A Robust Optimization Model of Delay Estimation and Signal Timing for Parallel Flow Intersection

A robust scenario-based optimization control method is proposed to address poor coordination of the main signal and the pre-signal caused by traffic fluctuations, and the issue of vehicle queue overflows in displaced left-turn lanes at parallel flow intersections. By analyzing the mechanism of traffic operation of parallel flow inter-sections, it is found that the operational stability is affected by the stochastic fluctuations in traffic demand, saturation flow rates, and traffic speeds. Thus, the coupling characteristics between time-varying traffic supply and the control of parallel flow intersection are established. Then, an objective function is defined as the mean and standard deviation of vehicle average delay, which utilizes weighting coefficients to intuitively reflect preferences of decision-makers for traffic efficiency and stability. Moreover, a robust optimization model for parallel flow intersections is developed by considering constraints such as the coordinated control of main pre-signals, functional allocation of lanes and clearance of lanes. A delay model is derived by integrating traffic rules for displaced left-turn vehicles from the diagram of vehicle arrivals and departures. The simulation results of the delay model show that the average absolute error of delay for left-turn and through vehicles does not exceed 3%, and the maximum error does not exceed 6%, which indicates a good fit. In the case study, the proposed optimization method results in a mere 2.24% increase in the average delay while it achieves a significant 21.23% reduction in the standard deviation of delay compared to the deterministic optimization. It shows that robust optimization enhances the operational stability of parallel flow intersections without sacrificing the throughput efficiency of intersections, which enables signal control more aligned with practical requirements. In the sensitivity analysis, the objective function exhibits an initial decreasing and then an increasing trend as the length of the displaced left-turn lane and design speed increase. It means the length of the displaced left-turn lane should align with the traffic demand during the design phase. However, the design speed should be slightly higher than the average speed obtained from field surveys when calculating the phase difference of through traffic for the main and pre-signals.