Graphics Programs Reference
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in which transitions t
2
and t
3
are enabled. Firing transition t
2
a new tangible
marking is finally reached:
M
5
= p
1
+ p
3
+ p
7
t
5
,t
9
,t
2
−→
M
5
takes zero time: i.e., an external observer who is only capable of perceiving
states where the system spends some time, would see the previously de-
scribed state evolution as an atomic transition leading from M
1
to M
5
(i.e.,
markings M
2
of priority level 3, M
3
of priority level 1, and M
4
of priority
level 2 would vanish).
We could extend this concept of observability to higher levels of priority, so
that a level j observer can perceive the firing of transitions up to priority
level j, while firing sequences of higher priority transitions are seen as indi-
visible actions, and markings of priority level greater than j become, from
his point of view, “vanishing”.
Choosing the second priority assignment for t2, t
3
, t
4
, t
5
, t
8
, and t
9
, the
firing sequence leading from M
2
to M
5
would be
in which t
1
and t
7
are enabled. Notice that the firing sequence M
2
t
9
−→
M
0
3
t
2
−→
M
0
4
t
5
−→
M
5
M
2
where marking M
2
enables t
8
and t
9
(hence it has priority level 3), marking
M
0
3
enables t
2
and t
3
(hence it has priority level 2), marking M
0
4
enables t
4
and t
5
(hence it has priority level 1).
Notice that the main difference between the two firing sequences just de-
scribed, is in the firing of transition t
5
: it is deterministic in the first firing
sequence while it implies a conflict resolution in the second one.
4.2
Conflicts, Confusion and Priority
In this section we study how the notions of conflict and confusion are
modified when a priority structure is associated with transitions. The j-
observability concept just introduced in the previous section, helps in un-
derstanding the new notions. Conflict and related concepts are important
in the framework of GSPNs where conflict resolution is performed proba-
bilistically rather than using nondeterminism. In GSPN models, a suitable
probability distribution is associated with sets of conflicting transitions for
this purpose.
For example, suppose that in the readers & writers system, 30% of the
incoming requests are reads, while 70% are writes. Then, every time there
is a conflict between t
2
and t
3
, the probability that the former is fired should
be 0.3 while the probability that the latter is fired should be 0.7. Since t
2
and t
3
are always enabled together, this requirement can be included in the
model by associating a weight equal to 0.3 with t
2
and a weight equal to 0.7
with t
3
.
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