URBAN TRANSPORTATION PLANNING

IV B TECH I SEM
DEPARTMENT OF CIVIL ENGINEERING

SRKIT, ENIKEPADU
VIJAYAWADA
Urban transport planning , SRKIT 2023

IV B TECH I SEM CH.RAJESH ASSISTANT PROFESSER

Urban transport planning , SRKIT 2023

Unit 4
Mode choice and traffic assignment:

Mode choice

The choice of transport mode is probably one of the most important classic models in transport
planning. This is because of the key role played by public transport in policy making. Public
transport modes make use of road space more efficiently than private transport. Also they have more
social benefits like if more people begin to use public transport, there will be less congestion on the
roads and the accidents will be less. Again in public transport, we can travel with low cost. In
addition, the fuel is used more efficiently. Main characteristics of public transport is that they will
have some particular schedule, frequency etc.

On the other hand, private transport is highly flexible. It provides more comfortable and convenient
travel. It has better accessibility also. The issue of mode choice, therefore, is probably the single
most important element in transport planning and policy making. It affects the general efficiency
with which we can travel in urban areas. It is important then to develop and use models which are
sensitive to those travel attributes that influence individual choices of mode.

Mode choice behavior

Mode choice is a key aspect of travel demand modeling. The choice of travel mode is a
complicated behavioral process and as such is a core focus in Travel Behavior

Factors influencing the choice of mode

The factors may be listed under three groups:

1. Characteristics of the trip maker : The following features are found to be important:
(a) car availability and/or ownership;
(b) possession of a driving license;
(c) household structure (young couple, couple with children, retired people etc.);
(d) income;
(e) decisions made elsewhere, for example the need to use a car at work, take children to
school, etc;
(f) residential density.

2. Characteristics of the journey: Mode choice is strongly inuenced by:

(a) The trip purpose; for example, the journey to work is normally easier to undertake by public
transport than other journeys because of its regularity and the adjustment possible in the long
run;
(b) Time of the day when the journey is undertaken.
(c) Late trips are more di_cult to accommodate by public transport.

3. Characteristics of the transport facility: There are two types of factors.One is quantitative
and the other is qualitative. Quantitative factors are:
(a) relative travel time: in-vehicle, waiting and walking times by each mode;

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(b) relative monetary costs (fares, fuel and direct costs);
(c) availability and cost of parking
Qualitative factors which are less easy to measure are:
(a) comfort and convenience
(b) reliability and regularity
(c) protection, security
A good mode choice should include the most important of these factors.

Types of modal split models

Trip-end modal split models

Traditionally, the objective of transportation planning was to forecast the growth in demand for car
trips so that investment could be planned to meet the demand. When personal characteristics were
thought to be the most important determinants of mode choice, attempts were made to apply modal-
split models immediately after trip generation. Such a model is called trip-end modal split model. In
this way different characteristics of the person could be preserved and used to estimate modal split.
The modal split models of this time related the choice of mode only to features like income,
residential density and car ownership.
The advantage is that these models could be very accurate in the short run, if public transport is
available and there is little congestion. Limitation is that they are insensitive to policy decisions
example: Improving public transport, restricting parking etc. would have no effect on modal split
according to these trip-end models.

Trip-interchange modal split models

This is the post-distribution model; that is modal split is applied after the distribution stage. This has
the advantage that it is possible to include the characteristics of the journey and that of the
alternative modes available to undertake them. It is also possible to include policy decisions. This is
beneficial for long term modeling.

Aggregate and disaggregate models & approaches

In urban transport planning, the concepts of aggregate and disaggregate approaches refer to different
levels of detail and analysis when studying transportation systems. These approaches help planners
understand and address transportation issues at both a broad, system-wide level (aggregate) and a more
detailed, individual level (disaggregate). Let's explore these concepts further:

1. Aggregate Approach:
 Overview: The aggregate approach involves looking at the transportation system as a whole,
considering overall patterns, trends, and averages for a large group of people or vehicles.
 Data and Analysis: Data is often aggregated, or combined, to provide a high-level view of
transportation patterns. This may involve looking at average travel times, traffic volumes, or
mode share for an entire city or region.
 Benefits:
 Provides a big-picture understanding of the transportation system.
 Useful for long-term strategic planning and policy development.
 Helps identify general trends and patterns.
2. Disaggregate Approach:
 Overview: The disaggregate approach involves examining transportation at a more detailed,
individual level. This can include analyzing the travel behavior of specific individuals,
households, or vehicles.

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 Data and Analysis: Data is broken down into smaller units, allowing for a more nuanced
understanding of travel patterns. This might involve detailed surveys, interviews, or the use of
individual travel diaries.
 Benefits:
 Captures variations in travel behavior among different demographic groups.
 Allows for a more precise understanding of individual travel choices.
 Useful for designing interventions that target specific user groups or address specific
issues.
3. Integration of Approaches:
 In practice, urban transport planning often involves a combination of both aggregate and
disaggregate approaches.
 Example: Planners might use aggregate data to identify general traffic flow patterns in a city
and then use disaggregate data to understand the preferences and behaviors of specific user
groups, such as commuters or public transit users.
4. Application:
 Aggregate Approach Application: Long-term infrastructure planning, traffic flow modeling,
and policy development for the entire urban area.
 Disaggregate Approach Application: Designing transportation services tailored to specific
user needs, understanding individual travel choices, and assessing the impact of specific
interventions.
5. Challenges:
 Aggregate Approach Challenges: May overlook individual variations and specific needs, and
generalizations may not apply universally.
 Disaggregate Approach Challenges: Gathering detailed individual-level data can be resource-
intensive, and extrapolating findings to the broader population requires careful consideration.

In summary, the choice between aggregate and disaggregate approaches in urban transport planning
depends on the specific goals, context, and available resources. A balanced approach that integrates
insights from both levels of analysis often leads to more comprehensive and effective transportation
planning strategies.

Discrete Choice Analysis (DCA) is a widely used method in urban transport planning to understand
and model individuals' choices among different transportation modes or alternatives. It is grounded in
the idea that individuals make discrete decisions among a set of alternatives based on their preferences
and the attributes of those alternatives. Here are the key components and steps involved in discrete
choice analysis in the context of urban transport planning:

1. Choice Set Definition:

 Define the set of alternatives that individuals can choose from. In urban transport planning, these
alternatives could include different modes of transportation (e.g., car, bus, bicycle) or variations
within a mode (e.g., different bus routes).
2. Attributes and Variables:
 Identify the attributes or variables that influence individuals' choices. These can include travel
time, cost, reliability, comfort, environmental impact, and other relevant factors.
3. Choice Model Specification:
 Choose a specific model form to represent how individuals make choices. Common models
include Multinomial Logit (MNL), Nested Logit, and Mixed Logit models. These models
mathematically describe the probability that an individual will choose a particular alternative
based on the attributes of the alternatives.
4. Data Collection:

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 Collect data on individuals' choices and the corresponding attributes of the alternatives. This
often involves surveys, interviews, or observations. Individuals may be asked about their
preferences and choices in hypothetical or real scenarios.
5. Utility Function:
 Develop a utility function that quantifies the perceived satisfaction or desirability of each
alternative based on the identified attributes. The utility function is a key component of choice
models and reflects individuals' preferences.
6. Estimation:
 Use statistical techniques to estimate the parameters of the chosen choice model based on the
collected data. This step involves determining how sensitive individuals are to changes in the
attributes of the alternatives.
7. Prediction and Simulation:
 Apply the estimated model to predict choices in different scenarios or simulate the impact of
changes in the attributes. This can help evaluate the potential effects of policy interventions or
changes in the transportation system.
8. Policy Analysis:
 Use the model to assess the impact of different policies, infrastructure changes, or other
interventions on individuals' choices and overall transportation outcomes. This information can
guide decision-makers in making informed choices for urban transport planning.
9. Sensitivity Analysis:
 Conduct sensitivity analyses to understand how changes in model parameters or assumptions
might affect the results. This helps assess the robustness of the model and its predictions.

Discrete Choice Analysis is valuable in urban transport planning because it provides a systematic and
quantitative framework for understanding the factors influencing mode choice. It helps planners and
policymakers design transportation systems and policies that align with the preferences of the
population, ultimately contributing to more efficient and sustainable urban mobility solutions.

Maximum utility :

In urban transport planning, the concept of maximum utility refers to the idea of optimizing the overall
satisfaction or well-being of individuals and the community in terms of transportation services and
infrastructure. Achieving maximum utility involves considering various factors such as efficiency,
accessibility, environmental sustainability, and social equity. Here are several key considerations for
maximizing utility in urban transport planning:

1. Accessibility and Connectivity:

 Ensure that transportation networks are well-connected, providing easy access to various
destinations within the urban area.
 Promote integrated transportation systems that seamlessly connect different modes of transport,
such as buses, trains, bicycles, and pedestrian pathways.
2. Efficiency and Reliability:
 Optimize the efficiency of transportation systems to minimize travel time and reduce delays.
 Implement technologies and strategies, such as intelligent traffic management systems, to
improve the reliability of public transportation and reduce congestion.
3. Environmental Sustainability:
 Prioritize sustainable modes of transportation, such as public transit, walking, cycling, and
electric vehicles, to reduce the environmental impact of urban transport.
 Encourage the use of clean and energy-efficient technologies in public transportation and
promote the development of eco-friendly infrastructure.

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4. Safety:
 Prioritize the safety of all users, including pedestrians, cyclists, and motorists, by implementing
measures such as well-designed crosswalks, traffic signals, and speed limits.
 Invest in infrastructure improvements that enhance overall road safety, such as well-maintained
roads, lighting, and signage.
5. Affordability and Accessibility:
 Ensure that transportation options are affordable for a wide range of income groups to promote
social equity.
 Design infrastructure that is accessible to people with disabilities, including accessible public
transit, sidewalks, and public spaces.
6. Community Engagement:
 Involve the community in the planning process to understand their needs and preferences.
 Consider the social and cultural aspects of transportation planning to ensure that the
transportation system meets the diverse needs of the community.
7. Land Use Planning:
 Integrate land use and transportation planning to create compact, mixed-use developments that
reduce the need for extensive travel.
 Encourage transit-oriented development to promote the efficient use of public transportation.
8. Innovation and Technology:
 Embrace emerging technologies to enhance the efficiency and effectiveness of transportation
systems, such as smart traffic management, ride-sharing, and autonomous vehicles.
9. Data-Driven Decision Making:
 Utilize data analytics and modeling tools to make informed decisions in urban transport
planning, including predicting travel patterns, optimizing routes, and identifying areas for
improvement.

By integrating these considerations into urban transport planning, authorities can work towards
achieving maximum utility by creating a transportation system that is efficient, sustainable, safe, and
inclusive for all members of the community

Choice sets:
In urban transport planning, a "choice set" refers to the range of options or alternatives available to
individuals when making travel-related decisions. These decisions can include choosing a mode of
transportation, selecting a route, deciding on the timing of travel, and more. The concept of choice sets
is fundamental in understanding and modeling traveler behavior in urban areas. Here are some key
aspects related to choice sets in urban transport planning:

1. Mode Choice Sets:

 Individuals often have various transportation modes to choose from, such as walking, cycling,
public transit, carpooling, and private car usage.
 The mode choice set represents the available alternatives that a traveler considers when deciding
how to move from one location to another.
2. Route Choice Sets:
 In urban areas, there can be multiple routes to reach a destination, especially with the presence
of road networks, public transit lines, and pedestrian pathways.
 Route choice sets involve the options available to travelers when selecting a specific path or
route for their journey.
3. Time-of-Day Choice Sets:
 The timing of travel can also be a significant factor in urban transport planning. Travelers may
have the flexibility to choose when they travel, considering factors like peak hours, off-peak
hours, and time-of-day variations in congestion and transit service frequency.

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 Time-of-day choice sets involve the different time slots within which individuals can plan their
trips.
4. Trip Purpose Choice Sets:
 People travel for various reasons, such as commuting to work, running errands, leisure activities,
etc.
 The trip purpose choice set involves the different purposes for which individuals may be
traveling and the corresponding transportation options available for each purpose.
5. Spatial Choice Sets:
 Urban areas are characterized by a mix of land uses, and individuals may have different
destinations or origins for their trips.
 Spatial choice sets involve the set of locations or destinations that individuals can choose from
when planning their trips.
6. Access and Egress Choice Sets:
 For each mode of transportation, there are choices related to access (getting to the transportation
mode) and egress (getting from the transportation mode to the final destination).
 Access and egress choice sets involve the alternatives available for accessing and egressing from
different transportation modes.

Understanding and analyzing these choice sets is crucial for urban transport planners and policymakers.
It helps in developing effective transportation strategies, designing infrastructure, and implementing
policies that align with the preferences and behaviors of the urban population. Modeling these choice
sets can be done through various transportation demand models, which simulate and predict travel
behavior based on different factors and scenarios.

Mode choice could be aggregate if they are based on zonal and inter-zonal information. They can be
called disaggregate if they are based on household or individual data.
Trip End Modal Split Model Trip Interchange Modal Split Model
Performs modal split after trip generation Performs modal split after trip distribution
Performed in medium and small sized cities Performed for large urban areas
Assumes that modal patronage is relatively Incorporates measures of relative service
insensitive to the service characteristics of characteristics of competing modes
transport modes
Determined based on socio-economic Determined based on socio-economic
characteristics of trip maker characteristics of trip maker
Emphasize on transit captives Emphasize on choice transit riders
E.g. Southeastern Wisconsin Transportation E.g. Toronto Model
Study

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LAND
USE

TRIP GENERATION
EQUATION

MODAL SPLIT MODEL TRIP DISTRIBUTION MODELS

TRIP ENDS BY MODE ORIGIN DESTINATION VOLUMES

TRIP DISTRIBUTION MODELS MODAL SPLIT MODEL

O-D VOLUMES BY MODE O-D VOLUMES BY MODE

Trip Assignment

Purpose of traffic assignment

The last phase of the four-step sequential transportation demand forecasting process is concerned
with the trip maker’s choice of path between pairs of zones by a travel mode. This results in
vehicular flows on the multimodal transportation network. This step may be viewed as the
equilibrium model between the demand for travel, estimated earlier in the process, and the supply of
transportation in terms of the physical facilities. In the case of the various possible mass transit
modes, it includes the frequency of service being provided. Incidentally, this conceptual framework
of economic theory is applicable to earlier steps of the process as well and has been so treated by
many researchers.

Traffic assignment is the stage in the transport planning process wherein the trip interchanges are
allocated to different parts of the network forming the transportation system. In this stage:

• The route to be traveled is determined and

• The inter-zonal flows are assigned to the selected routes.
• The traffic assignment to the network has following applications:
• To determine the deficiencies in the existing transportation system by assigning the
future trips to the existing system.
• To evaluate the effects of limited improvements and additions to the existing
transportation system by assigning estimated future trips to the improved network.
• To develop construction priorities by assigning estimated future trips for intermediate
years to the transportation system proposed for those years.
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• To test alternative transportation system proposals by systematic and readily repeatable
procedures.
• To provide design hour traffic volumes on highway and turning movements at
junctions.Thus the assignment process is useful both to the transports planners and the
highway facility designers, to the former because of the need to evaluate how the
proposed transport system will work, and to the latter, for geometric design of
individual links and intersections.
The advent the modern digital computers has facilitated the growth of assignment techniques, which
involve computations too laborious for manual handling.

raffic assignment, diversion curves, and coding and routing properties are fundamental concepts in
transportation engineering and network analysis. Let's break down each of these elements:

1. Traffic Assignment:
 Definition: Traffic assignment is the process of determining how trips (travel demand) will be
distributed across a transportation network.
 Objective: The goal is to understand how traffic flows through the network, considering factors
such as travel time, cost, or distance.
 Methods: Various methods are used for traffic assignment, including static assignment (e.g., All-
or-Nothing Assignment) and dynamic assignment (e.g., User Equilibrium Assignment, System
Optimum Assignment).
2. Diversion Curves:
 Definition: Diversion curves illustrate the relationship between travel time and the percentage of
traffic diverted from one route to another in response to changes in travel conditions.
 Purpose: Diversion curves help in understanding how changes in travel conditions, such as
increased congestion or tolls, impact route choice behavior.
 Representation: Typically, diversion curves are presented as graphs showing the diversion
percentage on the y-axis and the change in travel time or cost on the x-axis.
3. Basic Elements of Transport Networks:
 Nodes: Points in the network where transportation paths intersect, such as intersections,
terminals, or decision points.
 Links: Connections between nodes, representing the physical or logical paths that vehicles or
travelers can take.
 Zones: Geographic areas used to aggregate trip origins and destinations for analysis.
 Attributes: Characteristics of nodes and links, such as travel time, capacity, and cost.
4. Coding and Routing Properties:
 Coding: Refers to the representation of network elements in a computer system. Nodes, links,
and attributes need to be coded for computational analysis.
 Routing Properties: Describes how vehicles or travelers choose their paths through the network.
This can be influenced by factors such as travel time, cost, and user preferences.
 Algorithms: Routing algorithms determine how trips are assigned to routes. Common algorithms
include Dijkstra's algorithm, A* algorithm, and various optimization methods for traffic
assignment.

In summary, these concepts are crucial for understanding and modeling transportation systems. Traffic
assignment methods help simulate how travelers make route choices, diversion curves illustrate the
sensitivity of these choices to changes, and the basic elements of transport networks provide the
foundation for coding and analysis. Routing properties and algorithms play a key role in optimizing and
predicting traffic flow within the network.

Transportation Networks

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Transportation Network primarily consists of two elements:
• Links
• Nodes
Link is defined as connectivity between two nodes. The links may have traffic movements either in
both the directions or in one direction only. Sometimes the links on which direction of travel is
marked are also known as an Arc.
The nodes are the location in space which provides an opportunity to the vehicle to enter or leave a
system or facilitate the movements in different directions. The node from which an arc is diverted
is termed it’s A-node and the node to which it is diverted is termed its B-node. A representative map
of the network system is shown in the figure below.

The above network is represented in the form of links and nodes showing the direction of movement
of the traffic along the links along with the travel attribute value written on the side of the link. The
travel attribute values may be in terms of travel time, travel cost, travel

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distance, etc. usually numbers are used to specify the nodes in the network from the point of view of
computational ease. One such network is represented in the figure below.

Connection Matrix:
A connection matrix defines the connectivity between different nodes available in a transportation
network. This helps in building a network in a systematic way. It has rows and columns. Rows
define the originating nodes and columns define the destination nodes. The numbers 0, 1 and -1
denotes no flow along the link, flow along the link and reverse direction flow along the link,
respectively. A connection matrix is shown in the figure below.

Node-Link Incidence Matrix

Node-link incidence matrix defines the connectivity from a node to different nodes of the network.
This also uses numbers to represent the connectivity as done in the connection matrix. This is shown
in the figure below.

Network Assignment Methods

The network assignment methods are basically single-path methods, which allocate trips on one
preferred path between each origin and destination pair. This technique is executed based on three
steps, in combination of what is listed initially as
requirement. These are:

• A driver route selection criteria

• A tree building technique
• Method of allocating trip interchanges between these routes

Driver route-selection Criteria

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Driver’s route-selection is based on Wardrop’s principles. Wardrop has given two principles, as
follows:

System Optimization criteria:

‘The trip times on all the routes actually used are equal and less than those which would be
experienced by a single vehicle on any unused route’.
The system optimization is based on ‘marginal cost concept’ of economics.
Let us consider a link carrying traffic volume in vehicle/hr. As the traffic volume increases the travel
time on the link also increases. This increase per unit volume becomes more after certain volume on
the link. In terms of marginal travel time, the increase becomes exponential after certain value of
traffic volume. As can be seen from the figure, the increase in average travel time per mile with
increase in traffic volume from nil to 3000 veh/hr is from 5 min/mile to 15 min/mile, whereas, the
increase in marginal travel time is from 5 min/mile to 105 min/mile during the same change in
volume. It indicates that the entry of one vehicle at a flow of 3000 veh/hr increases the travel time
effect by 90 min/mile (=105 – 15 min/mile).

User Optimization criteria:

‘The average journey time of all motorists is a minimum which implies that the aggregate
vehicle hours spent in traveling is a minimum.’
This criterion indicates towards the ‘average cost concept’ of economics. It means that every user
tries to minimize the individual travel time. Therefore, the user will base their route choice decision
on the average travel time relationship and will select the route according to the marginal travel time
criteria. Reacting to marginal travel time criteria will minimize the total travel time of all the
vehicles using the system.

Route Builiding Algorithm

Next step after finalization and coding of network is the computation of minimum travel path
between the zones. This is already discussed in one of the previous lectures. Some of the techniques
or algorithms used for finding the minimum travel path tree are:
1. Network analysis
2. Moore’s tree building algorithm
3. Shortreed and Wilson’s Modified tree-building algorithm
4. Dijkstra’s algorithm
5. D’Esopo’s algorithm

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Route Builiding Algorithm:

Moore’s Algorithm
For each origin centroid, a label is assigned to each node in the network of the following
form: Node ‘j’ label = [i, d(j)]
Where,
i = the node nearest to zone ‘j’ which is on the travel time path back to the
origin d(j) = the minimum travel time from node ‘j’ back to the origin
centroid
Initially, each node is assigned a d(j) magnitude which is very large, say, 999, with the exception
of the origin node where it is set to ‘0’. As the tree is built out from the origin, the following sum
is formed for each node
Node: Node ‘j’ sum = [d(i) +
l(i,j)] Where,
d(i) = travel time from the origin to node ‘i’ which has just been connected to the
origin l(i.j) = travel time along the link which connects node ‘j’ to node ‘i’
If the sum just formed is greater than the d(j) already recorded for node ‘j’, then the node is by-
paased. If the sum is less than the d(j) existing, then the d(j) is replaced by the newly
formed sum and ‘i’ is changed in the label to reflect the new connecting link for j back to the
origin.
This process is continued until all nodes have been reached.

Shortreed and wilson’s Method

(Moore’s modified method / computationally efficient method)

The improved efficiency results from the manner in which the node labels are stored and
updated. This algorithm uses three concepts which are known as the tree table, the link table and
the list.

Tree Table: It shows the sequence of node that defines the minimum path from any particular
centroid back to the origin centroid.

Link Table: It defines all the links in the network in terms of other nodes at either end or the
travel time along the link.

List: A table in which all of the links emerging from a specified node are entered along the
travel times or the links.

Steps for minimum path tree:

1. Initialize the tree table with all the total times equal to 999 with the exception of the
origin node which is set equal to 0 and this activity is shown in table above.
2. Add to the list all nodes connected to the nodes just added to the tree table.
3. Test all entries in the list to determine if “Node to” + “Total time from origin” travel
time is less than the “Total travel time” in the tree table and if so enter it in the tree
table.
4. Return to 2 and repeat until the list is empty.

Network coding:
• Ideally the network should be the smallest possible, in terms of links and nodes,
adequate for the purpose for which it is required.
• All redundant links and nodes should be removed beforehand. Dead end links apart
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from centroid and gateway connectors should be removed.

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• For some purposes, especially if minimum path costs only are required, the use of spider
network, in which groups of two or more links from the original network are combined
into a single link representing minimum cost paths between their end nodes, may be
appropriate, to reduce CPU time.
• Numbering the network nodes, including centroids, sequentially without gaps, as
suggested saves time in the initialization process and uses less computers core storage
• It may be assumed that the real network nodes start at node number Ncent+1 and hence,
at step 2(b)(ii), node k is entered into L and ensuring that paths do not pass through
centroids or gateways en route to other nodes.
• It is possible to avoid completely the need for tests to prevent centroids and gateways
from entering the loose ends table by separating their connector links from the real
network links.

Route Choice Behaviour

The most fundamental element of any traffic assignment is to select a criterion which explains the
choice by driver of one route between an origin-destination pair from among the number of potential
paths available.

All-or-Nothing assignment

All or Nothing assignment technique allocates the entire volume interchanging between pairs of
zones to the minimum path calculated on the basis of free-flow link impedances. This is the simplest
technique and is based on the premise that the route followed by traffic is the one having the least
travel resistance. The resistance itself can be measured in terms of travel time, distance, cost or a
suitable combination of these parameters. The traffic flows are assigned to the minimum path tree.
The assignment algorithm loads the matrix ‘T’ to the shortest path tree and produces flows VAB on
links between node A and B. two basic variations of the algorithm are given as follows:

Pair to Pair method

This is simplest but not necessarily results in the most efficient one. The steps are: Initialize all
VAB = 0, then for each pair (i, j):
1. Set B to destination ‘j’
2. If (A, B) is the back link of B then increment VAB by Tij i.e. VAB = VAB + Tij
3. Set B to A
4. If A = i, terminate (and process the next pair), otherwise return to step-2.

Once-Through method (Cascade method)

Allocates cumulative flows on minimum path trees using steps as follows:
1. Set all VA = 0 except for destination ‘j’ for which Vj = Tij.
2. Set B equal to the most distant node from ‘i’.
3. Increment VA by VB: VA = VA + VB (where A is back node of B).
4. Increment VAB by VB: VAB = VAB + VB
5. Set B equal to next most distant node; if B=I then origin has been reached; begin processing
the next origin; otherwise proceed with step-3.

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Capacity Restraint Techniques

Capacity restraint assignment is a process in which the travel resistance of a link is increased
according to a relation between the practical capacity of the link and the volumes assigned to the
link. This technique has been developed to overcome the inherent weakness of all-or- nothing
assignment technique which takes no account of the capacity of the system between a pair of zones.
The capacity restraint system, on the other hand, clearly restrains the number of vehicles that can
use any particular corridor and, in fact, the whole system, if the assigned

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volumes are beyond the capacity of the network, and redistributes the traffic to realistic alternative
paths.
Because of the iterative nature of the calculations involved, the capacity restraint technique is
carried out entirely by an electronic computer. The procedure is similar to the all-or-nothing
assignment as far as the initial data input are concerned. The additional data that is fed is the
capacity of each link. The best paths are determined in the same way as in all-or-thing technique
by building the minimum path trees. Traffic is then assigned to the minimum path, either fully or in
stages, and as the assigned volume on each link approaches the capacity of the link, the new set of
travel time of the link is calculated. This results in a new network with a different minimum path
tree, differing significantly from the earlier minimum path tree. As a consequence, assigning
interzonal volumes to the new tree produces a new volume on each link. This iterative process is
repeated until a satisfactory balance between volume and speed is achieved. Some of the methods of
capacity restraint are given below.

Smock Method
In this method, the all-or-nothing assignment is first worked out. In an iterative procedure, the link
travel ties are modified according to the function:

Where To = Original travel time or the travel time on a link when volume equals capacity
TA= adjusted travel time
V = assigned volume
C = computed link capacity
In the second iteration, the adjusted travel times TA are used to determine the minimum paths or
trees. The resulting link volumes are averaged and these are again used to calculate the adjusted
travel time for the next iteration.

WEYNE State Arterial method

This method is one of the earlier capacity restrained assignment methods. It is based on assigning
traffic to various routes between an origin-destination pair such that the travel time on these routes
are equal and any route between the origin-destination pair with zero flow will have a larger travel
time. Various steps of this method are as follows;
1. Construct a minimum travel path tree for all origin zones based on travel time computed
from average speeds on links, under typical flow conditions as existing.
2. Assign inter-zonal volumes to minimum travel path tree on A-O-N basis.
3. Compute the link travel times as (ith iteration)

Where, RI = Average assigned volume (from previous iteration) / capacity of the

link Average assigned volume = (Vi-1 + Vi-2)/2
To = original travel time on the link
4. Go to step 1 and repeat upto step 3 until equilibrium is reached i.e. Ti / Ti+1 ≈ 1.0 The
limitations of this method are: variations in travel time are taken into consideration, and A-O-N
assignment technique is used for assigning the volume to the network.

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Urban transport planning , SRKIT 2023
Multiple Route Assignment
All road users may not be able to judge the minimum path for themselves. It may also happen that
all road users may not have the same criteria for judging the shortest route. These limitations of the
all-or-nothing approach are recognized in the multiple route assignment technique. The method
consists of assigning inter-zonal flow to a series of routes, the proportion of the total flow assigned
to each being a function of the length of the route in relation to the shortest route. In an interesting
approach suggested by Burell, it is assumed that a driver does not know the actual travel times, but
that he associates with each link a supposed time. This supposed time is drawn from link time. The
driver is then assumed to select the route which minimizes the sum of his supposed link times.
Multiple route models have been found to yield more accurate assignment than all-or-nothing
assignments

User Equilibrium assignment (UE)

The user equilibrium assignment is based on Wardrop's first principle, which states that no driver
can unilaterally reduce his/her travel costs by shifting to another route. User Equilibrium (UE)
conditions can be written for a given O-D pair as:

where f is the flow on path k, ck is the travel cost on path k, and u is the minimum cost.
Equation labelqueue2 can have two states.
1. If ck - u = 0, from equation 10.1 f > 0. This means that all used paths will have same
travel time.
2. If ck - u > 0, then from equation 10.1 f = 0.
This means that all unused paths will have travel time greater than the minimum cost path.
where f is the flow on path k, ck is the travel cost on path k, and u is the minimum cost.

Assumptions in User Equilibrium Assignment

1. The user has perfect knowledge of the path cost.
2. Travel time on a given link is a function of the flow on that link only.
3. Travel time functions are positive and increasing.
The solution to the above equilibrium conditions given by the solution of an equivalent nonlinear
mathematical

Where k is the path, xa equilibrium flows in link a, ta travel time on link a, frs k flow on path k
connecting
O-D pair r-s, qrs trip rate between r and sand frs a;k is a definitional constraint and is given by

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Urban transport planning , SRKIT 2023

The equations above are simply flow conservation equations and non negativity constraints,
respectively. These constraints naturally hold the point that minimizes the objective function. These
equations state user equilibrium principle .The path connecting O-D pair can be divided into two
categories : those carrying the flow and those not carrying the flow on which the travel time is
greater than (or equal to)the minimum O-D travel time. If the flow pattern satistices these equations
no motorist can better o_ by unilaterally changing routes. All other routes have either equal or heavy
travel times. The user equilibrium criteria is thus met for every O-D pair. The UE problem is convex
because the link travel time functions are monotonically increasing function, and the link travel time
a particular link is independent of the flow and other links of the networks. To solve such convex
problem Frank Wolfe algorithm is useful.

Diversion Curves
One of the frequently used assignment techniques in initial years was the development and use of
diversion curves. These curves represent empirically derived relationships showing the proportion of
traffic that is likely to be diverted on a new facility (by pass, new expressway, new arterial street
etc.), once such a facility is constructed. The data collected on the pattern of travel in the past years
serve to build up such curves. Diversion curves can be constructed using a variety of variables such
as:
(i) Travel time saved
(ii) Distance saved
(iii) Travel time ratio
(iv) Distance ratio
(v) Travel time and distance saved
(vi) Distance and speed ratio
(vii) Travel cost ratio

Some of the diversion curve methods used in different parts of the world are discussed in the
following paragraphs.

Indiana US method (Brown method)

It compares two paths between same set of origin and destination. One is travel by personal car and
other is travel by transit. A person traveling by car has to cover distance equal to ‘c’, whereas,
person who travels by transit has to walk to the transit stop from home (say b1) and then again walks
from transit stop to the destination (say b2). The distance travel using transit is say ‘a’.

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Bureau of Public Roads method

A well-known example of diversion curves using travel time ratio to determine the traffic diverted to
expressway is the Bureau of Public Roads Curve. The curve is “S” shaped. The following formula
has been fitted to this type of curves:

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Urban transport planning , SRKIT 2023

California Diversion Curve method

Another well known example using two variables, distance and travel time saved while moving on
a motorway, is the California Diversion Curve.
The following formula has been developed to fit the above curves.

Where P = percentage of vehicles moving on freeway

d = distance saved (in miles) on the freeway
t = time saved (in minutes) on the freeway

Diversion curve assignments have the drawback that only two alternative routes for each pair of
zones are considered. The technique is, therefore, eminently suitable for new bypasses, new
motorways and such new facilities, but is of limited use in a complex urban network. Diversion
curves reflect the travel resistance as measured by present day travel, but their use for future travel
when the pattern can undergo radical changes is doubtful.

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Urban transport planning , SRKIT 2023

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