Some Results for Fixed-Time Traffic Signals

Abstract

Summary An investigation is made of the queues and delays which occur when a Poisson traffic stream is subjected to a blockage. It has been assumed that the traffic is free-flowing when the blockage commences, that when the blockage is terminated delayed vehicles depart with constant time separations, and that no queueing occurs after the system has emptied for the first time. A blockage of duration ρ causes j vehicles to be delayed a total time w. Expressions are obtained for the Laplace transform of the joint distribution of j and w, the marginal distribution of j and the Laplace transform of the marginal distribution of w. The expected delay at a fixed-time traffic signal is then obtained for the case where there is a negligible probability that vehicles are still queueing at the end of the green phase.