Graphics Programs Reference

In-Depth Information

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

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

model.

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.

Search WWH ::

Custom Search