Rare event simulation for highly dependable systems with fast repairs

Probabilistic model checking has been used recently to assess, among others, dependability measures for a variety of systems. However, the numerical methods employed, such as those supported by model checking tools such as PRISM and MRMC, suffer from the state-space explosion problem. The main alternative is statistical model checking, which uses standard Monte Carlo simulation, but this performs poorly when small probabilities need to be estimated. Therefore, we propose a method based on importance sampling to speed up the simulation process in cases where the failure probabilities are small due to the high speed of the system's repair units. This setting arises naturally in Markovian models of highly dependable systems. We show that our method compares favourably to standard simulation, to existing importance sampling techniques, and to the numerical techniques of PRISM.