Reliability analysis of interconnection networks using hierarchical composition

Based on the nature of the upper- and lower-bound block diagram models of multistage interconnection networks (MINs), a series system consisting of independent subsystems is considered. To model the reliability of such a system with online repair and imperfect coverage, the usual approach is to construct and solve a large, overall Markov model. A two-level hierarchical model is instead proposed in which each subsystem is modeled as a Markov chain and the system reliability is then modeled as a series system of independent Markov components. This technique is extended to compute the instantaneous availability of the system with imperfect coverage and online repair. Extensions to allow for transient faults and phase-type repair time distributions are straightforward. It should be possible to apply this approach to other fault-tolerant MINs and to any system that can be modeled as a series system where each subsystem has a parallel-redundant structure