Probabilistic validation using worst event driven and importance sampling simulation

Probabilistic validation is an approach for the validation of highly dependable and complex systems. It relies on a partial analysis on a system model and tries to prove that the failed event occurrences has a sufficiently low probability. We define a probabilistic validation method using worst event driven and an importance sampling simulation. The system which must be validated is modeled by a stochastic Petri net. An efficient simulation of the net must be able to sample complex and improbable trajectories which eventually reach critical markings. Two problems have to be solved. The sequence of transition firings which may lead to critical markings must be characterized ad the Petri net level. The second problem is to sample these sequences and to build an accurate estimate of the incorrect behavior probability. We discuss several simulation algorithms in the Markovian and non-Markovian cases. We show the effectiveness of these techniques on the validation of several examples