This study considers an optimal coordinated traffic signal control under both deterministic and stochastic demands. We first present a new mixed integer linear programming (MILP) for the deterministic signal optimization wherein traffic flow is modeled based on the variational theory and the constraints on a signal control pattern are linearly formulated. The resulting MILP has a clear network structure and requires fewer binary variables and constraints as compared with those in the existing formulations. We then extend the problem so as to treat the stochastic fluctuations in traffic demand. We here develop an accurate and efficient approximation method of expected delays and a solution method for the stochastic version of the signal optimization by exploiting the network structure of the problem. Using a set of proposed methods, we finally examine the optimal control parameters for deterministic and stochastic coordinated signal controls and discuss their characteristics.
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