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

Lyes Ikhlef, Djamil Aïssani and Ouiza Lekadir

International Journal of Mathematics in Operational Research, 2023, vol. 26, issue 3, 373-392

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. (search for similar items in EconPapers)
Date: 2023
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