A non-regenerative model of a redundant repairable system: bounds for the unavailability and asymptotical insensitivity to the lifetime distribution. (1996)

• Record Type: Journal Article
• Authors: Kovalenko, Igor N.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 2(1996)
• Page Start: 97
• Page End: 105
• Publication Date: 1996
• Subjects: availability -- light traffic -- perturbation analysis -- redundancy -- repairable systems -- non-regenerative models -- fast repair -- renewal rate; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000135
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In this paper we investigate steady state reliability parameters of an F : r -out-of-N redundant repairable system with m ( 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 and m channels, respectively. Each of the N customers pass cyclically from one node to the other; the service time distributions are of a general form for both the nodes. It is an N -component system with a general distribution A ( t ) of free-of-failure periods of the components is considered. Failed components are repaired by an m -channel queueing system with a general distribution B ( t ) of repair times. The system is assumed to be failed if and only if the number of failed components is at least r . (Only the rather difficult case r ≥ m + 1 is considered.) Let μ be the intensity of the stationary point process of the occurrences of (partial) busy periods within which systems failures happen at least once, and let Q be the steady-state unavailability of the system. Two-sided bounds are established for Q and μ based 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.