Graphics Programs Reference
In-Depth Information
9
The GSPN modelling paradigm is a versatile tool that can be used in many
different ways. We saw in previous chapters that the GSPN approach allows
the simple development of detailed, easy-to-understand models of complex
systems. With some additional effort in the modelling process, GSPNs can
also be used to develop compact, abstract models, where symmetries and
other behavioural properties are exploited to reduce the number of places,
transitions, and arcs with respect to the corresponding detailed models.
The major benefit of this abstraction process consists in the reduction of
the (tangible) reachability set, thus yielding much simpler analyses.
In this chapter we discuss the construction of compact GSPN models of a
multiserver random polling system by progressively abstracting the descrip-
tion of the system behaviour. In this way we will show that the abstraction
can yield very significant advantages in terms of the reduction of the size of
the state space of the underlying CTMC, at the expense of the effort and
ingenuity of the modeller. Moreover, as the abstraction process develops,
the intermediate results help us to understand the fundamental laws that
govern the behaviour of the system under investigation.
9.1
Polling Systems
The interest in polling systems has been steadily increasing over the last
two decades, due to a very wide range of application fields for which they
provide adequate descriptions and accurate performance estimates. Promi-
nent application areas of polling models are the fields of telecommunications,
computer science, and manufacturing. A comprehensive list of publications
on polling models and their applications was collected by H.Takagi [
68]
.
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