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Weak stability bounds for approximations of invariant measures with applications to queueing

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  • Badredine Issaadi

    (University of Boumerdes
    University of Bejaia, Targua Ouzemour)

Abstract

This paper investigate the approximation of invariant distributions for countable space Markov chains using truncations of the transition matrix. We use the weak perturbation theory to establish analytic error bounds in the GI/M/1 model and a tandem queue with blocking. Numerical examples are carried out to illustrate the quality of the obtained error bounds.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:1:d:10.1007_s11009-019-09708-6
    DOI: 10.1007/s11009-019-09708-6
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    References listed on IDEAS

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    1. Gibson, Diana & Seneta, E., 1987. "Monotone infinite stochastic matrices and their augmented truncations," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 287-292, May.
    2. Badredine Issaadi & Karim Abbas & Djamil Aïssani, 2017. "Perturbation Analysis of the GI/M/s Queue," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 819-841, September.
    3. Nico M. van Dijk, 1991. "Truncation of Markov Chains with Applications to Queueing," Operations Research, INFORMS, vol. 39(6), pages 1018-1026, December.
    4. Hervé, Loïc & Ledoux, James, 2014. "Approximating Markov chains and V-geometric ergodicity via weak perturbation theory," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 613-638.
    Full references (including those not matched with items on IDEAS)

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