Stochastic Petri net explained

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 = (P, T, F, M₀, Λ) where:

1. P is a set of states, called places.
2. T is a set of transitions.
3. F where F ⊂ (P × T) ∪ (T × P) is a set of flow relations called "arcs" between places and transitions (and between transitions and places).
4. M₀ is the initial marking.
5. Λ = is the array of firing rates λ associated with the transitions. The firing rate, a random variable, can also be a function λ(M) 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.

Software tools

• Platform Independent Petri net Editor^[1]
• ORIS Tool^[2]
• GreatSPN^[3]

External links

• Stochastic Petri Nets: an Introduction
• Stochastic Petri Nets

Notes and References

1. Dingle . N. J. . Knottenbelt . W. J. . Suto . T. . 10.1145/1530873.1530881 . PIPE2 . ACM SIGMETRICS Performance Evaluation Review . 36 . 4 . 34 . 2009 . 3265173 .
2. 10.1109/TSE.2012.42. A Quantitative Approach to Input Generation in Real-Time Testing of Stochastic Systems. IEEE Transactions on Software Engineering. 39. 3. 292. 2013. Carnevali . L. . Ridi . L. . Vicario . E. . 8064028.
3. Book: 10.1007/978-3-319-10696-0_13. A New GreatSPN GUI for GSPN Editing and CSLTA Model Checking. Quantitative Evaluation of Systems. 8657. 170–173. Lecture Notes in Computer Science. 2014. Amparore . E. G. . 978-3-319-10695-3.