ANALYSIS OF GSPN MODELS - Modelling with Generalised Stochastic Petri Nets - page 125

p 1 p 0 p 2 p 1 p 2 p 3

T 1 T 2 T 1

(a) (b)

Figure 6.8: Examples of complex marking dependency situations

we can define the marking dependency function as follows:
8
<

f(M /T 1 ) = δ(ED(T 1 ,M))M(p 1 )

and similarly (6.23)

:

f(M /T 2 ) = δ(ED(T 2 ,M))M(p 2 )

Fig. 6.8( b) represents instead a server whose speed depends on a linear
combination of the markings of all its input places. In this case the marking
dependency function may assume the form:

X X

α p ≥ 0,

f(M /T 1 ) = δ(ED(T 1 ,M)) α p M(p) α p = 1

p∈ • T 1 p∈ • T 1

(6.24)

6.2.2 An example GSPN system

Consider the example of a parallel system introduced in Chapter 1 (Fig. 1.8)
and discussed at some length in Chapter 5 (Fig. 5.1) . The GSPN system
comprises nine places and nine transitions (five of which are timed) and is
repeated in Fig. 6.9 for convenience. The characteristics of the transitions
of this model are summarized in Table 6.7; the initial marking is shown in
Table 6.8.
Three ECSs can be identified within this system. Two of them can be
considered “degenerate” ECSs as they comprise only one transition each
(transitions t start and t syn , respectively). The third ECS corresponds instead
to a free choice conflict among the two immediate transitions t OK and t KO
that have weights α and β, respectively.
Starting from the initial marking shown in Fig. 6.9, a possible evolution of
the GSPN state may be the following. After an exponentially distributed
random time with average 1/(2λ), transition T ndata fires, and one of the two