Parametric reachability analysis of Hybrid Petri nets with general transitions

By Anne Remke

In this lecture we present a new and efficient concept for the computation of all reachable locations of a model: Parametric reachability analysis. This technique separates the deterministic and the stochastic components of a HPNG by conditioning the deterministic evolution on the samples drawn from the probability distributions associated to general transitions. After all reachable parametric locations have been computed, several important performance metrics (such as the distribution of fluid over time) can be

derived by deconditioning: that is by integrating over the values of the probability distributions that characterize the general transitions. To simplify the presentation, in this work we concentrate only on systems characterized by a single general transition. However the proposed methodology can be extended to cases with more than one generally distributed transition. As opposed to similar SHM solution algorithms, our technique is not affected by the number of fluid places, which can then be arbitrary.