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The output process of an MMPP/M/1 queue

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Nigel Bean ,
David Green  and
Peter Taylor
Nigel Bean*
Affiliation:
University of Adelaide
David Green*
Affiliation:
University of Adelaide
Peter Taylor*
Affiliation:
University of Adelaide
*
∗Postal address: Department of Applied Mathematics, The University of Adelaide, Adelaide 5005, Australia. Email address: {nbean dgreen ptaylor}@maths.adelaide.edu.au.
∗Postal address: Department of Applied Mathematics, The University of Adelaide, Adelaide 5005, Australia. Email address: {nbean dgreen ptaylor}@maths.adelaide.edu.au.
∗Postal address: Department of Applied Mathematics, The University of Adelaide, Adelaide 5005, Australia. Email address: {nbean dgreen ptaylor}@maths.adelaide.edu.au.
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Abstract

Olivier and Walrand (1994) claimed that the departure process of an MMPP/M/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. They also conjectured that the departure process of an MAP/PH/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. We show that their proof of the first result has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/M/1 can be an MAP.

Keywords

Markov arrival process (MAP)Markov modulated Poisson process (MMPP)(PH) phase-renewal processnonlinear filtering

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 998 - 1002
Copyright
Copyright © Applied Probability Trust 1998 

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References

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