INTRODUCTION - Modelling with Generalised Stochastic Petri Nets - page 7

p active 1 p active 2

t request 1 t request 2

p idle

p requesting 1 p requesting 2

t start 1 t start 2

p accessing 1 p accessing 2

t end 1 t end 2

Figure 1.5: Reduced PN description of two users accessing a shared resource

transitions fire, and that defines the global state of the system. In our
example, the combination of the two PN submodels is not equivalent to the
independent combination of the state machines, in the sense that the state
space is not the Cartesian product of the state spaces of the two components.
Instead, the PN description in Fig. 1.4 is equivalent to a queuing model
where two customers request service from one server.
It is easy to see that in the PN in Fig. 1.4, the place p busy is redundant (the
same is also true for the place with the same name in Fig. 1.3) . Indeed, when
it contains one token, also one of the two places p accessing 1 and p accessing 2
must contain one token. The number of tokens in p busy can be expressed
as the sum of the numbers of tokens in p accessing 1 and in p accessing 2 . Fur-
thermore, the net structure is such that the number of tokens in p busy does
not condition the model dynamics. We can thus simplify the PN by remov-
ing place p busy , as shown in Fig. 1.5. This is very simple evidence of the
fact that PN models can be reduced. Much research effort was devoted to
the identification of PN reduction rules [ 10, 64] , but this topic will be only
marginally addressed in this topic.
When several identical users exist with similar characteristics, a different
representation is also possible. Indeed, we may collectively describe the
users' behaviour by placing as many tokens as there are users in the PN

visualize the model behaviour as that of a token cycling around the chain of places.