Traffic Signal Coordination Under Stochastic Demands and Turning Ratios Considering Spatial-Temporal Dependencies

Stochastic traffic demands and turning ratios are critical factors in coordinated signal control. However, existing studies ignore the spatial-temporal dependencies of traffic flows between adjacent intersections and signal cycles. Turning ratios are usually assumed to be deterministic. This study develops a two-stage stochastic programming model for two-way coordinated adaptive signal control under stochastic traffic demands and turning ratios. A hierarchical multi-objective function is developed for overflow management and operational efficiency under both over- and under-saturated traffic. The primary and secondary objective functions minimize residual queue lengths and average vehicle delays, respectively, which are formulated considering spatial-temporal dependencies for the coordinated traffic flow. In stage one, a base coordinated signal timing plan is optimized to maximize the expected performance under stochastic scenarios. In stage two, adaptive cycle lengths and green times are determined by setting the tolerance factor for the base green times to maintain the stable traffic flow. The concept of Phase Clearance Reliability (PCR) is extended to decouple the interaction between the two stages. The deterministic equivalent problem of the proposed model in one signal cycle is modified to optimize the base signal timing plan for serving the stochastic exogenous and endogenous traffic demands up to certain PCR values. A PCR-based gradient algorithm is designed for solutions. The experimental results demonstrate that the proposed model can significantly improve traffic operation compared to six benchmarks.