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

Changjiang Lai, Ehmet Kasim () and Ahmadjan Muhammadhaji
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Changjiang Lai: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Ehmet Kasim: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Ahmadjan Muhammadhaji: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Mathematics, 2024, vol. 12, issue 24, 1-34

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.

Keywords: standby system with working vacation; C 0 ?semigroup; well?posedness; asymptotic behavior; Dirichlet operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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