Dynamic user optimal traffic assignment model for many to one travel demand

A freeway or expressway corridor where all vehicles travel to the same destination such as the city centre is considered in this article, similar to the morning commute problem. A continuous time optimal control model that deals with the dynamic user optimal assignment for multiple origins and single destination is proposed. The splitting rates of traffic flows at each network node are defined as the control variables in this model. The optimality conditions are proved to be equivalent to the dynamic user optimal principle or user equilibrium of instantaneous travel cost. In order not to solve the complicated two-point boundary-value problem with substantial computational times for obtaining the optimal control solution, a steady state-costate solution algorithm is developed that generates an approximate solution to the network optimal control problem. This algorithm exploits advantage of the embedded network structure of the problem and would be computationally efficient. A numerical example with two peak period traffic demands which was drawn from the road network problem between Hong Kong and several adjacent cities of inland China is used to demonstrate the performance of the proposed algorithm.