Continuous-time dynamic system optimum for single-destination traffic networks with queue spillbacks

•We study continuous-time dynamic system optimal (DSO) problems.•DSO is modeled as an optimal control problem with constant time delays.•Double queue model is integrated into DSO to capture possible queue spillbacks.•Free-flow DSO solutions are obtained by reformulating the original DSO objective.•Operational network capacity can estimate a lower bound of the network evacuation time.

Dynamic system optimum (DSO) is a special case of the general dynamic traffic assignment (DTA). It predicts the optimal traffic states of a network under time-dependent traffic conditions from the perspective of the entire system. An optimal control framework is proposed in this paper for the continuous-time DSO problem for single-destination traffic networks. Departure time choice is part of this DSO model. Double-queue model is applied to capture the impact of downstream congestion and possible queue spillbacks. Feasibility conditions and model properties are discussed. A constructive procedure to compute a free-flow DSO solution is also proposed. A discretization method is described to the continuous-time systems and numerical results on two test networks are shown.