Stochastic analysis of a single server unreliable queue with balking and general retrial time

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Abstract

In this investigation, we consider an M/G/1 queue with general retrial times allowing balking and server subject to breakdowns and repairs. In addition, the customer whose service is interrupted can stay at the server waiting for repair or leave and return while the server is being repaired. The server is not allowed to begin service on other customers until the current customer has completed service, even if current customer is temporarily absent. This model has a potential application in various fields, such as in the cognitive radio network and the manufacturing systems, etc. The methodology is strongly based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary distribution of the embedded Markov chain of the considered system.

About the authors

Mohamed Boualem

University of Bejaia

Author for correspondence.
Email: robertt15dz@yahoo.fr

Full Professor, Professor of Applied Mathematics at the Department of Technology

Algeria

References

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  10. M. Boualem, M. Cherfaoui, and D. Aıssani, “Monotonicity properties for a single server queue with classical retrial policy and service interruptions,” Proceedings of the Jangjeon Mathematical Society, vol. 19, no. 2, pp. 225-236, 2016.
  11. M. Boualem, M. Cherfaoui, N. Djellab, and D. Aıssani, “A stochastic version analysis of an M/G/1 retrial queue with Bernoulli schedule,” Bulletin of the Iranian Mathematical Society, vol. 43, no. 5, pp. 1377- 1397, 2017.
  12. M. Boualem, M. Cherfaoui, N. Djellab, and D. Aıssani, “Inégalités stochastiques pour le modèle d’attente M/G/1/1 avec rappels,” French, Afrika Matematika, vol. 28, pp. 851-868, 2017. doi: 10.1007/s13370017-0492-x.
  13. M. Boualem, N. Djellab, and D. Aıssani, “Stochastic inequalities for M/G/1 retrial queues with vacations and constant retrial policy,” Mathematical and Computer Modelling, vol. 50, no. 1-2, pp. 207-212, 2009. doi: 10.1016/j.mcm.2009.03.009.
  14. M. Boualem, N. Djellab, and D. Aıssani, “Stochastic approximations and monotonicity of a single server feedback retrial queue,” Mathematical Problems in Engineering, vol. 2012, 12 pages, 2012. doi: 10.1155/2012/ 536982.
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