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Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate

Author

Listed:
  • Anatoly Nazarov

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
    These authors contributed equally to this work.)

  • Ekaterina Fedorova

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
    These authors contributed equally to this work.)

  • Olga Lizyura

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
    These authors contributed equally to this work.)

  • Radmir Salimzyanov

    (Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
    These authors contributed equally to this work.)

Abstract

In this paper, we consider a retrial queue with a state-dependent service rate as a mathematical model of a node of FANET communications. We suppose that the arrival process is Poisson, the delay duration is exponentially distributed, the orbit is unlimited, and there is multiple random access from the orbit. There is one server, and the service time of every call is distributed exponentially with a variable parameter depending on the number of calls in the orbit. The service rate has an infinite number of values. We propose the asymptotic diffusion method for the model study. The asymptotic diffusion approximation of the probability distribution of the number of calls in the orbit is derived. Some numerical examples are demonstrated.

Suggested Citation

  • Anatoly Nazarov & Ekaterina Fedorova & Olga Lizyura & Radmir Salimzyanov, 2023. "Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate," Mathematics, MDPI, vol. 11(14), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3140-:d:1195280
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    References listed on IDEAS

    as
    1. Anatoly Nazarov & Alexander Dudin & Alexander Moiseev, 2022. "Pseudo Steady-State Period in Non-Stationary Infinite-Server Queue with State Dependent Arrival Intensity," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    2. Ingolfsson, Armann & Almehdawe, Eman & Pedram, Ali & Tran, Monica, 2020. "Comparison of fluid approximations for service systems with state-dependent service rates and return probabilities," European Journal of Operational Research, Elsevier, vol. 283(2), pages 562-575.
    3. Opher Baron & Antonis Economou & Athanasia Manou, 2018. "The state-dependent M / G / 1 queue with orbit," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 89-123, October.
    4. Ioannis Dimitriou, 2013. "A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 542-571, October.
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