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Markov-modulated linear fluid networks with Markov additive input

Part of: Markov processes Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Wolfgang Stadje
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. Email address: mskella@mscc.huji.ac.il
∗∗ Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany.
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Abstract

We consider a network of dams to which the external input is a multivariate Markov additive process. For each state of the Markov chain modulating the Markov additive process, the release rates are linear (constant multiple of the content level). Each unit of material processed by a given station is then divided into fixed proportions each of which is routed to another station or leaves the system. For each state of the modulating process, this routeing is determined by some substochastic matrix. We identify simple conditions for stability and show how to compute transient and stationary characteristics of such networks.

Keywords

Linear stochastic fluid networkMarkov modulatedshot-noise process

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60G10: Stationary processes 60J25: Continuous-time Markov processes on general state spaces
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 413 - 420
Copyright
Copyright © Applied Probability Trust 2002 

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References

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