what is dynamic traffic assignment problem

Dynamic Traffic Assignment

Early Experiences

Current Practices

Research Needs

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Network Assignment

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(opens new window) is a hot topic in travel forecasting.

# Background

Traditional user equilibrium highway assignment models predict the effects of congestion and the routing changes of traffic as a result of that congestion. They neglect, however, many of the details of real-world traffic operations, such as queuing, shock waves, and signalization. Currently, it is common practice to feed the results of user equilibrium traffic assignments into dynamic network models as a mechanism for evaluating these policies. The simulation models themselves, however, do not predict the routing of traffic, and therefore are unable to account for re-routing owing to changes in congestion levels or policy, and can be inconsistent with the routes determined by the assignment. Dynamic network models overcome this dichotomy by combining a time-dependent shortest path algorithm with some type of simulation (often meso or macroscopic) of link travel times and delay. In doing so it allows added reality and consistency in the assignment step, as well as the ability to evaluate policies designed to improve traffic operations. These are some of the main benefits of dynamic network models .

DTA models can generally be classified by how they model link or intersection delay. Analytical DTA models treat it in the same manner as static equilibrium assignment models, with no explicit representation of signals. Link capacity functions, often similar or identical to those used in static assignment, are used to calculate link travel times. Analytical models have been widely used in research and for real-time control system applications. Simulation-based DTA models include explicit representation of traffic control devices. Such models require detailed signal parameters to include phasing, cycle length, and offsets for each signal in the network. Delay is calculated for each approach, with vehicles moving from one link to the next only if available downstream capacity is available. The underlying traffic model is often different, but at the network level such models behave in a similar fashion.

Demand is specified in the form of origin–destination matrices for short time intervals, typically 15 minutes each. Trips are typically randomly loaded onto the network during each time interval. As with traffic microsimulation models, adequate downstream capacity must be present to load the trips onto the network. The shortest paths through time and space are found for each origin–destination pair, and flows loaded to these paths. A generalized flowchart of the process is shown below.

As with static assignment models, the process shown above is iteratively solved until a stable solution is reached. The memory and computing requirements of DTA, however, are orders of magnitude larger than for static assignment, reducing the number of iterations and paths that can be kept in memory. Instead of a single time period, as with static assignment, DTA models must store data for each time interval as well. A three-hour static assignment would involve only one time interval. A DTA model of the same period, however, might require 12 intervals, each 15 minutes in duration. These are all in addition to the memory requirements imposed by the number of user classes and zones.

# Early Experiences

Research into DTA dates back several decades, but was largely limited to academics working on its formulation and theoretical aspects. DTA overcomes the limitations of static assignment models, although at the cost of increased data requirements and computational burden. Moreover, software platforms capable of solving the DTA problem for large urban systems and experience in their use are recent developments.

(opens new window) has been successfully applied to a large subarea of Calgary and to analyses of the Rue Notre-Dame in Montreal. Although user group presentations of both applications have been made, and reported very encouraging results, the work is currently unpublished and inaccessible except through contact with the developers.

(opens new window) . The network from the Atlanta Regional Commission (ARC) regional travel model formed the starting point for the DTA network. Intersections were coded, centroid connectors were re-defined, and network coding errors were corrected. A signal synthesizer derived locally optimal timing parameters for more than 2,200 signalized intersections in the network. Trip matrices from the ARC model were divided into 15-minute intervals for the specification of demand. Approximately 40 runs of the model were required to diagnose coding and software errors. Unfortunately, the execution time for the model was approximately one week per run. The resulting model eventually validated well to observed conditions; however, the length of time required to render it operational and the run time required prevented it from being used in studies as originally intended. Subsequent work by the developer has resulted in substantial reductions in run time, but this remains a significant issue that must be overcome before such models can be more widely used.

# Current Practices

# research needs.

A number of cities are currently testing DTA models, but are not far enough along in their work to share even preliminary results. At least a dozen such cases are known to be in varying stages of planning or execution, suggesting that the use of DTA models in planning applications is about to expand dramatically. However, in addition to the issue of long run times, a number of other issues must be addressed before such models are likely to be widely adopted:

• Criteria for the validation of such models have not been widely accepted. The paucity of traffic counts in most urban areas, and especially at 15, 30, or 60 minute intervals, is a significant barrier to definitive assessment of these models.

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• Theoretical Background
• System Requirements and Licensing

Dynamic Traffic Assignment ¶

Traffic assignment is the process that determines how the traffic demand – usually defined in terms of an origin-destination matrix – is loaded onto the network to determine the traffic flows on the network links. The underlying hypothesis is that as vehicles travel from their origin to their destination in the network they try to minimize their individual travel times. That is, drivers chose the routes they perceive as being the shortest under the prevailing traffic conditions.

This modeling hypothesis, based on the concept of user equilibrium, is expressed by J.G. Wardrop’s first principle: "the journey times on all routes actually used are equal and are not greater than those which would be experienced by a single vehicle on any unused route."

The advent of intelligent transport systems (ITS), advanced traffic management systems (ATMS), and advanced traffic information systems (ATIS) has prompted the need for models which account for how flow changes over time, that is dynamic models that can appropriately describe the time dependencies of traffic demand and the corresponding induced traffic flows.

The "dynamic traffic assignment problem" (DTA) can therefore be considered an extension of the traffic assignment problem described by Wardrop and solutions must be able to determine how time-varying link or path flows evolve in time and space in the network ( Mahmassani 2001 ).

The approaches proposed to solve the DTA problem fall into two classes: mathematical formulations looking for analytical solutions, and simulation models looking for approximate heuristic solutions.

General simulation-based approaches ( Tong and Wong 2000, Lo and Szeto 2002, Varia and Dingra 2004, Liu et al. 2005 ) explicitly or implicitly split the process into two components: a route choice mechanism determining how the time-dependent path flow rates are assigned to available paths at each time step; and a method to determine how these flows propagate in the network. A systematic approach based on these two components was proposed by Florian et al. 2001 and 2002 .

Simulation models, especially at the level of microsimulation, tend to focus on the description of the dynamics of traffic flows, while traffic assignment processes are not always modeled in accordance with the corresponding dynamic version of Wardrop's first principle Friesz et al. 1993 , Smith 1993, Ran and Boyce 1996 .

Consequently these simulation models cannot guarantee full network optimization. In these cases the route choice algorithms try to optimize route decisions based on currently available information, using either discrete choice theory or other probabilistic approaches ( Mahmassani 2001 ). These approaches can be considered to be dynamic traffic assignment procedures but do not qualify as a dynamic user equilibrium (DUE) model because they omit the traveler's process of longitudinal learning through repeated journeys.

Aimsun Next therefore utilizes a sophisticated set of route choice algorithms which include: static assignment based on Wardrop's equilibrium; dynamic assignment based on network conditions; and information supplied through ITS, to achieve a DUE where drivers react to their experience of the road network.

See also the following topics that relate to traffic assignment:

• Road Network Representation : How the route choice network is represented
• Link Cost Functions : How the perceived cost of traversing a road section is derived
• Route Paths : How route paths are found
• Path Selection : How vehicles choose their paths through the network, including the effect of information from ITS systems to cause vehicles to update path choice en route.
• Dynamic User Equilibrium : Builds on the traffic assignment work above and assigns traffic to the road network using driver knowledge derived from previous iterations.