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On the probability that the kth customer finds an M/M/1 queue empty

Published online by Cambridge University Press:  01 July 2016

Harshinder Singh*
Affiliation:
University of New Brunswick
Rameshwar D. Gupta*
Affiliation:
University of New Brunswick
*
Postal address: Department of Statistics, Panjab University, Chandigarh-160014, India.
∗∗Postal address: Division of Mathematics, Engineering and Computer Science, University of New Brunswick, Saint John, N.B., Canada, E2L4L5.
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Abstract

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A result relating the probability that kth customer finds the system empty to the distribution of the number of customers served in a busy period, for an M/M/1 queue, has been obtained. This relationship is similar to the relationship between the probability that the queue is empty at time t and the distribution of the length of the busy period.

MSC classification

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1992 

Footnotes

This work was done while this author was a Visiting Scientist at UNB.

Research supported in part by NSERC of Canada, Grant OGP0004850.

References

Abate, J. and Whitt, W. (1988) Transient behavior of the M/M/1 queue via Laplace transforms. Adv. Appl. Prob. 21, 145178.Google Scholar
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Riordan, J. (1962) Stochastic Service System. Wiley, New York.Google Scholar
Stanton, D. and White, D. (1986) Constructive Combinatorics. Springer-Verlag, New York.Google Scholar