Dynamic User Equilibrium Traffic Assignment Model Considered as a Discrete Optimal Control Problem

Abstract

Based on the inherent characteristic of link cost function, a dynamic traffic assignment model with simple and standard structure and satisfying the flow propagation constraint is formulated for general road network. Then, for many-to-one road network, using the optimal control theory approach, the necessary and sufficient conditions for optimal assignment solution are presented and the equivalence of the optimal assignment solution with Wardrop's first principle is demonstrated. To analyze the singularity of the solution, the concept of complete dissimilar links is defined and a conclusion is obtained that the optimal steady assignment solution is strictly nonsingular if all links are complete with each other. A simple and efficient algorithm for getting the optimal steady assignment solution is discussed and a numerical example is presented indicating that this class of model yields realistic results