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Unreliable Server M[X]/G/1 Retrial Feedback Queue with Balking, Working Vacation and Vacation Interruption

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Abstract

The bulk arrival general service retrial queue subject to balking, feedback and vacation interruption under multiple working vacation policy has been investigated. The server which provides the service is subjected to breakdowns and repairs. An arriving customer may balk from the system by noticing the status of the server in vacation or under repair state. The customer who remains unsatisfied with the service subsequently may rejoin the orbit to get another service and that customer is treated as a feedback customer. In this paper, supplementary variables are taken into account to represent the lapses of service time, repair, retrial attempts and vacation. The probability generating functions of the queue length distributions and explicit expressions of key performance indices are derived. Finally, numerical results along with the sensitivity analysis are given to validate the analytical results of key performance indices.

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Acknowledgements

Anshul Kumar thanks Council of Scientific and Industrial Research (CSIR) for funding this research via senior research fellowship (grant code 9013-12-061).

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Madhu Jain & Anshul Kumar

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  1. Madhu Jain
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  2. Anshul Kumar
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Correspondence to Anshul Kumar.

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Jain, M., Kumar, A. Unreliable Server M[X]/G/1 Retrial Feedback Queue with Balking, Working Vacation and Vacation Interruption. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 93, 57–73 (2023). https://doi.org/10.1007/s40010-022-00777-w

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  • DOI: https://doi.org/10.1007/s40010-022-00777-w

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