Discretization modeling, integer programming formulations and dynamic programming algorithms for robust traffic signal timing

Traffic volumes are naturally variable and fluctuate from day to day. Robust optimization approaches have been utilized to address the uncertainty in traffic signal timing optimization. However, due to complicated nonlinear programming models, obtaining a global optimal solution is difficult. Instead of working with nonlinear programming models, we propose a discretization modeling approach, where the cycle, green time, and traffic volume are divided into a finite number of discrete values. The robust signal timing problem is formulated as a binary integer program. Two dynamic programming algorithms are then developed. We obtain optimal solutions for all of the instances with respect to the inputs generated from the discretization.

Research highlights
► Developed a discretization approach, where the cycle, green time, and traffic volume were divided into a finite number of discrete values.
► Formulated the robust signal timing problem as a binary integer program.
► Designed a dynamic programming algorithm with bi-directional search enhancements.
► Obtained optimal solutions for all of the instances with respect to the inputs generated from the discretization.