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Dynamic Analysis of a Standby System with Retrial Strategies and Multiple Working Vacations

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  • Changjiang Lai

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
    Xinjiang Key Laboratory of Applied Mathematics, Xinjiang University, Urumqi 830046, China)

  • Ehmet Kasim

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
    Xinjiang Key Laboratory of Applied Mathematics, Xinjiang University, Urumqi 830046, China)

  • Ahmadjan Muhammadhaji

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
    Xinjiang Key Laboratory of Applied Mathematics, Xinjiang University, Urumqi 830046, China)

Abstract

In this paper, we developed a new standby system that combines a retrial strategy with multiple working vacations, and we performed a dynamic analysis of the system. We investigated its well−posedness and asymptotic behavior using the theory of the C 0 − semigroup in the functional analysis. First, the corresponding model was transformed into an abstract Cauchy problem in Banach space by introducing the state space, the main operator, and its domain of definition. Second, we demonstrated that the model had a unique non−negative time−dependent solution. Using Greiner’s boundary perturbation idea and the spectral properties of the corresponding operator, the non−negative time−dependent solution strongly converged to its steady−state solution. We also provide numerical examples to illustrate the effect of different parameters on the system’s reliability metrics.

Suggested Citation

  • Changjiang Lai & Ehmet Kasim & Ahmadjan Muhammadhaji, 2024. "Dynamic Analysis of a Standby System with Retrial Strategies and Multiple Working Vacations," Mathematics, MDPI, vol. 12(24), pages 1-34, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3999-:d:1547924
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    References listed on IDEAS

    as
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    8. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
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