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

Author

Listed:
  • Lyes Ikhlef
  • Djamil Aïssani
  • Ouiza Lekadir

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.

Suggested Citation

  • Lyes Ikhlef & Djamil Aïssani & Ouiza Lekadir, 2023. "Steady state analysis of M / G /1 retrial queue with vacation and server timeout using a Petri net formalism," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 26(3), pages 373-392.
    • Handle: RePEc:ids:ijmore:v:26:y:2023:i:3:p:373-392
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