Approximate Availability Analysis of VAXcluster Systems

We solve for the availability of an n-processor VAXcluster system using a hierarchical approach that allows us to: 1) obtain a closed-form answer to an apparently difficult problem, and 2) determine the optimal number of processors in the cluster for a given set of cluster parameters. Our novel approach is a 2-level hierarchical model in which the lower-level model is a 9-state Markov chain that is solved in a closed form. The 9-state Markov chain is then aggregated into a 3-state device analogous to a diode. Subsequently, the system availability is computed by analyzing a simple network.