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Expected number of departures in M/M/1 and G/G/1 queues

Published online by Cambridge University Press:  01 July 2016

Hydar Ali
Hydar Ali*
Affiliation:
The University of the West Indies
*
∗Postal address: Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad.
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Abstract

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For an initially empty M/M/1 queue, it is shown that the transform of the expectation of the number of departures in the interval (0, t] is invariant under an interchange of arrival and service rates. However, in the GI/G/1 queue with an initial single customer, the corresponding transform does not have this symmetric property.

Keywords

TRANSFORM: EXPECTATIONDEPARTURE PROCESS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 770 - 772
Copyright
Copyright © Applied Probability Trust 1990 

References

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Hubbard, J. R., Pegden, C. D. and Rosenshine, M. (1986) The departure process for the M/M/1 queue. J. Appl. Prob. 23, 249–255.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar