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Bounds on the Rate of Convergence for M t X / M t X /1 Queueing Models

Author

Listed:
  • Alexander Zeifman

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia
    Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova 44-2, 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
    Vologda Research Center of the Russian Academy of Sciences, 160014 Vologda, Russia)

  • Yacov Satin

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

  • Alexander Sipin

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

Abstract

We apply the method of differential inequalities for the computation of upper bounds for the rate of convergence to the limiting regime for one specific class of (in)homogeneous continuous-time Markov chains. Such an approach seems very general; the corresponding description and bounds were considered earlier for finite Markov chains with analytical in time intensity functions. Now we generalize this method to locally integrable intensity functions. Special attention is paid to the situation of a countable Markov chain. To obtain these estimates, we investigate the corresponding forward system of Kolmogorov differential equations as a differential equation in the space of sequences l 1 .

Suggested Citation

  • Alexander Zeifman & Yacov Satin & Alexander Sipin, 2021. "Bounds on the Rate of Convergence for M t X / M t X /1 Queueing Models," Mathematics, MDPI, vol. 9(15), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1752-:d:601079
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