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Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

David M. Lucantoni  and
Marcel F. Neuts
David M. Lucantoni*
Affiliation:
AT&T Bell Laboratories
Marcel F. Neuts*
Affiliation:
University of Arizona
*
∗ Postal address: Room 1L-224, AT&T Bell Laboratories, Holmdel, NJ 07733, USA.
∗∗ Postal address: Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721.
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Abstract

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in the MAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for the MAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.

Keywords

BUSY PERIODSAMPLE PATHS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 235 - 243
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported in part by Grant Nr. DDM-8915235 from the National Science Foundation.

References

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