Truncation of Markov chains with applications to queueing

Truncation of Markov chains with applications to queueing

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Article ID: iaor19931588
Country: United States
Volume: 39
Issue: 6
Start Page Number: 1018
End Page Number: 1026
Publication Date: Nov 1991
Journal: Operations Research
Authors:
Keywords: markov processes
Abstract:

State-space truncation is frequently demanded for computation of large or infinite Markov chains. Conditions are given that guarantee an error bound or rate of convergence. Roughly, these conditions apply either when probabilities of large states are sufficiently small, or when transition probabilities (rates) for state increases become small in sufficiently large states. The verification of these conditions is based on establishing bounds for bias terms of reward structures. The conditions and their verification are illustrated by two nonproduct form queueing examples: an overflow model and a tandem queue with blocking. A concrete truncation and explicit error bound are obtained. Some numerical support is provided.

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