Queues for a Vehicle-Actuated Traffic Light

J. N. Darroch, G. F. Newell and R. W. J. Morris
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J. N. Darroch: Mathematics Department, University of Adelaide, South Australia
G. F. Newell: Mathematics Department, University of Adelaide, South Australia
R. W. J. Morris: Traffic Engineering Branch, South Australia Highways and Local Government Department

Operations Research, 1964, vol. 12, issue 6, 882-895

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 .

Date: 1964
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