many reasons. Separate truck
speed limits are applied on high speed roadways where heavy commercial vehicles must be
Page 141
.
limited to slower speeds than passenger cars for safety reasons. Minimum speed limits are applied
on high speed roads like expressways, freeways etc. where safety is again a predominant reason.
Very slow vehicles may present hazard to themselves and other vehicles also.
Movement series: They contain a number of signs that affect specific vehicle maneuvers. These
include turn signs, alignment signs, exclusion signs, one way signs etc. Turn signs include turn
prohibitions and lane use control signs. Lane use signs make use of arrows to specify the
movements which all vehicles in the lane must take. Turn signs are used to safely accommodate
turns in unsignalized intersections.
Parking series: They include parking signs which indicate not only parking prohibitions
or restrictions, but also indicate places where parking is permitted, the type of vehicle to be
parked, duration for parking etc.
Pedestrian series: They include both legend and symbol signs. These signs are meant for the
safety of pedestrians and include signs indicating pedestrian only roads, pedestrian crossing sites etc.
Miscellaneous: Wide variety of signs that are included in this category are: a "KEEP OF
MEDIAN" sign,
signs
indicating
road
closures,
signs
restricting
vehicles
carrying
hazardous cargo or substances, signs indicating vehicle weight limitations etc.
Figure 5.7: Examples of regulatory signs ( stop sign, give way sign, signs for no entry, sign
indicating prohibition for right turn, vehicle width limit sign, speed limit sign)
5.2.2. Warning Signs

Warning signs call attention to unexpected conditions on or adjacent to a highway or street
and to situations that might not be readily apparent to road users. Warning signs alert road users
to conditions that might call for a reduction of speed or an action in the interest of safety and
efficient traffic operations.
Page 142
.
Most
warning
signs
are
diamond-shaped, with black lettering or symbols on a yellow
background. A pennant shape is used for the "No Passing Zone" sign, used in conjunction
with passing restrictions on two lane, two-way rural highways. A rectangular shape is used
for some arrow indications. A circular shape is used for railroad crossing warnings.
The MUTCD indicates that warning signs shall be used only in conjunction with an engineering
study or based on engineering judgment. While this is a fairly loose requirement, it emphasizes
the need to avoid over use of such signs. A warning sign should be used only to alert drivers of
conditions that they could not be normally expected to discern on their own. Overuse of warning
signs encourages drivers to ignore them, which could lead to dangerous situations.
When used, warning signs must be placed far enough in advance of the hazard to allow
drivers adequate time to perform the required adjustments. Warning signs may be used with
supplementary panels indicating either the distance to the hazard or an advisory speed. The
advisory speed is the recommended safe speed through the hazardous area and is determined by
an engineering study of the location. Warning signs are used to inform drivers of a variety
of potentially hazardous circumstances, including:
Changes in horizontal alignment
Intersections
Advance warning of control devices
Converging traffic lanes
Narrow roadways
Changes in highway design
Grades
Roadway surface conditions
Railroad crossings
Figure 5.8: Examples of cautionary signs ( right hand curve sign board,
signs for narrow road, sign indicating railway track ahead)
Page 143
.
5.2.3. Guide/Informative/ Signs

Guide signs provide information to road users concerning destinations, available services,
and historical/recreational facilities. They serve a unique purpose in that drivers who
are familiar or regular users of a route will generally not need to use them; they
provide critical information, however, to unfamiliar road users. The background
varies by the type of information contained on the sign. Directional or destination
information is provided by signs with a green background; information on services is
provided by signs with a blue background; cultural, historical, and/or recreational in
formation is provided by signs with a brown back ground. Route markers,
included in this category, have varying shapes and colors depending on the type and
jurisdiction of the route.
The MUTCD provides guide-signing information for three types of facilities:
conventional roads, free ways, and expressways. Guide signing is somewhat different
from other types in that overuse is generally not a serious issue, unless it leads to
confusion. Clarity and consistency of message is the most important aspect of guide
signing. Several general principles may be applied:
1. If a route services a number of destinations, the most important of these should be listed.
2. No guide sign should list more than three (four may be acceptable in some
circumstances) destinations on a single sign. This, in conjunction with the first
principle, makes the selection of priority destinations a critical part of effective guide
signing.
3. Where roadways have both a name and a route number, both should be indicated on
the sign if space permits. In cases where only one may be listed, the route number
takes precedence. Road maps show route numbers prominently, while not all
facility names are included. Unfamiliar
drivers
are,
therefore, more
likely
to
know the route number than the facility name.

4. Wherever possible, advance signing of important junctions should be given. This is
more difficult on conventional highways, where junctions may be frequent and
closely spaced.
On free ways and expressways, this is critical, as high approach
speeds make advance knowledge of upcoming junctions a significant safety issue.

5. Wherever possible, advance signing of important junctions should be given. This is
Page 144
.
more difficult on conventional highways, where junctions may be frequent and

closely spaced.
On free ways and expressways, this is critical, as high approach
speeds make advance knowledge of upcoming junctions a significant safety issue.

6. Confusion on
the part of
the
driver
must be avoided
at all cost.
Sign
sequencing should be logical and should naturally lead the driver to the desired
route selections. Overlapping sequences should be avoided wherever possible. Lefthand exits
and other
unusual junction features
should
be signed
extremely
carefully.
7. The size, placement, and lettering of guide signs vary considerably, and the
manual
gives information on numerous options.
conditions affect these design features,
number
of
site-specific
and there is more latitude
and choice
involved than for other types of highway signs. The MUTCD should be consulted
directly for this information.
Figure 5.9: Examples of informative signs (route markers, destination signs,

mile posts, service centre information etc)
5.3 Traffic signal
The operation of signalized intersections is often complex, involving competing
vehicular and pedestrian movements. Appropriate methodologies for design and
timing of signals and for the operational analysis of signalized intersections require
that the behavior of drivers and pedestrians at a signalized intersection be modeled in a
form that can be easily manipulated and optimized.
Objectives of Signal Timing
The main objectives of signal timing at an intersection are to reduce the average delay of
all vehicles and the probability of accidents. These objectives are achieved by minimizing
the possible conflict points when assigning the right of way to different traffic streams at
different times. The objective of reducing delay, however, sometimes conflicts with that
Page 145
.
of accident reduction. This is because the number of distinct phases should be kept to a
minimum to reduce average delay, whereas many more distinct phases may be required
to separate all traffic streams from each other. When this situation exists, it is essential
that engineering judgment be used to determine a compromise solution. In general,
however, it is usual to adapt a two-phase system whenever possible, using the shortest
practical cycle length that is consistent with the demand. At a complex intersection,
though, it may be necessary to use a multiphase (three or more phases) system to achieve
the main design objectives.
Types of Signal Operation
Traffic signals can operate on a pretimed basis or may be partially or fully actuated by arriving
vehicles sensed by detectors. In networks, or on arterials, signals may be coordinated through
computer control.
1. Pretimed operation. In pretimed operation, the cycle length, phase sequence, and timing of
each interval are constant. Each cycle of the signal follows the same predetermined plan. "Multidial" controllers will allow different pre timed settings to be established. An internal clock is
used to activate the appropriate timing. In such cases, it is typical to have at least an AM peak, a
PM peak, and an off-peak signal timing.
2.
Semi-actuated operation. In semi-actuated operation, detectors are placed on the minor
approach(es) to the intersection; there are no detectors on the major street. The light is green for
the major street at all times except when a "call" or actuation is noted on one of the minor
approaches. Then, subject to limitations such as a minimum major-street green, the green is
transferred to the minor street. The green returns to the major street when the maximum
minor street green is reached or when the detector senses that there is no further
demand on the minor street.
3 . Full actuated operation. In full actuated operation, every lane of every approach must be
monitored by a detector. Green time is allocated in for capturing and retaining the green. In
full actuated operation, the cycle length, sequence of phases, and green time split may vary
from cycle to cycle.
4. Computer control. Computer control is a system term. No individual signal
is "computer
controlled," unless the signal controller is considered to be a computer. In a computerSchool of Civil and Environmental Engineering, AAiT
Page 146
.
controlled system, the computer acts as a master controller, coordinating the timings of a
large number (hundreds) of signals. The computer selects or
calculates an
optimal
coordination plan based on input from detectors placed through out the system. In
general, such selections are made only once in advance of an AM or PM peak period.
The nature of a system transition from one timing plan to another is sufficiently
disruptive to be avoided during peak-demand periods. Individual signals in a
computer-controlled system generally operate in the pretimed mode. For coordination to
be effective, all signals in the network must use the same cycle length (or an even
multiple thereof), and it is therefore difficult to maintain a progressive pat tern where
cycle length or phase splits are allowed to vary.
Components of a Signal Cycle
The following terms describe portions and sub portions of a signal cycle. The most
fundamental unit in signal design and timing is the cycle, as defined below.
1. Cycle. A signal cycle is one complete rotation through all of the indications provided. In
general, every legal vehicular movement receives a "green" indication during each cycle,
although there are some exceptions to this rule.
2. Cycle length. The cycle length is the time (in seconds) that it takes to complete one full cycle
of indications. It is given the symbol "C."
3. Interval. The interval is a period of time during which no signal indication changes. It is
the smallest unit of time described within a signal cycle. There are several types of intervals with
in a signal cycle:
(a) Change interval. The change interval is the "yellow" indication for a given movement.
It is part of the transition from "green" to "red," in which movements about to lose
"green" are given a "yellow" signal, while all other movements have a "red" signal. It is
timed to allow a vehicle that cannot safely stop when the "green" is withdrawn to
enter the intersection legally. The change interval is given the symbol for
i
movement(s) i.
(b) Clearance interval. The clearance interval is also part of the transition from "green"
to "red" for a given set of movements. During the clearance interval, all movements have a
"red" signal. It is timed to allow a vehicle that legally enters the intersection on "yellow"
Page 147
.
to safely cross the intersection before conflicting flows are released. The clearance interval
is given the symbol "ar i (for "all red") for movement(s) i.
(c) Green interval. Each movement has one green interval during the signal cycle.
During
a green interval, the movements permitted have a "green" light, while all other
movements have a "red" light. The green interval is given the symbol "G i for
movement(s) i.
(d)
Red interval. Each movement has a red interval during the signal cycle. All
movements not permitted have a "red" light, while those permitted to move have a
"green" light. In general, the red interval overlaps the green intervals for all other
movements in the inter section. The red interval is given the symbol "R i for
movement(s) i.
4. Phase. A signal phase consists of a green interval, plus the change and clearance intervals
that follow it. It is a set of intervals that allows a designated movement or set of movements
to flow and to be safely halted before release of a conflicting set of movements.
Signal Timing at Isolated Intersections
An isolated intersection is one in which the signal time is not coordinated with that of any other
intersection and therefore operates independently. The cycle length for an intersection of this type
should be short, preferably between 35 and 60 sec, although it may be necessary to use longer cycles
when approach volumes are very high. However, cycle lengths should be kept below 120 sec, since
very long cycle lengths will result in excessive delay. Several methods have been developed for
determining the optimal cycle length at an intersection and, in most cases, the yellow interval is
considered as a component of the green time. Before discussing two of these methods, we will
discuss the basis for selecting the yellow interval at an intersection.
Yellow Interval
The main purpose of the yellow indication after the green is to alert motorists to the fact that the
green light is about to change to red and to allow vehicles already in the intersection to cross it. A
bad choice of yellow interval may lead to the creation of a dilemma zone, an area close to an
intersection in which a vehicle can neither stop safely before the intersection nor clear the
intersection without speeding before the red signal comes on. The required yellow interval is the
time period that guarantees that an approaching vehicle can either stop safely or proceed through
the intersection without speeding.
Page 148
.
Figure 5.10 schematic of a dilemma zone.

For the dilemma zone to be eliminated the distance X o should be equal to the distance X c . Let
be the yellow interval (sec) and let the distance traveled during the change interval without
min
accelerating be u o ( ), with u o = speed limit on approach (m/sec). If the vehicle just clears the
min
intersection, then
X c = u o (min ) (W + L)
Where: X c is the distance within which a vehicle traveling at the speed limit (u o ) during the yellow
interval time cannot stop before encroaching on the intersection. Vehicles within this distance at
the start of the yellow interval will therefore have to go through the intersection;
W =width of
intersection (m); L = length of vehicle (m)

For vehicles to be able to stop, however,
Where: X o = the minimum distance from the intersection for which a vehicle traveling at the speed
limit u o during the clearance interval Y o cannot go through the intersection without accelerating; any
vehicle at this distance or at a distance greater than this has to stop;
= perception-
reaction time; a = constant rate of braking deceleration (m/sec2)

For the dilemma zones to be eliminated, X o must be equal to X c . Accordingly,
Page 149
.
u o (min ) (W + L)
=
min
If the effect of grade is added,
=
min
Where, = the minimum yellow interval, (sec)
min
= perception-reaction time (sec)

W = width of intersection, (m)
L = length of vehicle, (m)
u = speed (m/sec)
o
a = deceleration, (m/sec )
G = grade of the approach road, and
g = acceleration due to gravity
Yellow intervals of 3 to 5 sec are normally used. When longer yellow intervals than 5 see are
computed from the above equations, an all-red phase can be inserted to follow the yellow indication,
but the change interval, yellow plus all-red, must be at least the value computer from the equations.
Cycle lengths: - Several design methods have been developed to determine the optimum cycle, length,
one of which the Webster method is presented here.
Webster method
Webster has shown that for a wide range of practical conditions, minimum intersection delay is
obtained when the cycle length is obtained by the equation:
Where, C = optimum cycle length (sec)

o
L = total lost time per cycle (sec)

Y = maximum value of the ratios of approach flows to saturation flows for all traffic streams using phase i
i
(i.e., V / S )
ii
n = number of phases
Page 150
.
V = flow on lane j having the right of way during phase i

ij
S = saturation flow on lane i

j
Example 1 Figure 5.11a and table shown below shows peak-hour volumes for a major intersection
on an arterial highway. Using the Webster method, determine suitable signal timing for the
intersection using a fourphase system and the additional data given in the figure. Use a Yellow
interval of 3sec.
East Approach
West Approach
South Approach
North Approach
Lane
PHV
222
467
467
128
321
321
109
75
25
206
100
128
Solution:
First convert the mixed volumes to equivalent straight-through passenger cars. The equivalent
volumes are shown Figure 3-10b. The volumes were obtained by dividing by the PHF, and then by
applying the relevant factors for trucks and leftturning vehicles as necessary. No factors for rightturning vehicles were used because those volumes were very low. Assume the following phasing
system, where the arrows indicate traffic streams that have the right of way:
The critical lane volumes are (see Figure 3-10b)
Phase, n
Critical Lane volume
499
338
115
519
1471
Compute the total time using l =3.5sec. Since there is not an all-red phase-that is, AR=0 and there are
i
four phases,
Page 151
.
Figure 5.11a & b: Peak hour volume for major intersection on arterial highway
Page 152
.
Phase A (EB)
Phase B (WB)
Phase C (SB)
Phase D (NB)
Lane
V ij
335
499
499
189
338
338
115
79
37
519
105
217
Sj
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
2000
V ij
0.17
0.25
0.25
0.09
0.17
0.17
0.06
0.04
0.019
0.26
0.05
0.17
/S j
Yi
0.25
0.17
0.06
0.26
Determine the optimum cycle length
Find the total effective green time:

G te = C - L = 100 14 = 86 sec
Effective time for phase i is obtained from:
Yellow time i =3sec; then the actual green time for each phase can be calculated as:
Page 153
.
Actual green time for phase A:
x 86 + 3.5 3.0 = 30sec
x 86 + 3.5 3.0 = 20sec
x 86 + 3.5 3.0 = 7sec
x 86 + 3.5 3.0 = 31sec
References
Rojer P. Roess, Elena S. Passass and William R. MacShane, Traffic Engineering, PEARSON
Prentice Hall, 2004
Institute of Transportation Engineers, Transportation and Traffic Engineering Hand Book,
Prentice Hall, 1976
C.A. OFlaherty et.al, Transport Planning and Traffic Engineering, Elsevier, 1997
Page 154

Transport Engineering

Uploaded by

Document Informationclick to expand document information

Copyright:

Available Formats

Transport Engineering

Uploaded by

Document Information

Original Description:

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

Transport Engineering

Uploaded by

Copyright:

Available Formats

ADDIS ABABA UNIVERSITY

School of Civil and

Transportation Engineering (Ceng3301)

What is Transportation engineering?

Transportation engineering is a type of civil engineering which focuses on the infrastructure

Transportation Engineering (Ceng3301)

The characteristics of transportation system

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

Generally a transportation system has three elements this are

Vehicles: which includes Planes, trains, autos, buses, ships, trucks

Operators/Content : which includes Drivers, pilots, freight, passengers

History of transportation engineering

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

Transportation Engineering (Ceng3301)

Transportation Engineering (Ceng3301)

concern. The environmental impact assessment attempts in quantifying the environmental

Factors in Transportation Development

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

Role of transportation in society

Transportation Engineering (Ceng3301)

Economic role of transportation

Social role of transportation

Transportation Engineering (Ceng3301)

Environmental role of transportation

Transportation Engineering (Ceng3301)

Transportation Engineering (Ceng3301)

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

Transportation Engineering (Ceng3301)

Feedback to all steps

A problem is a deviation from expected or desired performance. Goals and objectives,

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

The transportation planning process is continuous- it is applied simultaneously at multiple levels,

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

Quantified objectives: Quantified objectives may indicate a requirement, for example, to

Solution-specific objectives: It is important to avoid specifying solutions within the

The transport policy formulation process

Transportation Engineering (Ceng3301)

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

Transportation Engineering (Ceng3301)

Figure 2.3 Model formulation process

To gain a more structural analysis of the complex transport system

AAIT, School of civil and Environmental Engineering

Transportation Engineering (Ceng3301)

To enable quantified calculations of expected effects in the transportation system when

AAIT, School of civil and Environmental Engineering