Generalized Stochastic Petri Nets

Description

Definition

Examples

References

 

 

 

Description:

Stochastic Petri Nets are marked Petri Nets with timed transitions. Moreover timed transitions are determined by a stochastic clock structure, and the transition function is probabilistic.

 

The word Generalized is sometimes added when immediate (not timed) transitions are also  included in the formalism.

Formal Definition:

A Generalized Stochastic Petri Net is a tuple

                        (P, T, T’, I, O, L, w, M, p, p0, G)

where

P – is a finite set of places,

T – is a finite set of transitions,

T’ – is a subset of T – set of immediate transitions,

I(e) – a set of normal input places for transition e,

O(e) – a set of output places for transition e,

L(e) – a set of inhibitor places for transition e,

w – a weight function for arcs,

M – marking,

p(s1; s, E*) – is a state transition probability, when events in E* (subset of E) occur simultaneously, 

p0 – a pmf of an initial marking (state),

G ={Gi , i∈E } – is a stochastic clock structure.

 

Note1: Another feature may be (and usually is) incorporated in this formalism – clock rates that in general depend on states. We are not considering this feature for now.

 

???? Events –Transitions ???? p(s’; s, e’) ????

Examples:

 

 

References:

  1. P. J. Haas, Stochastic Petri Nets, Springer, 2002.
  2. W. Reisig, G. Rozenberg (eds.), Lectures on Petri Nets I: Basic Models, Springer LNCS 1491, 1998.
  3. W. Reisig, G. Rozenberg (eds.), Lectures on Petri Nets II: Applications, Springer LNCS 1492, 1998.
  4. P. Buchholz, On-line lectures on Petri Nets,

http://www.iai.inf.tu-dresden.de/ms/lvbeschr/vwahl_petri.html