Dynamic user equilibrium with a path based cell transmission model for general traffic networks

This paper develops a formulation for the network level dynamic traffic equilibrium model with departure time choice and route choice. The embedded network loading procedure follows the cell transmission model without the holding‐back issues by using detailed representations of flows at merges and diverges. The problem is modeled using a complementarity approach. The existence of the equilibrium solution is discussed using techniques from generalized variational inequalities. Computational results are performed using state of the art solvers. Since these solvers fail to solve any reasonable size networks, a specialized projection algorithm is developed to solve the problem. Numerical results are presented to demonstrate the performance of the algorithm in various starting with simple networks and extending to reasonable size networks with different traffic parameters. It is shown that the solution procedure produces good dynamic equilibrium solutions for general transportation networks.