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On the busy periods for the M/G/1 queue with finite and with infinite waiting room

Published online by Cambridge University Press:  14 July 2016

J. W. Cohen
J. W. Cohen*
Affiliation:
Technological University, Delft
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Summary

The Laplace-Stieltjes transform of the distribution of the busy period for the M/G/1 system with infinite waiting room can be obtained by using an argument from branching theory. In the present paper it is shown that by applying this argument it is rather easy to derive the expression for the joint distribution of the busy period and the maximum number of customers present simultaneously during this busy period for the M/G/1 system with infinite waiting room as well as the expression for the distribution of the busy period for the M/G/1 system with finite waiting room.

Type
Short Communications
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 821 - 827
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar
[2] Cohen, J. W. (1969) The Single Server Queue. North Holland Publ. Co., Amsterdam.Google Scholar
[3] Cohen, J. W. (1967) Distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1. J. Appl. Prob. 4, 162–179.Google Scholar