Approximate Analysis of Hybrid Petri Nets with Probabilistic Timed Transitions

We extend the modelling formalism of Hybrid Petri nets with so-called Probabilistic Timed Transitions (PTT), whose ring times are chosen probabilistically from a discrete and nite support. In this setting, each state of the system can have several successor states, one for each element in the discrete support of the enabled PTTs; as a consequence, the state evolution is tree-shaped. We show that with this formalism it is possible to check the validity of certain prop-erties even when a large number of PTTs is present in the model. However, since the state evolution tree grows ex-ponentially in the size of the potential rings of PTTs, it is impossible to traverse the entire tree even with efficient graph traversal algorithms. Hence, we resort to checking whether the probability that a certain system property holds at a given time is more or less than a given threshold. For such probabilities, we iteratively compute an approximation, based on best-rst search, which can be rened by taking into account additional states, until we are able to decide whether the threshold is exceeded or not. We illustrate the feasibility of the approach on a model of a water renery plant with cascading failures.