Graphics Programs Reference
In-Depth Information
4
PETRI NETS WITH
PRIORITY
We noted in the previous chapter that the presence of both timed and imme-
diate transitions in the same timed PN model naturally leads to the concept
of priority. On one hand, the availability of different priority levels in PN
models increases their descriptive power, thus giving more flexibility and
freedom to the modeller. On the other hand, an extension of the standard
analysis techniques to priority PN models is necessary. In this chapter we
first extend the PN model formalism to include several priority levels for
transitions and define the dynamics of this new formalism; then we high-
light the influence that priorities have on the notion of conflict and related
concepts; finally we discuss which of the analysis techniques that are appli-
cable to PN models without priorities still apply to this extended model,
and which must be revised in order to account for the peculiarities induced
by priority rules.
Although the models considered in this chapter are untimed, the introduc-
tion of some concept is motivated in terms of its use in the GSPN framework.
4.1
Definition and Dynamics
The formal definition of a PN model with priority is similar to the usual
definition of a PN model given in Definition 2.1.1; the only difference is the
introduction of a priority function that assigns to each transition a natural
number corresponding to its priority level.
Definition 4.1.1 A PN model with priority is a 9-tuple
M π = { P,T,I,O,H, Π,PAR,PRED,MP } (4.1)
where
•M = { P,T,I,O,H,PAR,PRED,MP } defines a PN model and
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