PETRI NETS AND THEIR PROPERTIES - Modelling with Generalised Stochastic Petri Nets - page 25

When the RS is not finite, the RG is not finite as well. This happens when
some place in the PN system can contain an unlimited number of token s 2 .

2.3.3 Modelling issues

Let's now come back to our readers & writers example. The readers &
writers PN model in Fig. 2.1 refers to a system with K active processes.
The PN places define the local situations of the system components:

• p 1 may contain tokens modelling processes performing activities that
are not related to the database access;

• p 2 may contain tokens modelling processes that need the database,
but that have not yet specified whether their access implies a write or
a read;

• p 3 may contain tokens modelling processes that need the database for
a read;

• p 4 may contain tokens modelling processes that need the database for
a write;

• p 5 may contain one token that specifies the condition “no write in
progress”;

• p 6 may contain tokens modelling processes that are accessing the
database for a read;

• p 7 may contain a token modelling the process that is accessing the
database for a write.

Note that, since a token in p 5 expresses the condition that no process is
performing a write, if the model has to represent a readers & writers model,
then an obvious restriction on the initial marking is that if p 5 is marked, p 7
is not, and viceversa.
In general, as we already noted in Chapter 1, places in PN models can be
used to describe either (boolean) conditions (e.g., no user is performing a
write access), or physical locations that can contain objects (e.g., a buffer),
or logical situations for some object (e.g., reading). Places of the first kind
can contain either one or zero tokens, corresponding to the possible truth
values of the modelled conditions. In our example, place p 5 belongs to this
category: it represents the condition “no write is in progress”. Places of the
other kinds in general may contain several tokens representing the objects

A finite representation for infinite RG can be given, by providing only partial infor-
mation with the coverability tree . A description of this structure and of an algorithm for
constructing it can be found in [57] . The PN systems considered in the following chapters
are all bounded, so that we always use the classical reachability graph construction.

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