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Analysis of separable Markov-modulated rate models for information-handling systems

Published online by Cambridge University Press:  01 July 2016

Thomas E. Stern  and
Anwar I. Elwalid
Thomas E. Stern*
Affiliation:
Columbia University
Anwar I. Elwalid*
Affiliation:
Columbia University
*
∗Postal address for both authors: Department of Electrical Engineering and Center for Telecommunications Research, Columbia University, New York, NY 10027, USA.
∗Postal address for both authors: Department of Electrical Engineering and Center for Telecommunications Research, Columbia University, New York, NY 10027, USA.
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Abstract

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP).

In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

Keywords

KRONECKER PRODUCT FORMCONTINUOUS FLOW MODEL
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 1 , March 1991 , pp. 105 - 139
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Part of this work was performed when the first author was on sabbatical leave at INRIA Centre de Sophia Antipolis 06565 Valbonne, France. This work was partially supported by the National Science Foundation under grant CDR-84-21402, and the office of Naval Research under grant N00014-85-k0371.

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