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Some Time-Dependent Properties of Symmetric M/G/1 Queues

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella ,
Bert Zwart  and
Onno Boxma
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Bert Zwart*
Affiliation:
Eindhoven University of Technology and CWI
Onno Boxma*
Affiliation:
EURANDOM, Eindhoven University of Technology and CWI
*
∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. Email address: mskella@mscc.huji.ac.il
∗∗Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
∗∗Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
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Abstract

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We consider an M/G/1 queue that is idle at time 0. The number of customers sampled at an independent exponential time is shown to have the same geometric distribution under the preemptive-resume last-in-first-out and the processor-sharing disciplines. Hence, the marginal distribution of the queue length at any time is identical for both disciplines. We then give a detailed analysis of the time until the first departure for any symmetric queueing discipline. We characterize its distribution and show that it is insensitive to the service discipline. Finally, we study the tail behavior of this distribution.

Keywords

Symmetric queuetime-dependent analysisinsensitivityorder statisticrandom permutationtail behavior

MSC classification

Secondary: 60K25: Queueing theory 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 223 - 234
Copyright
© Applied Probability Trust 2005 

Footnotes

∗

Supported in part by grant 819/03 from the Israel Science Foundation.

∗∗∗

Supported by an NWO VENI grant.

∗∗∗∗

Work carried out within the Euro-NGI project

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