Graphics Programs Reference
In-Depth Information
p
1
T
1
T
2
p
2
p
3
T
3
T
4
Figure 3.2: A timed PN system
nication network, or to the work performed on a part by a machine tool
in a manufacturing system. It is important to note that the activity is as-
sumed to be in progress while the transition is enabled. This means that
in the evolution of more complex nets, an interruption of the activity may
take place if the transition loses its enabling condition before it can actu-
ally fire. The activity may be resumed later on, during the evolution of the
system in the case of a new enabling of the associated transition. This may
happen several times until the timer goes down to zero and the transition
finally fires. As an example of this type of behaviour, consider the timed PN
dynamic behaviour since they belong to a free-choice conflict, and the firing
of either one of them disables the other (with the notation introduced in
the previous chapter, T
1
SC T
2
, and T
3
MME T
4
). In fact, if the initial
marking is the one shown in the figure, the timers of T
1
and T
2
are set to
their initial values, say θ
1
and θ
2
, with θ
1
< θ
2
; after a time θ
1
, transition
T
1
fires, and the timer of T
2
is stopped. Now the timer of T
3
is started and
decremented at constant speed until it reaches the zero value. After T
3
fires,
the conflict comprising T
1
and T
2
is enabled again. The timer of T
1
must
be set again to an initial value (possibly, again θ
1
), whereas the timer of T
2
can either resume from the point at which it was previously interrupted, i.e.,
from θ
2
−
θ
1
, or be reset to a new initial value. The choice depends on the
behaviour of the modelled system, and defines the transition memory that
will be discussed in detail in a following section.
It is possible to define a timed transition sequence or timed execution of
a timed PN system as a transition sequence (as defined in Section 2.4)
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