Hybrid modelling with second order fluid stochastic Petri nets

Stochastic Petri nets have been extended for the modelling of hybrid systems by adding fluid places, that are filled and emptied continuously at a random (normally distributed) rate. The flow rates as well as the discrete transition rates may depend on the content a fluid place holds. The dynamics of the model are described by second order partial differential equations, that can be solved by using an implicit Crank-Nicolson scheme. Reward measures such as the fluid throughput can be computed from the continuous part of the solution. As an example we present a model of a chemical reactor