Graphics Programs Reference
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transition depends only on the characteristics of the activity modelled by the
transition. Thus, the temporal specification of a timed transition requires
no information on the other (possibly conflicting) timed transitions, or on
their temporal characteristics. On the contrary, for immediate transitions,
the specification of weights must be performed considering at one time all
transitions belonging to the same conflict set. Indeed, weights are normal-
ized to produce probabilities by considering all enabled transitions within
a conflict set, so that the specification of a weight, independent of those of
the other transitions in the same conflict set, is not possible.
As a first simple example of a GSPN model, we use again the parallel system
model that was described in the Introduction in its untimed version (see
Fig. 1.8) , and earlier in this chapter in its SPN version (see Fig. 5.1) . Now
we describe the GSPN version of the model, illustrated in Fig. 5.2.
Transitions T newdata , T par1 , T par2 , T I/O , and T check are timed also in this
version of the model, and are associated with the same rates as in the SPN
model of Fig. 5.1.
Instead, transitions t start , t syn , t OK , and t KO are immediate in the GSPN
The timed transition T newdata describes the activity by which a set of new
input data is read, and it is assumed to be timed with rate λ = 0.1. As soon
as the new data are available, two processes are started in parallel with the
fork operation described by the immediate transition t start , whose weight
is set to 1. The execution of the two processes consumes exponentially
distributed amounts of time with rates µ 1 and µ 2 , so that the two timed
transitions T par1 and T par2 are associated with rates µ 1 and µ 2 , respectively.
When both processes complete, a synchronization takes place through the
join operation described by the immediate transition t syn , whose weight is
again equal to 1. The two immediate transitions t OK and t KO form a free-
choice conflict set. If the probability of inconsistent results is 0.1, a weight
1 is assigned to transition t KO , and a weight 9 is assigned to transition t OK .
If the results are not consistent (t KO fires), the whole parallel execution is
repeated, after a further control modelled by the timed transition T check ,
with rate γ. Otherwise, the output of the results is modelled by transition
T I/O , which is timed with parameter δ.
It must be observed that the values of the weights associated with t start ,
and t syn are irrelevant, because these two transitions are never enabled in
conflict with other immediate transitions. On the contrary, the choice of the
weights associated with t OK and t KO is important for the model, since they
define the probability of inconsistent results after the parallel execution.
In the next chapter, we shall observe the differences resulting from the anal-
ysis of SPN and GSPN models. We can anticipate here that the GSPN
model produces a smaller reachability set, and is thus easier to analyse than
the SPN model, while producing very similar results.
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