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

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Harshinder Singh  and
Rameshwar D. Gupta
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.

Keywords

BUSY PERIODPOISSON PROCESS

MSC classification

Primary: 60K25: Queueing theory
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 238 - 239
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, 145–178.Google Scholar
Parzen, E. (1962) Stochastic Processes. Holden Day, San Francisco.Google Scholar
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