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Traffic light queues as a generalization to queueing theory

Published online by Cambridge University Press:  14 July 2016

Hisashi Mine and
Katsuhisa Ohno
Hisashi Mine
Affiliation:
Kyoto University
Katsuhisa Ohno
Affiliation:
Kyoto University
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Extract

Fixed-cycle traffic light queues have been investigated by probabilistic methods by many authors. Beckmann, McGuire and Winsten (1956) considered a discrete time queueing model with binomial arrivals and regular departure headways and derived a relation between the stationary mean delay per vehicle and the stationary mean queue-length at the beginning of a red period of the traffic light. Haight (1959) and Buckley and Wheeler (1964) considered models with Poisson arrivals and regular departure headways and investigated certain properties of the queue-length. Newell (1960) dealt with the model proposed by the first authors and obtained the probability generating function of the stationary queue-length distribution. Darroch (1964) discussed a more general discrete time model with stationary, independent arrivals and regular departure headways and derived a necessary and sufficient condition for the stationary queue-length distribution to exist and obtained its probability generating function. The above two authors, Little (1961), Miller (1963), Newell (1965), McNeil (1968), Siskind (1970) and others gave approximate expressions for the stationary mean delay per vehicle for fixed-cycle traffic light queues of various types. All of the authors mentioned above dealt with the queue-length.

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Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971, pp. 480 - 493
Copyright
Copyright © Applied Probability Trust 1971 

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