Reliability Analysis of Interconnection Networks Using Hierarchical Composition

ConclusionsBased on the nature of the upperand lower-bound block diagram models of Multistage Interconnection Networks (MINs), we generalize and consider a series system consisting of independent subsystems. In order to model the reliability of such a system with on-line repair and imperfect coverage, the usual approach is to construct and solve a large, overall Markov model. Instead, we propose a 2-level hierarchical model 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. We extend this technique to compute the instantaneous availability of the system with imperfect coverage and on-line repair. We have thus extended the size of problems for which reliability/availability analysis, incorporating imperfect coverage and on-line repair, can be computed without resorting to a large, 1-level Markov model. Extensions to allow for transient faults and phase-type repair time distributions are straightforward. It should be possible to apply our 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.