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Transient analysis of the M/M/1 queue

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

P. Leguesdron ,
J. Pellaumail ,
G. Rubino  and
B. Sericola
P. Leguesdron*
Affiliation:
INSA, Rennes
J. Pellaumail*
Affiliation:
INSA, Rennes
G. Rubino*
Affiliation:
IRISA-INRIA, Rennes
B. Sericola*
Affiliation:
IRISA-INRIA, Rennes
*
∗ Postal address: INSA, 20 avenue des Buttes de Coësmes, 35043 Rennes Cédex, France.
∗ Postal address: INSA, 20 avenue des Buttes de Coësmes, 35043 Rennes Cédex, France.
∗∗ Postal address: IRISA-INRIA, Campus Universitaire de Beaulieu, 35042 Rennes Cédex, France.
∗∗ Postal address: IRISA-INRIA, Campus Universitaire de Beaulieu, 35042 Rennes Cédex, France.
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Abstract

A new approach is used to obtain the transient probabilities of the M/M/1 queueing system. The first step of this approach deals with the generating function of the transient probabilities of the uniformized Markov chain associated with this queue. The second step consists of the inversion of this generating function. A new analytical expression of the transient probabilities of the M/M/1 queue is then obtained.

Keywords

UNIFORMIZARONGENERATING FUNCTION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J35: Transition functions, generators and resolvents

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 3 , September 1993 , pp. 702 - 713
Copyright
Copyright © Applied Probability Trust 1993 

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References

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