TRAFFIC ASSIGNMENT METHODS

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• TRAFFIC ASSIGNMENT METHODS
• CE 673
• Syed Masiur Rahman
• Instructor Dr. Nedal Ratrout

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OUTLINE

• Objectives of Traffic Assignment (TA)
• Analysis of Basic TA Methods
• ALL OR NOTHING
• STOCHASTIC
• CONGESTED CONDITION
• USER EQUILIBRIUM
• STOCHASTIC USER EQUILIBRIUM
• Available Software

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Objectives of Traffic Assignment

• Primary
• To obtain good aggregate network measures
• To estimate zone-to-zone travel costs for a given
  level of demand
• To obtain reasonable link flows and to identify
  heavily congested links

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Objectives of Traffic Assignment (contd)

• Secondary
• To estimate the routes used between each O-D pair
• To analyze which O-D pairs use a particular link
  or route
• To obtain turning movements for the design of
  future junctions

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Analysis of Basic TA Methods

• All-or-Nothing
• The simplest route choice and assignment method
• Underlying Assumptions
• there are no congestion effects,
• all drivers consider the same attributes for
  route choice, and
• they perceive and weigh them in the same way

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Analysis of Basic TA Methods

• All-or-Nothing
• Basic Procedures
• The determination of minimum path time
• The assignment of all traffic flows by the
  appropriate minimum path, and
• the aggregation of total flows on each link in
  the defined network.

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An Example of All-Or-Nothing

• Assume x1, x2 0, t110, t2 15
• So, x112, x2 0
• Source (Mathew, 2006)

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Analysis of Basic TA Methods (contd)

• All-or-Nothing (contd)
• Advantages
• The all-or-nothing is the simplest route method
• Fast
• This method is appropriate for sparse and
  non-congested networks where there are few
  alternative routes and they are very different in
  cost.
• This is the basic building block for other types
  of assignment techniques

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Analysis of Basic TA Methods (contd)

• All-or-Nothing (contd)
• Disadvantages
• This method can not take care of congestion
  effects.
• Small difference in journey times can cause
  unrealistic journey paths when this technique is
  used.
• It generally shows problems of instability and
  lack of realism.
• It doesnt replicate base-year volume very
  accurately.
• This method does not consider subjective
  judgments rather assume that all drivers consider
  the same attributes for route choice and weigh
  them same way.

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Analysis of Basic TA Methods (contd)

• Stochastic Method
• Simulation-based Method
• uses ideas from stochastic simulation to
  introduce variability in perceived costs.
• The proportion-based method
• allocates flows to alternative routes from
  proportions calculated using logit-like
  expressions

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Analysis of Basic TA Methods (contd)

• Stochastic Method
• Emphasize on the variability in drivers
  perception of costs.
• Based on choice probability for each route from
  an origin to destination.
• Link travel time independent on link volume.
• Calculate the shortest route in terms of
  impedance and alternative routes with higher
  impedance.
• The demand is distributed across the alternatives
  (similarity of routes is considered during
  distribution).

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Analysis of Basic TA Methods (contd)

• Stochastic Method
• Advantages
• The stochastic simulation approach often produces
  a reasonable spread of trips.
• These methods are easy to program and
• do not require the choice or estimation of speed
  flow relationships.

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Analysis of Basic TA Methods (contd)

• Stochastic Method (contd)
• Disadvantages
• In stochastic simulation approach the final
  results are dependent on the series of random
  numbers used in the simulation.
• The link perceived costs are not independent, as
  drivers usually have preferences,
• The assumption of independence in perceived costs
  may lead to unrealistic switching between
  parallel routs connected by minor roads.
• No explicit allowance is made for congestion.

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Analysis of Basic TA Methods (contd)

• Wardrops Equilibrium
• These models usually attempt to approximate to
  the equilibrium conditions which is defined as
• 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
• Under equilibrium conditions traffic arranges
  itself in congested networks such that all used
  routes between O-D pair have equal and minimum
  costs while all unused routes have greater or
  equal costs.

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Analysis of Basic TA Methods (contd)

• Incremental Assignment
• Select an initial set of current link costs,
  usually free-flow travel times
• Total trip matrix T is divided into a number of
  fractional matrices
• The fractional matrices are then loaded,
  incrementally
• Calculate a new set of current link costs based
  on the last accumulated flows
• This process will continue unless all fractions
  of T have been assigned

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Analysis of Basic TA Methods (contd)

• Incremental Assignment (contd)
• Advantages
• It is very easy to program.
• Its results may be interpreted as the build-up of
  congestion for the peak period.
• Realistic approach

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Analysis of Basic TA Methods (contd)

• Incremental Assignment (contd)
• Disadvantages
• This algorithm does not necessarily converge to
  Wardrops equilibrium solution
• The calculation is ended after the specified
  number of steps has been executed without
  checking correspondence between the resulting
  traffic volume and link impedances.

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Analysis of Basic TA Methods (contd)

• User Equilibrium Assignment
• The user equilibrium procedure distributes demand
  according to Wardrop's first principle.
• The state of equilibrium is reached by
  incremental method as a starting solution.

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An Example of User Equilibrium

• Substituting x112-x2
• x15.8, x2 6.2
• Source (Mathew, 2006)

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An Example of System Optimization

• Substituting x112-x2
• Solution x15.3, x26.7

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Analysis of Basic TA Methods (contd)

• User Equilibrium Assignment
• Advantages
• Faster than MSA to reach convergence to the
  equilibrium.
• The procedure only terminates when all routes of
  any O-D relation are in the equilibrium state.
• The procedure provides more realistic results
  than the incremental procedure.
• Good for very congested networks.

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Analysis of Basic TA Methods (contd)

• User Equilibrium Assignment
• Disadvantages
• Long, iterative process
• For lower traffic volumes a similar result is
  achieved as with all-or-nothing assignment,
  because the route search does not find new
  routes.

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Analysis of Basic TA Methods (contd)

• Stochastic User Equilibrium (SUE)
• Addresses the effects of perceived route cost and
  capacity restraint effects.
• SUE tries to seek an equilibrium condition where
  
• Each user chooses the route with the minimum
  'perceived' travel cost in other words, under
  SUE no user has a route with lower 'perceived'
  costs and therefore all stay with their current
  routes

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Analysis of Basic TA Methods (contd)

• SUE (contd)
• Evaluation of the procedure
• More realistic behavior.
• The speed of convergence depends on the level of
  network congestion and on the dispersion
  parameter.
• Good in low to medium congested assignment
  problems.

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Available Traffic Assignment Softwares

• CONTRAM
• CONTRAM provides the dynamic traffic modeling
  features that are needed for
• Highly congested networks with time varying
  traffic flows
• Fuel consumption and emissions statistics
• Modeling incidents
• Key modeling features include
• Huge number of time slices
• Up to 32 user definable vehicle classes
• Advanced junction modeling
• Left or right hand drive
• Dynamic matrix estimation

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TRANSCAD

• Basic Traffic Assignment Methods available in
  TransCAD include    All-Or-Nothing Assignment
  (AON)    STOCH Assignment    Incremental
  Assignment    Capacity Restraint    User
  Equilibrium (UE)    Stochastic User Equilibrium
  (SUE)     System Optimum Assignment (SO)
• TransCAD also provides many advanced traffic
  assignment procedures

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Dynameq

• Dynameq is a new breed of equilibrium dynamic
  traffic assignment (DTA) for use on large,
  congested networks.
• It perform equilibrium dynamic traffic assignment
  on large networks.
• Dynamic traffic simulator provides realistic
  vehicle interactions.
• In fact, it combines the classical static model
  and micro-simulation.

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AIMSUN Planner

• This Component consists of an ad hoc version of a
  Static User Equilibrium model, the corresponding
  Frank-Wolfe algorithm for transport planning
  analysis, and all the associated visualisation
  functions.
• The static user equilibrium traffic assignment is
  based on Wardrop's principle.

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SATURN

• It is a combined simulation and assignment model,
  
• it can function both as a conventional traffic
  assignment model and as a pure junction
  simulation model.
• SATURN provides a wide range of assignment
  options such as generalized cost, all-or-nothing,
  Wardrop equilibrium, Burrell multiple-route
  assignment (SUE)

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Conclusions

• All-or-nothing can not take care of congestion
  effects
• The all-or-nothing is the simplest and fast
  route choice and assignment method
• This method is appropriate for sparse and
  non-congested networks
• The Stochastic Simulation approach often produces
  a reasonable spread of trips.
• UE provides more realistic results than the
  incremental assignment.

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Conclusions

• Incremental Assignment does not necessarily
  converge to Wardrops equilibrium solution.
• In Stochastic approach, no explicit allowance is
  made for congestion
• For very congested networks UE provides a good
  approximation to SUE and is faster in
  convergence.
• The use of SUE would only be advantageous in low
  to medium congested assignment problems.

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• THANK YOU