TIME IN PETRI NETS - Modelling with Generalised Stochastic Petri Nets - page 52

dealing with these problems, timing is indeed not relevant.
Very soon PNs were however recognized as possible models of real concur-
rent systems, capable of coping with all aspects of parallelism and conflict
in asynchronous activities with multiple actors. In this case, timing is not
important when considering only the logical relationships between the enti-
ties that are part of the real system. The concept of time becomes instead
of paramount importance when the interest is driven by real applications
whose e ciency is always a relevant design problem. Indeed, in areas like
hardware and computer architecture design, communication protocols, and
software system analysis, timing is crucial even to define the logical aspects
of the dynamic operations.
The pioneering works in the area of timed PNs were performed by P.M.Merlin
and D.J.Farber [ 48] , and by J.D.Noe and G.J.Nutt [56] . In the former work,
the authors applied PNs augmented with timing to communication protocol
modelling; in the latter case, a new type of timed nets was used for modelling
a computer architecture. In both cases, PNs were not viewed as a formalism
to statically model the logical relationships among the various entities that
form a real system, but as a tool for the description of the global behaviour
of complex structures. PNs were used to narrate all the possible stories that
the system can experience, and the temporal specifications were an essential
part of the picture.
Different ways of incorporating timing information into PN systems and
models were proposed by many researchers during the last two decades; the
different proposals are strongly influenced by the specific application fields.
In this chapter we do not discuss and compare the different approaches,
but only the temporal semantics used in SPNs and GSPNs. The reader
interested in other approaches to timed PNs is referred to the original papers
[ 60, 74, 33, 59, 48, 63, 20, 73] with a warning: the differences among the
various models are sometimes subtle and often not easy to identify at a first
glance.
When introducing time into PN models and systems, it would be extremely
useful not to modify the basic behaviour of the underlying untimed model.
By so doing, it is possible to study the timed PNs exploiting the properties
of the basic model as well as the available theoretical results. The addition
of temporal specifications therefore must not modify the unique and original
way of expressing synchronization and parallelism that is peculiar to PNs.
This requirement obviously conflicts with the user' wishes for extensions of
the basic PN formalism to allow a direct and easy representation of spe-
cific phenomena of interest. SPNs satisfy the first of these two requirements
and provide a formalism that allows the construction of models that can
be used both for behavioural analyses based on classic PN theory, and for
performance studies based on temporal specifications and probabilistic mod-
els. GSPNs represent instead a sort of compromise between the two needs,
since they include extensions that are very useful in practical modelling,