Graphics Programs Reference
In-Depth Information
T
1
p
1
t
2
p
a
t
3
p
b
Figure 3.6: Subnet modelling the migration of tokens from p
a
to p
b
when a
synchronizing event takes place
Figure 3.7: Non-conflicting concurrent transitions
obtained with immediate transitions, as shown in Fig.
3.6.
The firing of T
1
models the synchronizing event that generates the condition that induces
the migration of all the tokens from p
a
into p
b
. The marking of the net in
Fig.
3.6
models the state of the system just after the synchronizing event.
Transition t
3
is enabled and fires as many times as the number of tokens in
p
a
, thus removing all the tokens from p
a
and adding the same number of
tokens to p
b
. Then, the lack of tokens in p
a
deactivates the inhibitor arc to
t
2
, so that t
2
becomes enabled and fires, removing the token from p
1
. Tokens
can now be again collected in place p
a
, waiting for a new synchronization.
3.3
Parallelism and Conflict
The introduction of temporal specifications in PN models must not reduce
the modelling capabilities with respect to the untimed case. Let us verify
this condition as far as parallelism and conflict resolution are considered.
Pure parallelism can be modelled by two transitions that are independently
enabled in the same marking. The evolution of the two activities is measured
by the decrement of the clocks associated with the two transitions. Consider
completely independent concurrent activities. When one of the timers (for
example that associated with T
1
) reaches zero, the transition fires and a new
marking is produced. In the new marking, transition T
2
is still enabled and
its timer can either be reset or not; different ways of managing this timer
mainly to be able to implement the flushing of all tokens from one place using a single
action.
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