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

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

Mathematics, 2022, vol. 10, issue 10, 1-16

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.

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: 2022
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