# 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."

## Dynamic Traffic Assignment¶

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:

- Dynamic Traffic Assignment Algorithms
- 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.