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

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