Discrete-continuous modeling using Hybrid Stochastic Petri Nets

We present Hybrid Stochastic Petri Nets (HSPNs) as a revision and extension of the Fluid Stochastic Petri Nets (FSPNs). HSPNs can be used for modeling dynamic systems that comprise both discrete and continuous quantities. Discrete state changes are assumed to be Markovian and continuous variables are assumed to be deterministic. HSPNs are designed to improve the clarity and consistency of the graphical representation of the net. This is achieved by the introduction of a new class of transition and by a re-formulation of the enabling and firing rules. By utilizing a different numerical solution technique, we can overcome certain modeling limitations concerning instantaneous changes of state. The technique is based on an approximation of the hybrid system using a discrete-state stochastic process, from which a continuous-time Markov chain (CTMC) can be derived. Examples demonstrate the enhancements contained in the new formalism.