Graphics Programs Reference
In-Depth Information
π
2
= 2
π
4
= 3
π
6
= 0
t
2
p
3
t
4
p
6
t
6
π
8
= 1
π
1
= 0
p
5
p
8
t
8
p
1
t
1
p
2
K
t
9
t
3
p
4
t
5
p
7
t
7
π
9
= 1
π
3
= 2
π
5
= 3
π
7
= 0
Figure 4.1: A modified readers & writers model
without priority. This implies that some properties are not influenced by
the addition of a priority structure, while others are changed in a well-
determined way, as we shall see in a while.
An example — Let us consider a modified version of the readers & writ-
ers example depicted in Fig.
4.1.
The difference with respect to the former
model concerns the events following the end of an access: in the new PN
model a process can either execute in its local memory for a while before
requesting a new access (sequence of transitions t
8
, t
1
, followed by the choice
between t
2
and t
3
) or immediately proceed to the next access (transition t
9
followed by the choice between t
2
and t
3
).
A possible assignment of transition priorities that is consistent with the in-
terpretation of this PN model as a representation of the readers & writers
system is the following: π
1
= π
6
= π
7
= 0, and π
2
,π
3
,π
4
,π
5
,π
8
,π
9
> 0.
This priority specification is consistent with the timing specification given
assigned the lowest priority level (i.e., priority 0) reserved to timed tran-
sitions. Transitions t
2
and t
3
, that represent the choice between the two
access modes, transitions t
4
and t
5
, that represent the start of either access
mode, and transitions t
8
and t
9
, that represent the choice between execut-
ing in the local memory for a while and immediately proceeding to the next
access, are assigned a priority greater than zero (i.e., they are defined to be
immediate), meaning that the corresponding actions are assumed to take
place in zero time. Now we could choose either to assign priority level one
to all immediate transitions, or to assign a given priority level to t
2
and
t
3
, a different priority level to t
4
and t
5
, and yet another one to t
8
and t
9
.
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