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Comparison Results for Markov-Modulated Recursive Models

Published online by Cambridge University Press:  27 July 2009

Nicole Bäuerle  and
Ulrich Rieder
Nicole Bäuerle
Affiliation:
Department of Mathematics vii, University of Ulm, D-89059 Ulm, Germany
Ulrich Rieder
Affiliation:
Department of Mathematics vii, University of Ulm, D-89059 Ulm, Germany
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Abstract

We consider a general discrete-time stochastic recursive model that is influenced by an external Markov chain. Our aim is to investigate the effect that the transition matrix of the external process has on the system states of the model. To answer this question, we use new stochastic ordering concepts. Especially interesting are the results for infinite-stage Markov-modulated models. We illustrate our main results by three applications: an inventory model, a consumption model, and a queueing model for a time division multiplexing system.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 2 , April 1997 , pp. 203 - 217
Copyright
Copyright © Cambridge University Press 1997

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