The queue length in the queueing system with an autoregressive input flow with a heavy traffic

Recieved: 06/22/2023

Accepted: 07/05/2023

Published: 11/28/2023

Keywords: Poissonian flow, random intensity, relative priority, queue length, heavy traffic

To cite this article

Bergovin A.K. The queue length in the queueing system with an autoregressive input flow with a heavy traffic. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 4, p.9-16 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–4–9–16.

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))

Abstract

A one-line queueing system with two priority classes, relative priority, Poissonian input flow with random intensity and infinite number of places in queue for waiting is studied. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. The heavy traffic limiting distribution of the queue length for the least priority class is obtained.