A non-regenerative model of a redundant repairable system: bounds for the unavailability and asymptotical insensitivity to the lifetime distribution

[摘要] In this paper we investigate steady state reliability parameters of anF:r-out-of-Nredundant repairable system withm(1≤m≤r−1)repair channels in light traffic conditions. Such a system can also be treated as a closed queueing network of a simple kind. It includes two nodes, with infinite number of channels andmchannels, respectively. Each of theNcustomers pass cyclically from one node to the other; the service time distributions are of a general form for both the nodes.It is anN-component system with a general distributionA(t)of free-of-failure periods of the components is considered. Failed components are repaired by anm-channel queueing system with a general distributionB(t)of repair times. The system is assumed to be failed if and only if the number of failed components is at leastr. (Only the rather difficult caser≥m+1is considered.)Letμbe the intensity of the stationary point process of the occurrences of (partial) busy periods within which systems failures happen at least once, and letQbe the steady-state unavailability of the system.Two-sided bounds are established forQandμbased on the behavior of the renewal rate of an auxiliary renewal process. The bounds are used for deriving some asymptotical insensitivity properties in light traffic conditions.

[学科分类] 应用数学