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 = (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

References
  1. Dingle, N. J.; Knottenbelt, W. J.; Suto, T. (2009). "PIPE2". ACM SIGMETRICS Performance Evaluation Review. 36 (4): 34. doi:10.1145/1530873.1530881. S2CID 3265173.
  2. Carnevali, L.; Ridi, L.; Vicario, E. (2013). "A Quantitative Approach to Input Generation in Real-Time Testing of Stochastic Systems". IEEE Transactions on Software Engineering. 39 (3): 292. doi:10.1109/TSE.2012.42. S2CID 8064028.
  3. Amparore, E. G. (2014). "A New GreatSPN GUI for GSPN Editing and CSLTA Model Checking". Quantitative Evaluation of Systems. Lecture Notes in Computer Science. Vol. 8657. pp. 170–173. doi:10.1007/978-3-319-10696-0_13. ISBN 978-3-319-10695-3.
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