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EXACT RESULTS FOR A FLUID MODEL WITH STATE-DEPENDENT FLOW RATES

Published online by Cambridge University Press:  10 October 2002

Offer Kella  and
Wolfgang Stadje
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: mskella@mscc.huji.ac.il
Wolfgang Stadje
Affiliation:
Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
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Abstract

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We consider a modulated fluid system with a finite state-space Markov chain Jt as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (Wt, Jt), where Wt is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of Wt. Our results lead to explicit formulas in the case of two modulating states.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 16 , Issue 4 , October 2002 , pp. 389 - 402
Copyright
© 2002 Cambridge University Press