Stochastic Petri net
Stochastic Petri nets are a form of Petri net where the transitions fire after a probabilistic delay determined by a random variable.
Definition
A stochastic Petri net is a five-tuple SPN = where:- P is a set of states, called places.
- T is a set of transitions.
- F where F ⊂ ∪ is a set of flow relations called "arcs" between places and transitions.
- M0 is the initial marking.
- Λ = is the array of firing rates λ associated with the transitions. The firing rate, a random variable, can also be a function λ of the current marking.
Correspondence to Markov process
The reachability graph of stochastic Petri nets can be mapped directly to a Markov process. It satisfies the Markov property, since its states depend only on the current marking.Each state in the reachability graph is mapped to a state in the Markov process, and the firing of a transition with firing rate λ corresponds to a Markov state transition with probability λ.