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Transient Behavior of the MAP/M/1/N Queuing System

Author

Listed:
  • Vladimir Vishnevsky

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

Abstract

This paper investigates the characteristics of the MAP/M/1/N queuing system in the transient mode. The matrix method for solving the Kolmogorov equations is proposed. This method makes it possible, in general, to obtain the main characteristics of the considered queuing system in a non-stationary mode: the probability of losses, the time of the transient mode, the throughput, and the number of customers in the system at time t . The developed method is illustrated by numerical calculations of the characteristics of the M A P / M / 1 / 3 system in the transient mode.

Suggested Citation

  • Vladimir Vishnevsky & Konstantin Vytovtov & Elizaveta Barabanova & Olga Semenova, 2021. "Transient Behavior of the MAP/M/1/N Queuing System," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2559-:d:654882
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