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p
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T
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T
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Figure 3.8: Conflicting transitions
will be discussed in the next section.
tions are in free-choice conflict. In untimed PN systems, the choice of which
of the two transitions to fire is completely nondeterministic. In the case of
timed PN systems, the conflict resolution depends on the delays associated
with transitions and is obtained through the so-called race policy: when
several timed transitions are enabled in a given marking M, the transition
with the shortest associated delay fires first (thus disabling the possible con-
flicting transitions).
Having discussed the conflict resolution policy among timed transitions, it is
important to emphasize the fact that, when two or more immediate transi-
tions are enabled in the same marking, some rule must be specified to select
the one to fire first, thus ordering the firing of immediate transitions. Two
types of rules will be used when situations of this type occur in the following.
The first one is based on a deterministic choice of the transition to fire using
the mechanism of priority, whose introduction in PNs is discussed in the
next chapter. A second mechanism consists in the association of a discrete
probability distribution function with the set of conflicting transitions. In
this case the conflicts among immediate transitions are randomly solved.
In some cases, however, it may be desirable to separate conflict resolution
from timing specification of transitions. Immediate transitions can be used
to obtain this separation. The conflict can be transferred to a barrier of
conflicting immediate transitions, followed by a set of timed transitions, as
in Fig.
3.9.
The extensive use of this technique can eliminate from a net
all conflicts among timed transitions that are simultaneously enabled in a
given marking. If this mechanism is consistently used to prevent timed
transitions from entering into conflict situations, a preselection policy of the
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