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The joint distribution of the virtual waitingtime and the residual busy period for the M/G/1 queue

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
Purdue University
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Abstract

In the M/G/1 queue, the joint distribution of the virtual waitingtime and the residual duration of the busy period at any time t, is given by a formula analogous to the one for the virtual waitingtime by itself. In the limit, as t → ∞, the limiting joint distribution is given by a formula of the Pollaczek-Khintchine type.

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Type
Short Communications
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 224 - 229
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Takács, Lajos (1961) The transient behavior of a single server queueing process with Poisson input. Proc. Fourth Berkeley Symposium. U. of California Press. 535–567.Google Scholar
[2] Takács, Lajos (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar