TIME IN PETRI NETS - Modelling with Generalised Stochastic Petri Nets - page 51

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TIME IN PETRI NETS

In this chapter w e discuss the issues related to the introduction of temporal
concepts into PN models and systems. The goal of the chapter is not to
provide an exhaustive overview of the field of timed PN, that is out of the
scope of this topic, but instead to discuss the temporal semantics peculiar
to stochastic PNs (SPNs) and generalized SPNs (GSPNs). For this reason
we shall always assume that timed transitions are associated with tempo-
ral specifications such that the simultaneous firing of two or more timed
transitions can be neglected (this event has probability zero in SPNs and
GSPNs).

3.1 The Motivations for Timing

The PN models and systems that were considered in the previous chapter
include no notion of time. The concept of time was intentionally avoided in
the original work by C.A.Petri [58] , because of the effect that timing may
have on the behaviour of PNs. In fact, the association of timing constraints
with the activities represented in PN models or systems may prevent certain
transitions from firing, thus destroying the important assumption that all
possible behaviours of a real system are represented by the structure of the
PN.
In [ 57] , the first topic on PNs that dealt extensively with applications, the
only remark about timed PNs was the following: “The addition of timing
information might provide a powerful new feature for PNs, but may not be
possible in a manner consistent with the basic philosophy of PNs”. This
attitude towards timing in PN models is due to the fact that PNs were orig-
inally considered as formal automata and investigated in their theoretical
properties. Most of the early questions raised by researchers thus looked
into the fundamental properties of PN models and systems, into their anal-
ysis techniques and the associated computational complexity, and into the
equivalence between PNs and other models of parallel computation. When

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