On maxima of stationary delay in M/G/2 systems

Recieved: 12/20/2023

Accepted: 12/29/2023

Published: 04/02/2024

Keywords: stationary delay, two-server queueing system, extremal index

To cite this article

Peshkova I. V. On maxima of stationary delay in M/G/2 systems. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2024. N 2, p.38-46 https://doi.org/10.55959/MSU/0137-0782-15-2024-47-2-38-46.

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

Peshkova I. V. (Petrozavodsk State University)
(Institute of Applied Mathematical Research of the Karelian Scientific Center of the Russian Academy of Sciences)

Abstract

The paper investigates a two-server system with a Poisson input, in which the service times on the servers have a Pareto distribution with the parameter a > 1. Using known asymptotics for the distribution of stationary waiting time, the distribution of the maximum stationary delay is obtained for two cases: p < 1 and 1 < p < 2. Estimates of the extremal index of stationary waiting time were obtained in numerical experiments using regenerative modeling.