INTRODUCTION - Modelling with Generalised Stochastic Petri Nets - page 13

three users are described with similar subnets, comprising places p idle i ,
p wait i , and p transmit i , with i = 1, 2, 3. The three triplets of places model
conditions that represent the present state of each user: either idle, with no
message to transmit, or waiting for the token because a message is ready
for transmission, or transmitting the message. We assume that each user
handles one message at a time. The three transitions t arrival i , t start tx i ,
and t end tx i model the events that modify the state of the individual user.
Of particular interest in this case is to describe the if-then-else behaviour
when the token reaches a user. Indeed, when a user is polled, if a message
is waiting, then it must be transmitted; else the token must proceed to the
next user. The two alternatives are described with transitions t start tx i ,
and t proceed i . The former is enabled when one token is in places p poll i ,
and p wait i . The second must be enabled when one token is in place p poll i ,
but p wait i contains zero tokens. The test for zero is implemented with a
new construct: the inhibitor arc, which is represented as a circle-headed
arc originating from the place that must be tested for the zero marking
condition. Implementing the test for zero with normal arcs is not possible
in general. The addition of inhibitor arcs is an important extension of the
modelling power of PNs, which gives them the same modelling power as
Turing machines [57] .
The reader is encouraged to play with the examples presented in this chapter
for a while before moving on to the next one. In particular, it may be helpful
to use markers to execute the networks by playing the so-called token game
(pushpins are the normal choice - do not hurt yourself! - but headache
pills may become a multipurpose instrument if you plan to play for a longer
time).
The main purpose of this chapter was to introduce PNs and their notation
informally, and to show that PNs can be an adequate tool for the devel-
opment of models of a wide variety of real systems. The next chapter will
provide a formal introduction to the same concepts, and will also show what
sort of results can be obtained with the analysis of PN models. Further chap-
ters will discuss the introduction of priorities and temporal concepts into PN
models, leading to the definition of GSPNs, the modelling paradigm adopted
for the PN-based stochastic analysis of the application examples described
in the second part of the topic.