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On the stationary waiting time distribution in the queue. GI/G/1

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde*
Affiliation:
Australian National University

Extract

In this note, a representation, originally due to Smith, of the stationary waiting time distribution in the queue GI/G/1 is obtained under the least restrictive conditions possible.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1964 

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References

[1] Copson, E. T. (1935) An Introduction to the Theory of Functions of a Complex Variable. Clarendon Press, Oxford.Google Scholar
[2] Kingman, J. F. C. (1962) The use of Spitzer's identity in the investigation of the busy period and other quantities in the queue GI/G/1. J. Aust. Math. Soc. 2, 345356.CrossRefGoogle Scholar
[3] Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277289.Google Scholar
[4] Lukacs, E. (1960) Characteristic Functions. Griffin, London.Google Scholar
[5] Smith, W. L. (1953) Distribution of queueing times. Proc. Camb. Phil. Soc. 49, 449461.CrossRefGoogle Scholar
[6] Spitzer, F. (1956) A combinatorial lemma and its applications to probability theory. Trans. Amer. Math. Soc. 82, 323339.Google Scholar
[7] Spitzer, F. (1957) The Wiener-Hopf equation whose kernel is a probability density. Duke Math. J. 24, 327343.Google Scholar