Willem R.W. Scheinhardt

Rare event simulation for highly dependable systems with fast repairs

Stochastic model checking has been used recently to assess, among others, dependability measures for a variety of systems. However, the employed numerical methods, as, e.g., 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 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.

Automated rare event simulation for stochastic petri nets

We introduce an automated approach for applying rare event simulation to stochastic Petri net (SPN) models of highly reliable systems. Rare event simulation can be much faster than standard simulation because it is able to exploit information about the typical behaviour of the system. Previously, such information came from heuristics, human insight, or analysis on the full state space. We present a formal algorithm that obtains the required information from the high-level SPN-description, without generating the full state space. Essentially, our algorithm reduces the state space of the model into a (much smaller) graph in which each node represents a set of states for which the most likely path to failure has the same form. We empirically demonstrate the efficiency of the method with two case studies.

On hypothesis testing for statistical model checking

Hypothesis testing is an important part of statistical model checking (SMC). It is typically used to verify statements of the form

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