Queues for a Vehicle-Actuated Traffic Light

Abstract

A vehicle-actuated traffic light controls two intersecting traffic streams keeping the light green for lane i , i = 1 or 2 until any existing queue has been discharged and a headway of duration at least β ı , is detected in the subsequent arrivals. The object of this paper is to investigate how one should choose the β i so as to minimize the average delay per vehicle at the intersection. A model is considered in which the arrival headways are exponentially distributed random variables, departure headways have any specified distribution, and there is a random lost time for each switch of the traffic light. Formulas are derived for the moments of the cycle times, the average wait per vehicle, and the optimal β i .