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On the Positive Recurrence of Finite Regenerative Stochastic Models

Author

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  • Evsey Morozov

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185035 Petrozavodsk, Russia
    Department of Applied Mathematics and Informatics, Yaroslav-the-Wise Novgorod State University, 173020 Veliky Novgorod, Russia
    Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
    These authors contributed equally to this work.)

  • Vladimir Rykov

    (Department of Applied Mathematics and Computer Modelling, National University of Oil and Gas (Gubkin University), 119991 Moscow, Russia
    Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia
    These authors contributed equally to this work.)

Abstract

We consider a general approach to establish the positive recurrence (stability) of regenerative stochastic systems. The approach is based on the renewal theory and a characterization of the remaining renewal time of the embedded renewal process generated by regeneration. We discuss how this analysis is simplified for some classes of the stochastic systems. The general approach is then illustrated by the stability analysis of a k -out-of- n repairable system containing n unreliable components with exponential lifetimes. Then we extend the stability analysis to the system with non-exponential lifetimes.

Suggested Citation

  • Evsey Morozov & Vladimir Rykov, 2023. "On the Positive Recurrence of Finite Regenerative Stochastic Models," Mathematics, MDPI, vol. 11(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4754-:d:1287242
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    References listed on IDEAS

    as
    1. Karl Sigman, 1990. "One-Dependent Regenerative Processes and Queues in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 175-189, February.
    2. Yonit Barron & Uri Yechiali, 2017. "Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems," IISE Transactions, Taylor & Francis Journals, vol. 49(11), pages 1031-1049, November.
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