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

Vladimir Vishnevsky, Konstantin Vytovtov, Elizaveta Barabanova and Olga Semenova
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Vladimir Vishnevsky: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
Konstantin Vytovtov: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
Elizaveta Barabanova: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia
Olga Semenova: V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia

Mathematics, 2021, vol. 9, issue 20, 1-16

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.

Keywords: queuing system; transient mode; MAP flow; matrix method; Kolmogorov equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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