Modeling of Traffic Flow at Signalized Links

A rigorous mathematical modeling and analysis of the traffic dynamics downstream of traffic signals and in links between signalized intersections is presented in this paper. The approach taken here is macroscopic in nature and traffic is treated as a continuum fluid. The existence and behavior of shock waves generated periodically downstream of a traffic signal is demonstrated and analytical expressions are derived for describing their propagation along the road. The formation and dissipation of traffic queues at the downstream signal in both time and space is studied and analytical expressions are presented for describing the evolution of the tail end of the queue in time. Due to the large number of possible queue length developments, a methodology for numerical solution to the problem is presented along with numerical examples.