Graphics Programs Reference
In-Depth Information
A simple example will help the reader understand the three semantics. Con-
enablings are associated with three activities whose durations are 3, 2, and
4 time units, respectively. We describe next the detailed behaviour of the
net, considering the three different semantics with reference to Fig.
3.14
that illustrates the firing epochs.
1. Single-server semantics: the serial execution of the activities induces
the following sequence of events:
•
t = 0: T
1
is enabled and the first activity starts.
•
t = 3: the first activity (duration 3) ends, T
1
fires and the second
activity starts.
•
t = 5: the second activity (duration 2) ends, T
1
fires and the third
activity starts.
•
t = 9: the third activity (duration 4) ends and T
1
is disabled.
2. Infinite-server semantics: the parallel execution of the activities in-
duces the following sequence of events:
•
t = 0: T
1
is enabled and all the activities start.
•
t = 2: T
1
fires because of the completion of the second activity
(duration 2).
•
t = 3: T
1
fires because of the completion of the first activity (du-
ration 3).
•
t = 4: T
1
fires because of the completion of the third activity
(duration 4), and it is disabled.
3. Multiple-server semantics: in this case we assume that the maximum
parallelism is K = 2. This induces the following sequence of events:
•
t = 0: T
1
is enabled and the first two activities start.
•
t = 2: T
1
fires because of the completion of the second activity
(duration 2) thus the third activity can start.
•
t = 3: T
1
fires because of the completion of the first activity (du-
ration 3).
•
t = 6: T
1
fires because of the completion of the third activity
(duration 4), and it is disabled.
The introduction of these different firing semantics permits the definition of
PN systems that are graphically simple without losing any of the character-
istics that allow the analysis of their underlying behaviours.
An example of this type of situation is represented by the well-known queue-
ing network model of a timesharing computer system with a fixed number
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