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Stationary solution to the fluid queue fed by an M/M/1 queue

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

N. Barbot  and
B. Sericola
N. Barbot*
Affiliation:
IRISA, Rennes
B. Sericola*
Affiliation:
IRISA and INRIA, Rennes
*
∗ Postal address: IRISA, Campus universitaire de Beaulieu, 35042 Rennes cedex, France.
∗ Postal address: IRISA, Campus universitaire de Beaulieu, 35042 Rennes cedex, France.
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Abstract

We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.

Keywords

Fluid queueM/M/1 queuegenerating functions

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 359 - 369
Copyright
Copyright © Applied Probability Trust 2002 

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References

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