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Markov-renewal fluid queues

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Guy Latouche  and
Tetsuya Takine
Guy Latouche*
Affiliation:
Université Libre de Bruxelles
Tetsuya Takine*
Affiliation:
Kyoto University
*
∗ Postal address: Université Libre de Bruxelles, Département d'Informatique, Boulevard du Triomphe, CP 212, 1050 Bruxelles, Belgium. Email address: [email protected]
∗∗ Postal address: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. Email address: [email protected]
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Abstract

We consider a fluid queue controlled by a semi-Markov process and we apply the Markov-renewal approach developed earlier in the context of quasi-birth-and-death processes and of Markovian fluid queues. We analyze two subfamilies of semi-Markov processes. In the first family, we assume that the intervals during which the input rate is negative have an exponential distribution. In the second family, we take the complementary case and assume that the intervals during which the input rate is positive have an exponential distribution. We thoroughly characterize the structure of the stationary distribution in both cases.

Keywords

Fluid queuesemi-Markov environmentMarkov-renewal analysis

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K37: Processes in random environments
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 746 - 757
Copyright
Copyright © Applied Probability Trust 2004 

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