Interval Availability Analysis Using Denumerable Markov Processes: Application to Multiprocessor Subject to Breakdowns and Repair

Interval availability is a dependability measure defined by the fraction of time during which a system is operational over a finite observation period. The computation of its distribution allows the user to ensure that the probability that its system will achieve a given availability level is high enough. The system is assumed to be modeled as a Markov process with countable state space. We propose a new algorithm to compute the interval availability distribution. One of its main advantages is that, in some cases, it applies even to infinite state spaces. This is useful, for instance, in case of models taking into account contention with unbounded buffers. This important feature is illustrated on models of multiprocessor systems subject to breakdowns and repair. When the model is finite, we show through a numerical example that the new technique can perform very well. Index terms Denumerable Markov processes, dependability prediction, interval availability distribution, repairable computer systems, transient analysis, queues with breakdowns, uniformization.