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Characterization of the Output Rate Process for a Markovian Storage Model

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Samuli Aalto
Samuli Aalto*
Affiliation:
Helsinki University of Technology
*
∗Laboratory of Telecommunications Technology, Helsinki University of Technology, PO Box 3000, FIN-02015 HUT, Finland. e-mail address: samuli.aalto@hut.fi
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Abstract

We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process

Keywords

Storage modelsMarkov modulationoutput rate processbusy periodfluid flow approximationteletraffic theorymultiplexer

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 184 - 199
Copyright
Copyright © Applied Probability Trust 1998 

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