Continuous-Time Dynamic System Optimal for Single-Destination (DSO) Traffic Networks Considering Queue Spillbacks

Dynamic system optimal (DSO) is a special case of the general dynamic traffic assignment (DTA) and it predicts the optimal traffic states of a network under time-dependent traffic conditions from the perspective of the entire system. In this paper, an optimal control framework is proposed for the continuous-time DSO problem for single-destination traffic networks. Departure time choice is part of the DSO formulation to properly capture the waiting time of vehicles at the origins. The double-queue model is also applied to capture possible queue spillbacks. Solution existence conditions and model properties are discussed. A continuous-time holding-free condition for the DSO model is given. Reformulation schemes of the objective function to achieve desired DSO solutions such as the free-flow and holding-free solutions are proposed. Discretization method is applied and numerical results on a small testing network are shown.