TIME IN PETRI NETS - Modelling with Generalised Stochastic Petri Nets - page 56

(a) (b)

Figure 3.4: Timed (a) and immediate (b) transitions

single transition. Moreover, the state change can depend on the present state
in a complex manner. As a result, the correct evolution of the timed PN
model can often be conveniently described with subnets of transitions that
consume no time and describe the logics or the algorithm of state evolution
induced by the complex event.
To cope with both these situations in timed PN models, it is convenient to
introduce a second type of transition called immediate. Immediate transi-
tions fire as soon as they become enabled (with a null delay), thus acquiring
a sort of precedence over timed transitions, thus leading to the choice of
giving priority to immediate transitions in the definition of GSPNs. In this
topic immediate transitions are depicted as thin bars, as shown in Fig. 3.4,
whereas timed transitions are depicted as boxes or thick bars.

3.2.2 Two examples

The basic concepts deriving from the introduction of timed and immediate
transitions are of paramount importance in understanding the definitions
and the results presented in the later chapters of this topic. To make sure
that these concepts are clear to the reader, we present two simple examples
of timed PN systems.
In Chapter 1, we described an example of a PN system with two users ac-
cessing a shared resource (see Fig. 1.5) . We now revisit that model, adding
temporal specifications to transitions. The timed PN system is shown in
Fig. 3.5. Transitions T request 1 and T request 2 model the operations of the
two users when they are not requesting or accessing the shared resource.
Transitions T end 1 and T end 2 model the operations of the two users when
accessing the shared resource. All these activities are time-consuming and
thus the four transitions are timed. On the contrary, transitions t start 1 and
t start 2 model the acquisition of the resource; this operation may be assumed
to require a negligible amount of time, so that transitions t start 1 and t start 2
are immediate. The timed PN system in Fig. 3.5 may be interpreted as a
simple model of the behaviour of a two-processor system with two private
memories (one for each processor), and one shared memory. Transitions
T request 1 and T request 2 model the activities performed by the processors