Approximate Performability Analysis Using Generalized Stochastic Petri Nets (Revised).

摘要

Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will in general also be large and complex. Therefore, calculating performability measures from these models is a difficult and time-consuming task. To alleviate the largeness and complexity problem to some extent, we use generalized stochastic Petri nets to describe the models and to automatically generate the underlying Markov reward models. Still however, many models can not be solved with the current numerical techniques, although they are conveniently and often compactly described. We discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible performability models, we derive explicit lower and upper bounds on the exact steady state performability. For a much wider class, a truncation theorem that allows one to obtain bounds for the error made in the truncation exists. We discuss this theorem in the context of approximate performability models and comment on its applicability.