Volume 55, Number 4, July-August 2021
|Page(s)||2223 - 2240|
|Published online||29 July 2021|
Ergodicity and perturbation bounds for Mt/Mt/1 queue with balking, catastrophes, server failures and repairs
Vologda State University, Institute of Informatics Problems, FRC CSC RAS, Vologda Research Center RAS, Vologda, Russia
2 Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, Russia
3 Vologda State University, Vologda, Russia
4 Department of Mathematics, Faculty of Science, Menofia University, Shebin El Kom, Egypt
5 Department of Mathematics, College of Science, Taibah University, Medinah, Saudi Arabia
* Corresponding author: firstname.lastname@example.org
Accepted: 8 July 2021
In this paper, we display methods for the computation of convergence and perturbation bounds for Mt/Mt/1 system with balking, catastrophes, server failures and repairs. Based on the logarithmic norm of linear operators, the bounds on the rate of convergence, perturbation bounds, and the main limiting characteristics of the queue-length process are obtained. Finally, we consider the application of all obtained estimates to a specific model.
Mathematics Subject Classification: 60J27 / 60J28 / 60K25
Key words: Applied probability / ergodicity bounds; perturbation bounds / Mt/Mt/1 system with balking / catastrophes / server failures and repairs / limiting characteristics for the queue-length process
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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