Five Performability Algorithms: A Comparison

Since the introduction by John F. Meyer in 1980, various algorithms have been proposed to evaluate the performability distribution. In this paper we describe and compare five algorithms that have been proposed recently to evaluate this distribution: Picard's method, a uniformisation-based method, a path-exploration method, a discretisation approach and a fully Markovian approximation. As a result of our study, we recommend Picard's method not to be used (due to numerical stability problems). Furthermore, the path exploration method turns out to be heavily dependent on the branching structure of the Markov-reward model under study. For small models, the uniformisation method is preferable; however, its complexity is such that it is impractical for larger models. The discretisation method performs well, also for larger models; however, it does not easily apply in all cases. The recently proposed Markovian approximation works best, even for large models; however, error bounds cannot be given for it.