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A Simple Numerical Approach for Infinite-State Markov Chains

Published online by Cambridge University Press:  27 July 2009

Henk C. Tijms  and
Michel C. T. Van De Coevering
Henk C. Tijms
Affiliation:
Department of Econometrics Vrije University, 1081 HV Amsterdam, The Netherlands
Michel C. T. Van De Coevering
Affiliation:
Department of Econometrics Vrije University, 1081 HV Amsterdam, The Netherlands
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Abstract

This paper presents a simple and practical approach to solving the equilibrium equations for a class of Markov chains with an infinite number of states. Markov chains arising in queueing and inventory applications often have the property that the state probabilities exhibit a geometric tail behavior. The basic idea of the approach is to reduce the infinite system of linear equations to a finite system using the geometric tail behavior of the equilibrium probabilities. The reduction typically leads to a remarkably small system of linear equations that can be routinely solved by a Gaussian elimination method. An application is given to the single-server queue with scheduled arrivals.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 3 , July 1991 , pp. 285 - 295
Copyright
Copyright © Cambridge University Press 1991

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References

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