Analytical derivation of the optimal traffic signal timing: Minimizing delay variability and spillback probability for undersaturated intersections

Individual vehicles experience a large variability of delay at signalized intersections in urban networks. Existing traffic signal optimization frameworks often overlook the implications of delay variability and spillback for design and analysis of signal timing plans. This paper presents an analytical solution based on the shockwave theory to estimate delay variability at an undersaturated intersection. We also propose a new optimal signal timing formulation that minimizes the delay variability and probability of spillback in addition to total delay. Several algorithms are proposed to attain the global optimal signal timing for prefixed (given) and dynamic (optimal) cycle length control strategies. Illustrative microsimulation and numerical studies demonstrate the effectiveness of the proposed formulated models and signal optimization algorithms.