Availability analysis of repairable n-server ni-replicated systems

This paper develops an exact closed-form expression for the steady-state availability of a repairable, n-server system in which the ith server contains ni identical, reconfigurable, breakdown-prone units. The approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. The paper illustrates this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.