GSPN BASICS - Modelling with Generalised Stochastic Petri Nets - page 93

5

GSPN BASICS

In this chapter we provide an intuitive explanation of the characteristics
and dynamics of the PN models obtained by associating a random, expo-
nentially distributed firing delay with timed transitions. In the first section
we consider the case of nets with timed transitions only, thus obtaining an
informal introduction to the models that are known by the name Stochastic
PNs (SPNs). A discussion on the impact of the introduction of immediate
transitions in SPN models is contained in the other sections of the chapter.
Some restrictions are initially assumed, for the sake of simplicity, leading to
a first approach to generalized SPN (GSPN), which is limited to the case
of free-choice conflicts, marking-independent firing rates and weights, and
one level of priority for immediate transitions. The general case of mul-
tiple priorities, non-free-choice conflicts, and marking-dependency is then
informally described, and subsequently the formal definition of GSPNs is
provided. Simple examples of SPN and GSPN models are used throughout
the chapter, to illustrate in some details the concepts introduced and the
differences among the various definitions.
Some subtleties relating to the basic GSPN behaviour are finally addressed
in the last part of this chapter.

5.1 Exponential Distributions for Transition De-

lays

In Chapter 3 we observed that a simple su cient condition to guarantee that
the qualitative behaviour of PN models with timed transitions is identical
to the qualitative behaviour of the underlying untimed PN model, that is,
to guarantee that the possible transition sequences are the same in the two
models, is that the delays associated with transitions be random variables
whose distributions have infinite support.
If this is the case, a probabilistic metrics transforms the nondeterminism of
the untimed PN model into the probabilism of the timed PN model, so that

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