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

Mathematics

Vladimir Vishnevsky¹  Konstantin Vytovtov¹  Olga Semenova¹  Elizaveta Barabanova¹ 

[1] V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Science, 65 Profsoyuznaya Street, 117997 Moscow, Russia;

关键词: queuing system;    transient mode;    MAP flow;    matrix method;    Kolmogorov equations;   

DOI  :  10.3390/math10101684

来源: DOAJ

【 摘 要 】

This paper considers a queuing system with a finite buffer, a constant main $MAP$ 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.

【 授权许可】

Unknown