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Keywords = k/n(G) retrial system

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53 pages, 473 KB  
Article
Analysis of a k/n(G) Retrial System with Multiple Working Vacations
by Changjiang Lai, Rena Eskar and Ehmet Kasim
Axioms 2025, 14(11), 853; https://doi.org/10.3390/axioms14110853 - 20 Nov 2025
Viewed by 214
Abstract
In this paper, a k/n(G) retrial system with multiple working vacations is considered, and a mathematical model of the system is established by supplementary variable method, and a dynamic analysis of the system is carried out. Firstly, the [...] Read more.
In this paper, a k/n(G) retrial system with multiple working vacations is considered, and a mathematical model of the system is established by supplementary variable method, and a dynamic analysis of the system is carried out. Firstly, the model is transformed into an abstract Cauchy problem in Banach space by introducing the state space, main operator and its definition domain. Secondly, the C0-semigroup theory in functional analysis and the spectral theory of linear operators are used to prove that the main operator of the model generates a positive contraction C0-semigroup, which leads to the existence of a unique, non-negative time-dependent solution of the system that satisfies the probabilistic properties. Finally, Greiner’s boundary perturbation idea and the spectral properties of the corresponding operators are used to show that the time-dependent solution strongly converges to its steady-state solution. Full article
18 pages, 402 KB  
Article
Shock Model of K/N: G Repairable Retrial System Based on Discrete PH Repair Time
by Xiaoyun Yu, Linmin Hu and Zebin Hu
Axioms 2024, 13(12), 814; https://doi.org/10.3390/axioms13120814 - 21 Nov 2024
Viewed by 893
Abstract
A discrete time modeling method is employed in this paper to analyze and evaluate the reliability of a discrete time K/N: G repairable retrial system with Bernoulli shocks and two-stage repair. Lifetime and shocks are two factors that lead to [...] Read more.
A discrete time modeling method is employed in this paper to analyze and evaluate the reliability of a discrete time K/N: G repairable retrial system with Bernoulli shocks and two-stage repair. Lifetime and shocks are two factors that lead to component failure, and both of them can lead to the simultaneous failure of multiple components. When the repairman is busy, the newly failed component enters retrial orbit and retries in accordance with the first-in-first-out (FIFO) rule to obtain the repair. The repairman provides two-stage repair for failed components, all of which require basic repair and some of which require optional repair. The discrete PH distribution controls the repair times for two stages. Based on discrete time stochastic model properties, priority rules are defined when multiple events occur simultaneously. The state transition probability matrix and state set analysis are used to evaluate the system performance indexes. Numerical experiments are used to illustrate the main performance indexes of the developed discrete time model, and the impact of each parameter variation on the system indexes is examined. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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