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Bounds and Maxima for the Workload in a Multiclass Orbit Queue

Author

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  • Evsey V. Morozov

    (Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
    Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia
    These authors contributed equally to this work.)

  • Irina V. Peshkova

    (Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
    Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    These authors contributed equally to this work.)

  • Alexander S. Rumyantsev

    (Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia
    Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    These authors contributed equally to this work.)

Abstract

In this research, a single-server M -class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical M / G / 1 systems where the service time has M -component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes.

Suggested Citation

  • Evsey V. Morozov & Irina V. Peshkova & Alexander S. Rumyantsev, 2023. "Bounds and Maxima for the Workload in a Multiclass Orbit Queue," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:564-:d:1043097
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    References listed on IDEAS

    as
    1. Asmussen, Søren & Klüppelberg, Claudia & Sigman, Karl, 1999. "Sampling at subexponential times, with queueing applications," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 265-286, February.
    2. Hooghiemstra, Gerard & Meester, Ludolf E., 1996. "Computing the extremal index of special Markov chains and queues," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 171-185, December.
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