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Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model

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  • V., Saravanan
  • V., Poongothai
  • P., Godhandaraman

Abstract

In this paper, we investigate a Markovian multi server retrial queueing system with unreliable servers, discouraged customers and vacation. The model is explored with a view to reduce the impact of unreliable servers on the system performance. This is attained by providing regular maintenance to the servers through synchronised vacation. Further, the customer facing service interruption on account of server breakdown is directed to the orbit from where the customer can retry seeking service. In this study, the stationary system size distribution is framed by quasi-birth–death (QBD) process. The rate matrix and steady state probabilities are established using matrix geometric method (MGM). The performance measures are derived by using matrix form expressions. The effects induced by the system parameters on the performance metrics are numerically and graphically analysed. Through numerical investigation, we provide insightful information that enables to manage the system to give enhanced system performance.

Suggested Citation

  • V., Saravanan & V., Poongothai & P., Godhandaraman, 2023. "Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 204-226.
    • Handle: RePEc:eee:matcom:v:214:y:2023:i:c:p:204-226
    DOI: 10.1016/j.matcom.2023.07.008
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    References listed on IDEAS

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    1. Shan Gao & Hua Dong & Xianchao Wang, 2021. "Correction to: Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 645-646, March.
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    3. Economou, Antonis & Logothetis, Dimitrios & Manou, Athanasia, 2022. "The value of reneging for strategic customers in queueing systems with server vacations/failures," European Journal of Operational Research, Elsevier, vol. 299(3), pages 960-976.
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    5. R. Sudhesh & A. Azhagappan, 2019. "Analysis of an M/M/c queue with heterogeneous servers, balking and reneging," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 36(3), pages 293-309.
    6. D. Arivudainambi & P. Godhandaraman, 2015. "Retrial queueing system with balking, optional service and vacation," Annals of Operations Research, Springer, vol. 229(1), pages 67-84, June.
    7. Amit Choudhury & Pallabi Medhi, 2011. "Balking and reneging in multiserver Markovian queuing system," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(4), pages 377-394.
    8. Rakesh Kumar & Sapana Sharma, 2018. "Transient analysis of an M/M/c queuing system with balking and retention of reneging customers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(6), pages 1318-1327, March.
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    10. Shan Gao & Hua Dong & Xianchao Wang, 2021. "Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 621-643, March.
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