A feedback queueing network model for traffic signal control at intersections considering congestion propagation in dynamic stochastic environments

Capturing congestion propagation among different facilities at intersections in dynamic stochastic traffic environments poses significant challenges, particularly under oversaturated conditions. In this paper, we present an Mt/ G(x)/C/C feedback fluid queueing network model to address CPDSE, integrating random traffic demand, time-varying transition probabilities, and state-dependent stochastic service capabilities. A recursive algorithm is developed to analyze the feedback queueing network model. Simulation experiments reveal that the proposed model and algorithm perform effectively, irrespective of variations in traffic intensity. Compared to the mean results of 200 simulations, the average absolute error is 0.5152 vehicles, and the average relative error is 6.43% across three demand scenarios. Based on the proposed feedback queueing network model, two optimization frameworks are established for traffic signal control, aimed at minimizing either the average vehicle delay time or total costs, including fuel consumption. We propose a rolling optimization strategy that incorporates the mesh adaptive direct search algorithm to achieve real-time traffic signal control. Numerical experiments using actual survey data from Kunshan City yield several noteworthy findings: (1) An optimal moderate-sized time step exists for rolling optimization to minimize either the average delay time or total costs; specifically, an excessively small time step may increase vehicle average delay time or total costs; (2) The percentage of delay reduction achieved by our method, compared to Synchro software, reaches a maximum of approximately 70% when traffic demand is moderate and the initial state is low; and (3) The percentage reduction in average delay or total costs compared to Synchro initially increases and then decreases with rising traffic intensity.