INTRODUCTION - Modelling with Generalised Stochastic Petri Nets - page 3

t switch of f

p on p of f

t switch on

Figure 1.1: PN description of a switch

Tokens are indistinguishable markers that reside in places, and are used to
specify the PN state (usually called the PN marking). If a place describes
a condition, and thus can contain either zero or one token, the condition is
true if a token is present in the place, and false otherwise. If a place defines
a situation, the number of tokens contained in the place is used to specify
the situation.
A PN model 2 is graphically represented by a directed bipartite graph in
which places are drawn as circles, and transitions are drawn as either bars
or boxes. Tokens are drawn as black dots within places. A very simple
first example of a PN model is given in Fig. 1.1, where two places p on and
p of f , and two transitions t switch on and t switch of f are connected with four
arcs. Both places define conditions (that we may call the “on condition”
and “off condition”). The state depicted in the drawing is such that place
p of f contains one token; thus the “off condition” is true; instead, since place
p on is empty, the “on condition” is false.
The dynamic behaviour of the PN is governed by the firing rule. A tran-
sition can fire (an event takes place) if all the transition input places (i.e.,
those places connected to the transition with an arc whose direction is from
the place to the transition), contain at least one token. In this case the
transition is said to be enabled. The firing of an enabled transition removes
one token from all of its input places, and generates one token in each of
its output places (i.e., those places connected to the transition with an arc
whose direction is from the transition to the place). When arc weights larger

In this chapter, with the term “PN model” we indicate a model of a real system
that uses PNs as the description paradigm. In the rest of the topic, starting with the
next chapter, the term “PN model” will be used in a formal manner, to indicate a Petri
net with a parametric marking. The term “PN system” will indicate a Petri net with a
numeric marking, and the term “Petri net” will be used for the cases in which the marking
is not considered.

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