Enhancing hybrid state Petri nets with the analysis power of stochastic hybrid processes

Abstract

This paper presents a power hierarchy of Petri nets and stochastic hybrid processes. At the left-hand-side of this power hierarchy are stochastic Petri net models at the bottom, and high level Petri nets at the top. At the right-hand-side of this power hierarchy are Markov chains at the bottom, and generalized hybrid state Markov processes at the top. The Petri net side of the power hierarchy makes it possible to specify a stochastic system model in a compositional way. The Markov process side of the power hierarchy exploits the available stochastic analysis tools. Between the Petri nets on the left and the Markov processes on the right are mathematical one-to-one mappings, which enable taking advantage of both the modelling power of hybrid state Petri nets and the analysis capability of stochastic hybrid Markov processes.