Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 2, Pages 97-105
A non-regenerative model of a redundant repairable system: bounds for the unavailability and asymptotical insensitivity to the lifetime distribution
STORM Research Centre, University of North London, London N7 8DB, UK
Received 1 October 1995; Revised 1 February 1996
Copyright © 1996 Igor N. Kovalenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we investigate steady state reliability parameters of an -out-of- redundant repairable system with 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 channels, respectively. Each of the customers pass cyclically from one
node to the other; the service time distributions are of a general form for both the
It is an -component system with a general distribution of free-of-failure periods of the components is considered. Failed components are repaired by
an -channel queueing system with a general distribution of repair times.
The system is assumed to be failed if and only if the number of failed
components is at least . (Only the rather difficult case is considered.)
Let 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
be the steady-state unavailability of the system.
Two-sided bounds are established for and 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.