Graphics Programs Reference
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p 1
T
p 2
Figure 3.1: A timed transition
without losing, except for some special cases, the possibility of performing
quantitative and qualitative studies.
3.2
Timed Transitions
The firing of a transition in a PN model corresponds to the event that
changes the state of the real system. This change of state can be due to
one of two reasons: it may either result from the verification of some logical
condition in the system, or be induced by the completion of some activity.
Considering the second case, we note that transitions can be used to model
activities, so that transition enabling periods correspond to activity execu-
tions and transition firings correspond to activity completions. Hence, time
can be naturally associated with transitions.
We now look in some detail at the semantics of transitions with associated
temporal specifications that are called timed transitions; they are graphically
represented by boxes or thick bars and are denoted with names that usually
start with T.
Consider, as the simplest possible example, the timed transition T in Fig. 3.1.
Transition T can be associated with a local clock or timer. When a token
is generated in place p 1 , T becomes enabled, and the associated timer is
set to an initial value. The timer is then decremented at constant speed,
and the transition fires when the timer reaches the value zero. The timer
associated with the transition can thus be used to model the duration of
an activity whose completion induces the state change that is represented
by the change of marking produced by the firing of T. The type of activity
associated with the transition, whose duration is measured by the timer,
depends on the modelled real system: it may correspond to the execution
of a task by a processor, or to the transmission of a message in a commu-
 
 
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