Traffic Signal Timing Optimization By Modelling The Lost Time Effect In The Shock Wave Delay Model

Over the years, studies presented on shock wave model optimization have been limited to the proposal of optimization control policies using queue length constraints in oversaturated conditions, and also finding the optimum cycle time and green splits based on either a known cycle time from the field or an optimum cycle time obtained from other methods. To our best knowledge, we can say after reviewing the literature that no attempt has been made to use the shock wave model to find the optimum cycle time for a general isolated intersection, because minimizing this model generates very small values, close to zero for an optimum cycle time, which is unacceptable.In this paper, we propose an optimization model that provides the optimum cycle time and green splits when the total average delay at a general isolated signalized intersection is minimized for all vehicles present. To do so, we model the lost time effect in the shock wave delay model, which creates the most desirable optimum cycle time values. In our optimization process, the key strategy is to keep both approaches in the undersaturated condition. Therefore, our model works when the total amount of volume-to-capacity ratio of both approaches is less than 2.0; otherwise, where both approaches are oversaturated, other control policies should be considered and utilized. A comparison of the results with a widely-used formula in the literature reveals that our model is superior.