Connected Vehicles Based Traffic Signal Timing Optimization

We study the traffic signal control problem with connected vehicles by assuming a fixed cycle length so that the proposed model can be extended readily for the coordination of multiple signals. The problem can be first formulated as a mixed-integer nonlinear program, by considering the information of individual vehicle's trajectories (i.e., second-by-second vehicle locations and speeds) and their realistic driving/car-following behaviors. The objective function is to minimize the weighted sum of total fuel consumption and travel time. Due to the large dimension of the problem and the complexity of the nonlinear car-following model, solving the nonlinear program directly is challenging. We then reformulate the problem as a dynamic programming model by dividing the timing decisions into stages (one stage for a signal phase) and approximating the fuel consumption and travel time of a stage as functions of the state and decision variables of the stage. We also propose a two-step method to make sure that the obtained optimal solution can lead to the fixed cycle length. Numerical experiments are provided to test the performance of the proposed model using data generated by traffic simulation.