Title: Steady state analysis of M/G/1 retrial queue with vacation and server timeout using a Petri net formalism

Authors: Lyes Ikhlef; Djamil Aïssani; Ouiza Lekadir

Addresses: Department of Mathematics, Faculty of Sciences, University of Algiers, Algeria; Research Unit LaMOS (Modeling and Optimization of Systems), Bejaia University, Algeria ' Operation Research Department, Exact Sciences Faculty, Bejaia University, Algeria; Research Unit LaMOS (Modeling and Optimization of Systems), Bejaia University, Algeria ' Operation Research Department, Exact Sciences Faculty, Bejaia University, Algeria; Research Unit LaMOS (Modeling and Optimization of Systems), Bejaia University, Algeria

Abstract: In this paper, we analyse an M/G/1 retrial queue with vacation and server timeout. When the system is empty, the server waits for a random time. At the expiration of this time, if there is no arrival to the system, the server takes a vacation. If there is at least one customer in the system, the server commences service. So, we propose an unbounded Markov regenerative stochastic Petri net (MRSPN) to model this queueing system. For the qualitative analysis of this model, we combine the Markov regenerative approach and the generating function technique. Finally, numerical illustrations are performed.

Keywords: retrial systems; Markov regenerative stochastic Petri nets; MRSPN; M/G/1; renewal theory; steady state; vacation policy; server timeout.

DOI: 10.1504/IJMOR.2023.134839

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.3, pp.373 - 392

Received: 28 Jul 2022
Accepted: 02 Sep 2022
Published online: 14 Nov 2023 *

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