Open Access
September, 1960 Queues for a Fixed-Cycle Traffic Light
G. F. Newell
Ann. Math. Statist. 31(3): 589-597 (September, 1960). DOI: 10.1214/aoms/1177705787


In their book Studies in the Economics of Transportation, Beckmann, McGuire and Winsten (BMW) ([2], pp. 11-13, 40-42) proposed a simple queuing model for traffic flow through a fixed-cycle traffic light. Although they derived a relation between the average delay per car and the average length of the queue at the beginning of a red phase of the light, they only indicated some possible numerical schemes for evaluating the latter. Here we shall derive analytic expressions for the average queue length and consequently also the average delay under equilibrium conditions for the BMW model.


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G. F. Newell. "Queues for a Fixed-Cycle Traffic Light." Ann. Math. Statist. 31 (3) 589 - 597, September, 1960.


Published: September, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0094.12902
MathSciNet: MR121243
Digital Object Identifier: 10.1214/aoms/1177705787

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 3 • September, 1960
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