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Transient Analysis of Differentiated Breakdown Model

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  • Janani, B.

Abstract

The single server queueing system is investigated. When the system is idle or while serving a customer, it fails at random. System failure is classified into two types: hard failure and soft failure. Hard failure usually necessitates the repairman's physical presence and takes a long time. Soft failure, on the other hand, takes less time because the system can be restored to operation by simply rebooting it. When the system is being repaired, the server is forced to take a vacation and the repair process begins immediately. The model's transient state probabilities are derived and using the final value theorem of the Laplace transform, steady state probabilities are derived from transient state probabilities. Finally, numerical illustrations are provided to demonstrate the system's behaviour as the parameters' values are varied.

Suggested Citation

  • Janani, B., 2022. "Transient Analysis of Differentiated Breakdown Model," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008614
    DOI: 10.1016/j.amc.2021.126779
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    References listed on IDEAS

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    1. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
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    4. Oliver C. Ibe, 2016. "Vacation Queueing Models of Service Systems Subject to Failure and Repair," Springer Series in Reliability Engineering, in: Lance Fiondella & Antonio Puliafito (ed.), Principles of Performance and Reliability Modeling and Evaluation, pages 481-496, Springer.
    5. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
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    Cited by:

    1. Li, Mingjia & Hu, Linmin & Wu, Shaomin & Zhao, Bing & Wang, Yan, 2023. "Reliability assessment for consecutive-k-out-of-n: F retrial systems under Poisson shocks," Applied Mathematics and Computation, Elsevier, vol. 448(C).

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