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Hitting time in an M/G/1 queue

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Sheldon M. Ross  and
Sridhar Seshadri
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
Sridhar Seshadri*
Affiliation:
New York University
*
∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: smross@euler.berkeley.edu
∗∗Postal address: Department of Statistics and Operations Research & Operations Management Area, Leonard N. Stern School of Business, New York University, NY 10012, USA.
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Abstract

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.

Keywords

M/G/1 queue

MSC classification

Secondary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 934 - 940
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

The research of Sheldon M. Ross was supported by the National Science Foundation Grant DMI-9610046 with the University of California.

References

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Cohen, J. W. (1982). The Single Server Queue, Revised edn. North-Holland, Amsterdam.Google Scholar
Ross, S. M. (1983). Stochastic Processes, 2nd edn. Wiley, New York.Google Scholar
Wolff, R. W. (1989). Stochastic Modeling and the Theory of Queues. Prentice Hall, Englewood Cliffs, NJ.Google Scholar