Reliability evaluation and simulation of shock model for repairable retrial systems with $$N$$ N -policy

Jian Liu, Linmin Hu () and Yiyan Zhou
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Jian Liu: Yanshan University
Linmin Hu: Yanshan University
Yiyan Zhou: Yanshan University

Operational Research, 2025, vol. 25, issue 2, No 24, 35 pages

Abstract: Abstract System design based on retrial mechanism has extensive applications in the field of computer networks, and the N-policy is a crucial maintenance strategy in the design of repairable system. The impact of external shocks is unavoidable for network communication systems. Based on such actual situations, this paper proposes a shock model for a repairable $$k$$ k -out-of- $$n$$ n :G retrial systems with the N-policy. Component failure is caused by both self-degradation and external shocks. The shock may cause multiple component failures at the same time. Based on stochastic process theory, state probability equations of the system are constructed, and steady-state indexes and the state probabilities of the system are evaluated. A simulation algorithm for the developed shock model is proposed, by utilizing the Monte Carlo method. The running process of the system is simulated by numerical experiments, and the analytical solutions of the system steady-state indexes are compared with the simulated values. In order to show the influence of different parameters on the steady-state indexes, the sensitivity analysis is conducted on system availability and the number of operating components. Based on the constructed system cost function, the optimal number of operating components and the optimal N-policy value of the system are analyzed and determined.

Keywords: $$N$$ N -policy; Retrial; $$k$$ k -out-of- $$n$$ n :G; Shock; Monte Carlo method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12351-025-00931-3

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