Graphics Programs Reference

In-Depth Information

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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