Traffic assignment

BY:
NIKHIL MATHUR
TRAFFIC
ASSIGNMENT

Traffic assignment models are used to estimate the traffic flows on a network.
These models take as input a matrix of flows that indicate the volume of traffic
between origin and destination (O-D) pairs.They also take input on the network
topology, link characteristics, and link performance functions.The flows for each
O-D pair are loaded onto the network based on the travel time or impedance of
the alternative paths that could carry this traffic.
Traffic assignment is a key element in the urban travel demand forecasting
process.The traffic assignment model predicts the network flows that are
associated with future planning scenarios, and generates estimates of the link
travel times and related attributes that are the basis for benefits estimation and
air quality impacts.The traffic assignment model is also used to generate the
estimates of network performance that are used in the mode choice and trip
distribution or destination choice stages of many models.
WHAT IS TRAFFIC ASSIGNMENT?

Aims ofTraffic Assignment procedures
1. To estimate the volume of traffic on the links of the network and
possibly the turning movements at intersections.
2. To furnish estimates of travel costs between trip origins and
destinations for use in trip distribution.
3. To obtain aggregate network measures, e.g. total vehicular flows,
total distance covered by the vehicle, total system travel time.
4. To estimate zone-to-zone travel costs(times) for a given level of
demand.
5. To obtain reasonable link flows and to identify heavily congested
links.
6. To estimate the routes used between each origin to destination(O-
D) pair.
7. To analyse which O-D pairs that uses a particular link or path.
8. To obtain turning movements for the design of future junctions.

1. All-or-nothing assignment
• In this method the trips from any origin zone to any destination zone are loaded
onto a single, minimum cost, path between them. This model is unrealistic as
only one path between every O-D pair is utilised even if there is another path with
the same or nearly same travel cost.
• Also, traffic on links is assigned without consideration of whether or not there is
adequate capacity or heavy congestion; travel time is 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.
•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.

Example :
To demonstrate how this assignment works, an example network is considered.
This network has two nodes having two paths as links. Let us suppose a case
where travel time is not a function of flow as shown in other words it is constant
as shown in the figure below.
Solution
The travel time functions for both the links is given by: t1 = 10 t2 = 15
and total flows from 1 to 2 is given by. q12 = 12
Since the shortest path is Link 1 all flows are assigned to it making
x1 =12 and x2 = 0.

2. 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:
fk(ck − u) = 0 : ∀k < 10.1>
ck − u >= 0 : ∀k < 10.2>
where fk 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 fk ≥ 0.This means that all used paths will have same
travel time.
2. If ck − u ≥ 0, then from equation 10.1 fk = 0.
This means that all unused paths will have travel time greater than the minimum cost
path. where fk is the flow on path k, ck is the travel cost on path k, and u is the
minimum cost. Assumptions in User EquilibriumAssignment
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 optimization program,

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 satisfies these equations no
motorist can better off 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.

3. System Optimum Assignment (SO)
The system optimum assignment is based on Wardrop’s second principle, which states
that drivers cooperate with one another in order to minimize total system travel time.This
assignment can be thought of as a model in which congestion is minimized when drivers
are told which routes to use. Obviously, this is not a behaviorally realistic model, but it can
be useful to transport planners and engineers, trying to manage the traffic to minimize
travel costs and therefore achieve an optimum social equilibrium.

Differentiate the above equation to zero, and solving for x1 and then x2 leads
to the solution
x1 = 5.3, x2= 6.7 which gives
Z(x) = 327.55

Other assignment methods
1. Incremental assignment :
Incremental assignment is a process in which fractions of traffic volumes are assigned in
steps.In each step, a fixed proportion of total demand is assigned, based on all-or-
nothing assignment.After each step, link travel times are recalculated based on link
volumes.When there are many increments used, the flows may resemble an equilibrium
assignment ; however, this method does not yield an equilibrium solution.
Consequently, there will be inconsistencies between link volumes and travel times that
can lead to errors in evaluation measures. Also, incremental assignment is influenced by
the order in which volumes for O-D pairs are assigned, raising the possibility of
additional bias in results.
2. Capacity restraint assignment :
Capacity restraint assignment attempts to approximate an equilibrium solution by
iterating between all-ornothing traffic loadings and recalculating link travel times based
on a congestion function that reflects link capacity. Unfortunately, this method does not
converge and can flip-flop back and forth in loadings on some links.

TransCAD SOFTWARE provides the widest array of traffic assignment
procedures that can be used for modeling urban traffic.These procedures
include numerous variants that can be used for modeling intercity passenger
and freight traffic.
TransCAD is the first and onlyGeographic Information System (GIS) designed
specifically for use by transportation professionals to store, display, manage,
and analyze transportation data.TransCAD combines GIS and transportation
modeling capabilities in a single integrated platform, providing capabilities
that are unmatched by any other package.TransCAD can be used for all modes
of transportation, at any scale or level of detail.TransCAD provides:
1. A powerful GIS engine with special extensions for transportation
2. Mapping, visualization, and analysis tools designed for transportation
applications
3. Application modules for routing, travel demand forecasting, public transit,
logistics, site location, and territory management.
Traffic assignment Software :
TransCAD

A Powerful GIS forTransportation
• TransCAD is a state-of-the-art GIS that you can use to create and customize maps,
build and maintain geographic data sets, and perform many different types of spatial
analysis.
• TransCAD is the only software package that fully integrates GIS with demand modeling
and logistics functionality.This makes it possible for models to be much more accurate
and efficient.
• InTransCAD, different modeling equations can easily be derived and applied for
different geographic subareas. Similarly,TransCAD brings new and much-needed
capabilities for measuring geographic accessibility.The GIS approach also provides a
graphical solution that is easily understood.
• TransCAD extends the traditional GIS data model to include transportation data
objects such as transportation networks, matrices, routes systems, and linear-referenced
data.These extensions makeTransCAD the best data management and analysis tool for
working with transportation data.You can use the GIS functions to prepare, visualize,
analyze, and present your work, and use the application modules to solve transportation
problems with greater ease and efficiency than with any other product. Networks and
matrices can be of virtually unlimited size.

Networks:
Transportation networks are specialized data structures
that govern flow over a network. Networks are stored in a
highly-efficient way, enablingTransCAD to solve routing
problems very quickly. Networks can include detailed
characteristics such as:
1. Turn delays or restrictions
2. Overpasses, underpasses, and one-way links
3. Intersection and junction attributes
4. Intermodal or interline terminals, transfer points, and
delay functions
5. Zonal centroid connectors
6. Link classifications and performance functions
7. Transit access, egress, and walk transfer links

Matrices:
Matrices hold data such as distance, travel times, and origin-
destination flows that are essential for many transportation
applications.TransCAD provides functions for creating and
manipulating matrices, and tools for spatial analysis and advanced
visualization of matrix data.This combination lets you see and
understand transportation flows and network characteristics in
new and different ways
Routes & Route Systems:
Routes indicate paths taken by trucks, rail, cars, buses, or individuals
traveling from place to place.TransCAD includes tools to create,
display, edit, and manipulate routes, and unique display technology
for mapping routes in a clear and compelling fashion.You can
organize a set of related routes into a single route system layer, and
include route attributes, stop locations, and vehicle schedules.

Linear Referencing:
TransCAD allows you to identify the location of transportation
features as a distance from a fixed point along a route.TransCAD
can display and analyze these data sets without conversion, and
includes dynamic segmentation functions to merge and analyze
multiple linear-referenced data sets.This makesTransCAD a
natural choice for:
1. Facility infrastructure and operations data
2. Accident locations
3. Pavement or rail condition ratings
4. Traffic flows and transit ridership data
5. Facility alignments
6. Capital project data

Traffic assignment

More Related Content

What's hot (20)

Similar to Traffic assignment (20)

Recently uploaded (20)

Traffic assignment