INTRODUCTION - Modelling with Generalised Stochastic Petri Nets - page 5

p active

p idle

t request

p requesting t start

t start p busy

p accessing

t end

t end

(b)

(a)

Figure 1.2: PN description of the user (a), and of the resource (b)

that does not involve the shared resource), requesting, and accessing. The
behaviour of the user corresponds to cycling through these three conditions.
We can describe the user behaviour with the PN in Fig 1.2( a), where three
places describe the three user conditions (p active , p requesting , and p accessing ),
and three transitions describe the three events that modify the user condi-
tion, from active to requesting (t request ), from requesting to accessing (t start ),
and from accessing back to active (t end ).
The combined description of one user and one resource is obtained by merg-
ing the two PNs in Fig. 1.2 via the superposition of the transitions named
t start and t end , so as to obtain the PN in Fig. 1.3. The description can
be immediately extended to the case of two users competing for the access
to the same resource, that now becomes shared. In this case the transitions
named t start and t end in the resource model are superposed to the transitions
t start 1 and t end 1 in the model of the first user, as well as to the transitions
t start 2 and t end 2 in the model of the second user, as shown in Fig. 1.4.
It is interesting to observe that the PN descriptions of the user and resource
are equivalent to their state machine representations. Indeed, the two PNs
in Fig. 1.2 contain only one token that “moves” 3 from place to place when

3 Actually, tokens do not move; the one in the input place is destroyed, and a new one
is created in the output place at every transition firing.

However, in this case we can