Stochastic Petri nets are a form of
Petri net where the transitions fire after a probabilistic delay determined by a
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
.
Definition
A ''stochastic Petri net'' is a five-tuple ''SPN'' = (''P'', ''T'', ''F'', ''M''
0, ''Λ'') where:
# ''P'' is a set of states, called ''places''.
# ''T'' is a set of ''transitions''.
# ''F'' where ''F''
⊂ (''P'' × ''T'')
∪ (''T'' × ''P'') is a set of flow relations called "arcs" between places and transitions (and between transitions and places).
# ''M''
0 is the ''initial marking''.
# ''Λ = '' is the array of ''firing rates λ'' associated with the transitions. The firing rate, a
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
, 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
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...
. 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 EditorORIS Toolref>
References
{{Reflist
External links
Stochastic Petri Nets: an IntroductionStochastic Petri Nets
Petri nets
Formal specification languages
Models of computation
Concurrency (computer science)