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Stochastic disaster recovery systems with external resources. (English) Zbl 1052.90024

Summary: This paper deals with a complex reliability system of main unreliable, spare, and auxiliary spare machines, subject to random breakdowns, repairs, and two replacement policies: one for busy, and another for idle or vacation periods. During vacation periods, when the system performs a mandatory routine maintenance, auxiliary machines are being used for back-ups; the information on the system is naturally delayed. We utilize an analog of the \(N\)-policy to restrict the usage of auxiliary machines to some reasonable quantity. Analytically, tractable results are obtained by using a duality principle (which enables us to treat a more rudimentary system), semiregenerative analysis, and the theory of fluctuations of multivariate marked renewal processes. The results are demonstrated in the framework of optimization problems.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
90C15 Stochastic programming
90B22 Queues and service in operations research
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