Asymptotically optimal component assembly plans in repairable systems and server allocation in parallel multiserver queues

V.D. Dinopoulou and C. Melolidakis

Naval Research Logistics (NRL), 2001, vol. 48, issue 8, 732-746

Abstract: T identical exponential lifetime components out of which G are initially functioning (and B are not) are to be allocated to N subsystems, which are connected either in parallel or in series. Subsystem i, i = 1,…, N, functions when at least Ki of its components function and the whole system is maintained by a single repairman. Component repair times are identical independent exponentials and repaired components are as good as new. The problem of the determination of the assembly plan that will maximize the system reliability at any (arbitrary) time instant t is solved when the component failure rate is sufficiently small. For the parallel configuration, the optimal assembly plan allocates as many components as possible to the subsystem with the smallest Ki and allocates functioning components to subsystems in increasing order of the Ki's. For the series configuration, the optimal assembly plan allocates both the surplus and the functioning components equally to all subsystems whenever possible, and when not possible it favors subsystems in decreasing order of the Ki's. The solution is interpreted in the context of the optimal allocation of processors and an initial number of jobs in a problem of routing time consuming jobs to parallel multiprocessor queues. © John Wiley & Sons, Inc. Naval Research Logistics 48: 732–746, 2001

Date: 2001
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