Importance Sampling for Model Checking of Continuous Time Markov Chains
Benoît Barbot, Serge Haddad, Claudine Picaronny, Ecole Normale, Supérieure De Cachan, Benoît Barbot, Serge Haddad, Claudine Picaronny · 2012
Abstract—Model checking real time properties on proba-bilistic systems requires computing transient probabilities on continuous time Markov chains. Beyond numerical analysis ability, a probabilistic framing can only be obtained using simulation. This statistical approach fails when directly applied to the estimation of very small probabilities. Here combining the uniformization technique and extending our previous re-sults, we design a method which applies to continuous time Markov chains and formulas of a timed temporal logic. The corresponding algorithm has been implemented in our tool COSMOS. We present experimentations on a relevant system. Our method produces a reliable confidence interval with respect to classical statistical model checking on rare events. Keywords-statistical model checking; rare events; importance sampling; coupling; uniformization I.