Queues with Server Vacations as a Model for Pretimed Signalized Urban Traffic

A queuing system resulting from a signalized intersection regulated by pretimed control in a network of urban traffic is considered. Modeling the queue length and the delay of vehicles is crucial to evaluate the performance of intersections equipped with traffic signals. Air quality and rational use of energy also depend on an efficient management of the intersections. These traffic systems have the specificity that the server (green signal) is deactivated (red signal) during a fixed period of time. In the present work, an M/D/1 queue with a server that occasionally takes vacations is analyzed. The mean delays of vehicles and the mean queue length are computed and compared with those obtained by using a detailed simulation model in a case study. We find that, in general, the mean delays of vehicles given by the proposed queuing model provide a good approximation, but the model can provide slightly smaller values than those obtained in the simulation model for large traffic flows. This result is of interest for traffic engineers, as the approaches one can find in the literature for large signalized urban traffic flows are subject to criticism.