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AN INTERMITTENT FLUID SYSTEM WITH EXPONENTIAL ON-TIMES AND SEMI-MARKOV INPUT RATES

Published online by Cambridge University Press:  10 April 2001

Onno Boxma ,
Offer Kella  and
David Perry
Onno Boxma
Affiliation:
EURANDOM and Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, and, CWI, 1090 GB Amsterdam, The Netherlands, E-mail: [email protected]
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: [email protected]
David Perry
Affiliation:
Department of Statistics, University of Haifa, Haifa 31905, Israel, E-mail: [email protected]
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Abstract

We consider a fluid system in which during off-times the buffer content increases as a piecewise linear process according to some general semi-Markov process, and during on-times, it decreases with a state-dependent rate (or remains at zero). The lengths of off-times are exponentially distributed. We show that such a system has a stationary distribution which satisfies a decomposition property where one component in the decomposition is associated with some dam process and the other with a clearing process. For the cases of constant and linear decrease rates, the steady-state Laplace–Stieltjes transform and moments of the buffer content are computed explicitly.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 2 , April 2001 , pp. 189 - 198
Copyright
© 2001 Cambridge University Press

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