This paper proposes an efficient two-stage network flow approach for finding the optimal integrated traffic routing and signal timing for evacuating real-sized urban networks with several threat zones, where the threat levels may be non-uniform among the zones. The objective is to minimize the total exposure to the threat (severity times the duration) for all evacuees during the evacuation. The traffic flow dynamics in the problem formulation are based on the well-known Point Queue (PQ) 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 based on insights into the optimal flow of traffic at intersections in the solution of the evacuation routing problem. In terms of efficiency, the computational time associated with the decomposition method for solving the integrated optimal routing and signal control problem is shown to be practically equal to the time required for solving the same optimal routing problem (without optimizing the intersection control plan), as the computation time for determining the optimal signal control is negligible. The proposed solution method is proven to be optimal. The method is implemented and applied to a real-sized evacuation scenario in the transportation network of Tucson, AZ. The method is stress-tested with some inflated demand scenarios and the computational aspects are reported.
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