Stochastic Petri net

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Stochastic Petri nets are a form of Petri net where the transitions fire after a probabilistic delay determined by a random variable.

Definition[edit]

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[edit]

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[edit]

References[edit]

  1. ^ Dingle, N. J.; Knottenbelt, W. J.; Suto, T. (2009). "PIPE2". ACM SIGMETRICS Performance Evaluation Review 36 (4): 34. doi:10.1145/1530873.1530881.  edit

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