Dynamic Traffic Assignment: A Survey of Mathematical Models and Techniques

This paper presents a survey of the mathematical methods used for modeling and solutions for the traffic assignment problem. It covers the static (steady-state) traffic assignment techniques as well as dynamic traffic assignment in lumped parameter and distributed parameter settings. Moreover, it also surveys simulation-based solutions. The paper shows the models for static assignment, variational inequality method, projection dynamics for dynamic travel routing, discrete time and continuous time dynamic traffic assignment, and macroscopic dynamic traffic assignment (DTA). The paper then presents the macroscopic DTA in terms of the Wardrop principle and derives a partial differential equation for experienced travel time function that can be integrated with the macroscopic DTA framework.

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