The availability of an n-processor VAX cluster system is determined using a hierarchical approach that allows: (1) a closed-form answer to an apparently difficult problem to be obtained, and (2) the determination of the optimal number of processors in the cluster for a given set of cluster parameters. The approach is a two-level hierarchical model in which the lower-level model is a nine-state Markov chain that is solved in a closed form. The nine-state Markov chain is then aggregated into a three-state device analogous to a diode. Subsequently, the system availability is computed by analyzing a simple network.>
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Ibe et al. (1989) studied this question.
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