Network Flow Solution Method for Optimal Evacuation Traffic Routing and Signal Control with Nonuniform Threat

An efficient two-stage network flow approach is proposed for the determination of optimal scenarios for integrated traffic routing and signal timing in the evacuation of real-sized urban networks with several threat zones, where the threat levels may be nonuniform across zones. The objective is to minimize total exposure to the threat (severity multiplied by duration) for all evacuees during the evacuation. In the problem formulation, traffic flow dynamics are based on the well-known point queue model in a time-expanded network representation. The proposed solution approach is adapted from a general relaxation-based decomposition method in a network flow formulation. The decomposition method is developed on the basis of insights into the optimal flow of traffic at intersections in the solution of the evacuation routing problem. As for efficiency, the computation time associated with the decomposition method for solving the integrated optimal routing and signal control problem is equivalent to the time required for solving the same optimal routing problem (without optimizing the intersection control plan) because the computation time required for determining the optimal signal control is negligible. The proposed solution method proves to be optimal. The method is implemented and applied to a real-sized evacuation scenario in the transportation network of Tucson, Arizona. The method is stress-tested with some inflated demand scenarios, and computation aspects are reported.