On the queue length in the queueing system with mixed priorities with a heavy traffic

Recieved: 02/19/2024

Accepted: 02/26/2024

Published: 06/26/2024

Keywords: Poissonian flow, mixed priority, nonpreemptive priority, preemptive priority, queue length, heavy traffic

To cite this article

Bergovin A.K., Ushakov V.G. On the queue length in the queueing system with mixed priorities with a heavy traffic. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2024. N 3, p.54-59 https://doi.org/10.55959/MSU/0137-0782-15-2024-47-3-54-59.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Bergovin A.K. (Lomonosov Moscow State University (MSU))
Ushakov V.G. (Lomonosov Moscow State University (MSU))
(Federal Research Center "Science and Management", Russian Academy of Sciences, Moscow, Russia)

Abstract

A one-line queueing system with three incoming Poissonian flows is studied. Service time distributions are general and absolutely continuous for each flow. The first class requirements have nonpreemptive priority over the second class requirements and preemptive-repeat-different priority over the third class requirements. The second class requirements have nonpreemptive priority over the third class requirements. The heavy traffic limiting distribution of the queue length for the third class is obtained while the system load tends to 1 and time tends to infinity.