Exact results for a fluid model with state-dependent flow rates

Offer Kella*, Wolfgang Stadje

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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.

Original languageAmerican English
Pages (from-to)389-402
Number of pages14
JournalProbability in the Engineering and Informational Sciences
Volume16
Issue number4
DOIs
StatePublished - 2002

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