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The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1

Published online by Cambridge University Press:  14 July 2016

J. W. Cohen
J. W. Cohen*
Affiliation:
Mathematical Institute, Technological University, Delft, Holland
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Abstract

The distribution of the maximum number of customers simultaneously present during a busy period is studied for the queueing systems M/G/1 and G/M/1. These distributions are obtained by using taboo probabilities. Some new relations for transition probabilities and entrance time distributions are derived.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 1 , November 1967 , pp. 162 - 179
Copyright
Copyright © Applied Probability Trust 

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References

[1] Chung, K. L. (1960) Markov Chains with Stationary Transition Probabilities. Springer Verlag, Berlin.CrossRefGoogle Scholar
[2] Heathcote, C. R. (1965) On the maximum of the queue GI/M/1. J. Appl. Prob. 2, 206–214.Google Scholar
[3] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar