Title: Strong perturbation bounds for the stationary distribution of the main multi-server retrial queue model

Authors: Nabil Ait Yala; Badredine Issaadi; Karim Abbas

Addresses: Research Unit LaMOS – Laboratory of Modeling and Optimization of Systems, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria; Mathematics Department, Faculty of Sciences and Applied Sciences, University of Bouira, 10000 Bouira, Algeria ' Laboratoire LITAN, École Supérieure en Sciences et Technologie de l'Informatique et du Num´erique, RN 75, Amizour 06300, Bejaia, Algeria; Research Unit LaMOS – Laboratory of Modeling and Optimization of Systems, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' Research Unit LaMOS – Laboratory of Modeling and Optimization of Systems, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria

Abstract: Many queuing models are represented by Markov chains with infinite countable state space and we will often want to know their stationary distributions in order to deduce their characteristics, but the calculation of these distributions is generally difficult, if not impossible, and do not have closed form solutions because of the infinite number of equations to solve. This is why researchers try to obtain approximations that converge quickly to these distributions. Perturbation theory for Markov chains addresses the question of what impact can occur on a stationary distribution of a Markov chain if its transition matrix is slightly disturbed. In this paper, we use the strong stability approach based on the drift condition to establish analytic error bounds for the generalised truncation of a main multi-server retrial queue model. At the end of this article, we give numerical examples in order to show the quality of the error bounds obtained.

Keywords: Markov chains; perturbation theory; truncation; strong stability; Lyapunov function; drift condition; retrial queueing systems.

DOI: 10.1504/IJMOR.2025.146359

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.1, pp.1 - 40

Received: 15 Aug 2023
Accepted: 20 Aug 2023
Published online: 27 May 2025 *

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