Asymptotic analysis of a priority model with backup and repair

Abstract

One of the problems in mathematical reliability theory is to estimate the reliability of systems with repair. In general, the problem can be stated in the following terms. Given is a system of n elements; one of the operational elements in the system should be busy at any given time. In case of failure, the failed element is routed to a repair unit, repaired, and returned to the system. The state of the system at any given moment is defined by a binary vector which shows the operational and the failed elements at that moment. The system state set is partitioned into two subsets -operational and failed states. Over time, the system repeatedly switches from operational to failed and back. A major problem in reliability theory is to compute or estimate the basic reliability characteristics, e.g., the time distributions of the operational and the failed states and their means. In mathematical terms, a model of this kind is a queueing model with customers represented by failed elements routed for repair and service represented by the repairs on these elements.