An intermittent fluid system with exponential on-times and semi-Markov input rates

An intermittent fluid system with exponential on-times and semi-Markov input rates

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Article ID: iaor20023413
Country: United States
Volume: 15
Issue: 2
Start Page Number: 189
End Page Number: 198
Publication Date: Jan 2001
Journal: Probability in the Engineering and Informational Sciences
Authors: , ,
Keywords: queues: theory
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.

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