Traffic Signal Optimization: Combining Static and Dynamic Models

In this paper, we present a cyclically time-expanded network model for simultaneous optimization of traffic assignment and traffic signal parameters, in particular, offsets, split times, and phase orders. Since travel times are of great importance for developing realistic solutions for traffic assignment and traffic signal coordination in urban road networks, we perform an extensive analysis of the model. We give an example showing that a linear time-expanded model can reproduce realistic nonconvex travel times especially for use with traffic signals and we verify this by simulation. Furthermore, we show how exact mathematical programming techniques-namely, mixed-integer linear programming-can be used for optimizing the control of traffic signals. We provide computational results for real-world instances and demonstrate the capabilities of the cyclically time-expanded model by simulation results obtained with state-of-the-art traffic simulation tools.