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

Authors:
Onno Boxma;Offer Kella;David Perry
Affiliations:
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: boxma@wi ...;Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: mskella@mscc.huji.ac.il;Department of Statistics, University of Haifa, Haifa 31905, Israel, E-mail: dperry@stat.haifa.ac.il
Venue:
Probability in the Engineering and Informational Sciences
Year:
2001

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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.