Sensitivity analysis of signal control with physical queuing: Delay derivatives and an application

This paper develops a novel sensitivity analysis of signal control with physical queues. We derive a set of travel delay derivatives with respect to the signal control elements. The contribution of these derivatives is that they explicitly take the effects of physical queuing into account, including queue spillback and blockage. We further develop an implementation of the derivatives through the cell transmission model. These derivatives determine the approximate descent directions of the control elements without resorting to repeated simulations of the whole traffic network, thus saving the computation effort tremendously. As an example of their applications, we develop a derivative-based heuristic algorithm for dynamic traffic control. We use an actual road network in Hong Kong to investigate the performances of the derivatives and the heuristic algorithm. The numerical results are encouraging, showing that the derivatives can identify good initial descent directions, which otherwise are difficult or inefficient to obtain. In addition to dynamic signal control, these delay derivatives can be applied for other transportation problems including dynamic traffic assignment and dynamic transport network design.