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Analysis of a MAP / M /1/ N Queue with Periodic and Non-Periodic Piecewise Constant Input Rate

Author

Listed:
  • Vladimir Vishnevsky

    (V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    These authors contributed equally to this work.)

  • Konstantin Vytovtov

    (V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    These authors contributed equally to this work.)

  • Elizaveta Barabanova

    (V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    These authors contributed equally to this work.)

  • Olga Semenova

    (V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
    These authors contributed equally to this work.)

Abstract

This paper considers a queuing system with a finite buffer, a constant main M A P flow, and an additional periodic (non-periodic) Poisson piecewise-constant flow of customers. The eigenvalues of the probability translation matrix of a Kolmogorov system with constant input intensities is analyzed. The definition of the transition mode time based on the analysis of the probability translation matrix determinant is introduced for the first time. An analytical solution to the Kolmogorov equation system for a queuing system with piecewise constant arrival and service intensities is found, the solutions for a queuing system with periodic arrival and service intensities are analyzed, and numerical calculations illustrating this approach are presented.

Suggested Citation

  • Vladimir Vishnevsky & Konstantin Vytovtov & Elizaveta Barabanova & Olga Semenova, 2022. "Analysis of a MAP / M /1/ N Queue with Periodic and Non-Periodic Piecewise Constant Input Rate," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1684-:d:815607
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    References listed on IDEAS

    as
    1. Michael H. Rothkopf & Shmuel S. Oren, 1979. "A Closure Approximation for the Nonstationary M/M/s Queue," Management Science, INFORMS, vol. 25(6), pages 522-534, June.
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