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An analysis of the fixed-cycle traffic-light problem

Published online by Cambridge University Press:  14 July 2016

Richard Cowan*
Affiliation:
CSIRO Division of Mathematics and Statistics, Sydney
*
Postal address: CSIRO Division of Mathematics and Statistics, Box 218, Lindfield, N.S.W. 2070, Australia.

Abstract

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 

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References

Cowan, R. (1975) Useful headway models. Transportation Res. 9, 371375.Google Scholar
Cowan, R. (1978) A new model for signalised intersections with vehicle-actuated control. J. Appl. Prob. 15, 384396.Google Scholar
Cowan, R. (1979) The uncontrolled traffic merge. J. Appl. Prob. 16, 384392.Google Scholar
Cowan, R. (1980) Further results on single lane traffic flow. J. Appl. Prob. 17, 523531.Google Scholar
Darroch, J. N. (1964) On the traffic light queue. Ann. Math. Statist. 35, 380388.Google Scholar
Mcneil, D. R. (1968) A solution to the fixed-cycle traffic light problem for compound Poisson arrivals. J. Appl. Prob. 5, 624635.CrossRefGoogle Scholar
Miller, A. J. (1963) Settings for fixed-cycle traffic signals. Operat. Res. Quart. 14, 373386.Google Scholar
Newell, G. F. (1965) Approximation methods for queues with applications to the fixed-cycle traffic light. SIAM Rev. 7, 223240.Google Scholar
Ohno, K. (1978) Computational algorithm for a fixed-cycle traffic signal and new approximate expressions for average delay. Transportation Sci. 12, 2947.Google Scholar
Webster, F. V. (1958) Traffic signal settings. Road Research Laboratory Tech. Rep. No. 39. HMSO, London.Google Scholar
Webster, F. V. and Cobbe, B. M. (1966) Traffic signals. Road Research Laboratory Tech. Rep. No. 56, HMSO, London.Google Scholar