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Truncation of Markov Chains with Applications to Queueing

Author

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  • Nico M. van Dijk

    (University of Amsterdam, Amsterdam, The Netherlands)

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.

Suggested Citation

  • Nico M. van Dijk, 1991. "Truncation of Markov Chains with Applications to Queueing," Operations Research, INFORMS, vol. 39(6), pages 1018-1026, December.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:6:p:1018-1026
    DOI: 10.1287/opre.39.6.1018
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    Cited by:

    1. Badredine Issaadi, 2020. "Weak stability bounds for approximations of invariant measures with applications to queueing," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 371-400, March.
    2. Simonot, F., 1995. "Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 133-149, March.
    3. van Dijk, Nico M., 2008. "Error bounds for state space truncation of finite Jackson networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 164-181, April.

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