INTRODUCTION - Modelling with Generalised Stochastic Petri Nets - page 11

and the fact that if the place that is common to t OK and t KO contains only
one token, the firing of one of the two transitions prevents the other from
doing the same. The conflict is free-choice because the two transitions are
always enabled together: the choice of which one to fire does not depend on
the marking of the net.

1.3 Kanban Process

Consider next a simple manufacturing process called Kanban, consisting of a
scheme for the coordination of production cells fed by parts. A very simple
description of the Kanban behaviour is represented by the PN in Fig. 1.9.
Incoming parts are deposited in place p input through the firing of transition
t arrive . These parts can enter the first Kanban cell by firing transition t enter 1
only if free cards are available in place p cards 1 . After entering the cell, parts
waiting for processing are stored in place p wait 1 , where they remain until
they are worked upon, and transition t work 1 fires, placing them in p out 1 .
Parts processed by the first cell can enter the second cell only when cards
from this new cell are available. While waiting for this situation to occur,
cards of the first cell are held by the parts. Whenever there are cards for
the second cell available (place p cards 2 contains tokens) one card is removed
from place p cards 2 and simultaneously one card is returned to place p cards 1 .
At the end of the processing in the second cell, transition t exit fires, releasing
one card, and placing a part in the output buffer modelled by place p output .
Finally, worked parts are removed through the firing of transition t leave .
Observe that, unlike the previous models, this one is such that an arbitrarily
large number of tokens can accumulate in p input and p output . In other words,
and with a terminology borrowed from the queuing jargon, this is an open
model.
Also in this case it is possible to observe that the PN formalism allows a
precise representation of all the important details of the behaviour of the
Kanban system, while a queuing network model of this same manufacturing
system would only convey the general idea, but would be forced to describe
the details with the help of additional informal specification sentences.

1.4 Token Ring LAN

As a final introductory example, consider a token 6 ring local area network
(LAN) with three users. An abstract description of the LAN behaviour is
represented by the PN in Fig. 1.10. The token “cycles” around the network
through transitions t move 1−2 , t move 2−3 , and t move 3−1 , and polls the three
stations when it reaches places p poll 1 , p poll 2 , and p poll 3 , respectively. The

6 The protocol token should not be confused with the PN tokens — unfortunately, the
terminologies in the two fields use the same word with quite different meanings.