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On the limit behavior of a multicompartment storage model with an underlying Markov chain

Published online by Cambridge University Press:  01 July 2016

Eric S. Tollar
Eric S. Tollar*
Affiliation:
The Florida State University
*
∗Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 32306, USA.
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Abstract

The present paper considers a multicompartment storage model with one-way flow. The inputs and outputs for each compartment are controlled by a denumerable-state Markov chain. Assuming finite first and second moments, it is shown that the amounts of material in certain compartments converge in distribution while for others they diverge, based on appropriate first-moment conditions on the inputs and outputs. It is also shown that the diverging compartments under suitable normalization converge to functionals of Brownian motion, independent of those compartments which converge without normalization.

Keywords

DUAL MARKOV CHAINAUXILIARY MARKOV CHAIN: MULTIVARIATE BROWNIAN MOTION
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 1 , March 1988 , pp. 208 - 227
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research supported by the U.S. Army Research Office under Grant DAAG 29–82-K-0168.

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