Graphics Programs Reference
In-Depth Information
The former modelling choice implies no specification of ordering among the
conflict resolutions associated with these three transition pairs in case they
are enabled together in a given marking. The latter modelling choice in-
stead precisely specifies such an ordering. Notice that since t
2
and t
3
have
the same input set, it would be meaningless not to assign them the same
priority level: indeed if π
2
> π
3
, t
3
could not be live in any marking, and
viceversa. The same observation applies to t
8
and t
9
. On the contrary, as-
signing different priority levels to t
4
and t
5
, we can model a system where
readers (writers) have priority over writers (readers).
Let us consider two examples of priority assignment, and discuss the corre-
sponding interpretation:
•
π
2
= π
3
= 2, π
4
= π
5
= 3,π
8
= π
9
= 1; this priority assignment
means that whenever a process chooses to make an access in a given
mode, the corresponding access should immediately start, provided
it is enabled, before any other process can make its choice. In other
words, whenever an immediately executable access mode is chosen, the
access choice and start events constitute an atomic action.
•
π
2
= π
3
= 2, π
4
= π
5
= 1,π
8
= π
9
= 3; this priority assignment means
that when several processes are going to choose their access mode,
then all of them must make their choice before any access can start.
Both these modelling alternatives are reasonable: the modellist may choose
one or neither, according to the actual system behaviour. For example, let us
choose the first alternative and play the token game on the resulting model.
To play the token game, we need to specify completely the initial marking
M
0
by assigning a suitable value to the parameter K; in this example we
assume K = 3. Let us play the token game starting from marking M
1
,
reachable from M
0
, defined below.
M
1
= p
1
+ p
4
+ p
7
Marking M
1
is tangible; indeed, two timed transitions are enabled in this
marking: t
1
and t
7
. Let us fire transition t
7
; we reach the vanishing marking
M
2
= p
1
+ p
4
+ p
5
+ p
8
from which t
5
can fire. Observe that in this marking transitions t
1
, t
8
and
t
9
have concession but they are not enabled.
Let us fire transition t
5
; we
reach the vanishing marking
M
3
= p
1
+ p
7
+ p
8
in which t
8
and t
9
are enabled.
If now t
9
is fired we reach the vanishing
marking
M
4
= p
1
+ p
2
+ p
7
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