Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown

S. Sundarapandiyan; S. Nandhini; S. Sundarapandiyan; S. Nandhini

doi:10.3934/math.20241022

AIMS Mathematics

2024, Volume 9, Issue 8: 21025-21052. doi: 10.3934/math.20241022

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Research article

Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown

S. Sundarapandiyan ,
S. Nandhini ^,

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamilnadu, India

Received: 15 April 2024 Revised: 25 May 2024 Accepted: 03 June 2024 Published: 28 June 2024
MSC : 60K25, 68M20, 90B22

This study investigated the steady-state characteristics of a non-Markovian feedback retrial queue with reneging, delayed repair, and working vacation. In this scenario, we assumed that consumers arrive through Poisson processes and the server provides service to consumers during both regular and working vacation periods. However, it is subject to breakdowns at any moment, resulting in a service interruption for a random duration. Additionally, the concept of delay time was also presented. The consumer that is dissatisfied with the service may re-enter the orbit to receive another service; this individual is considered a feedback consumer. The server will go on a working vacation if the orbit is empty after successfully serving a satisfied consumer. By utilizing the supplementary variable technique (SVT), we examined the steady-state probability generating function of the system and orbit sizes. Finally, numerical outcomes and a sensitivity analysis were given to verify the analytical findings of important performance indicators.
- retrial queue,
- working vacation,
- server breakdown,
- feedback,
- delayed repair,
- supplementary variable technique
Citation: S. Sundarapandiyan, S. Nandhini. Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown[J]. AIMS Mathematics, 2024, 9(8): 21025-21052. doi: 10.3934/math.20241022

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Abstract

This study investigated the steady-state characteristics of a non-Markovian feedback retrial queue with reneging, delayed repair, and working vacation. In this scenario, we assumed that consumers arrive through Poisson processes and the server provides service to consumers during both regular and working vacation periods. However, it is subject to breakdowns at any moment, resulting in a service interruption for a random duration. Additionally, the concept of delay time was also presented. The consumer that is dissatisfied with the service may re-enter the orbit to receive another service; this individual is considered a feedback consumer. The server will go on a working vacation if the orbit is empty after successfully serving a satisfied consumer. By utilizing the supplementary variable technique (SVT), we examined the steady-state probability generating function of the system and orbit sizes. Finally, numerical outcomes and a sensitivity analysis were given to verify the analytical findings of important performance indicators.

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