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A solution to the fixed-cycle traffic light problem for compound Poisson arrivals

Published online by Cambridge University Press:  14 July 2016

Donald R. McNeil
Donald R. McNeil*
Affiliation:
The Johns Hopkins University, Baltimore, Md.
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Extract

A basic problem in the mathematical theory of traffic flow is to obtain the expected delay to a vehicle at a fixed-cycle traffic light controlling an intersection. The factors affecting this expected delay are the cycle time, the fraction of time the traffic light is effectively red, the number of vehicles which can pass through when the signal is green, and the nature of the (random) arrival process for the vehicles. Once a solution is known, it is possible to fix the cycle time and the effective red period in such a way that the expected delay is minimized.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 3 , December 1968 , pp. 624 - 635
Copyright
Copyright © Applied Probability Trust 1968 

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References

Boudreau, P. E., Griffin, J. S. and Kac, M. (1962) An elementary queueing problem. Amer. Math. Monthly 69, 713–24.CrossRefGoogle Scholar
Crommelin, C. D. (1932) Delay probability formulae when the holding times are constant. Post Office Elect. Eng. 25, 41–50.Google Scholar
Miller, A. J. (1963) Settings for fixed-cycle traffic signals. Operat. Res. Quart. 14, 373–86.CrossRefGoogle Scholar
Newell, G. F. (1965) Approximation methods for queues with application to the fixed cycle traffic light. SIAM Rev. 7, 2, 223–40.CrossRefGoogle Scholar
Parzen, E. (1962) Stochastic Processes. Holden-Day, San Francisco.Google Scholar
Webster, F. V. (1958) Traffic signal settings. Road Research Laboratory Technical Report No. 39, H.M.S.O., London.Google Scholar
Whittaker, E. T., and Watson, G. N. (1963) A Course of Modern Analysis. 4th Edition. Cambridge.Google Scholar