From Petri Nets to Stochastic Petri Nets
Samir Tigane, Laid Kahloul, Abdelhamid Mellouk · 2025
Petri nets (PNs) represent a well-known and versatile paradigm for the modeling and verification of various discrete-event systems. This chapter introduces some intuitive aspects of Petri nets and describes stochastic Petri nets (SPN). It briefly presents transition systems and temporal logic. A Petri net is said to be live if every transition can always fire again in the future at any reachable marking. A marking of a Petri net is a home state if it can be reached from all reachable markings. The chapter considers two major classes of SPN, namely, SPN having exponential law, generalized SPN and their quantitative properties. Stochastic processes are used to model the evolution of systems that exhibit probabilistic behaviors. A particular class of stochastic processes, called Markov process, has found a wide range of applications in the research community.