Stochastic disaster recovery systems with external resources

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. (C) 2002 Elsevier Science Ltd. All rights reserved.