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Truncation of Markov chains with applications to queueing. (English) Zbl 0749.60069
Author’s 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.
MSC:
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
60K25Queueing theory