ANALYSIS OF GSPN MODELS - Modelling with Generalised Stochastic Petri Nets - page 122

p 0 t 0 p 1

w 0

t 1 p 3

(a)

β

α

p 2 t 2 p 4

p 0 t 0 p a t a p 1

w 0 w a

t 1 p 3

β (b)

α

p 2 t 2 p 4

Figure 6.7: Comparison of two simple confused GSPN systems

listed in Table 6.5, markings M 1 = p 3 and M 2 = (p 1 + p 4 ) are reached

with total probabilities

w 0
(w 0 + α)

β
(α + β)

α
(w 0 + α)

P { M 0 ,M 1 } = P { M 0 ,M 2 } = .

From these expressions we can see that, although the picture suggests tran-
sitions t 0 and t 2 as concurrent, and transitions t 1 and t 2 as members of a
conflict set, the first choice of firing either t 0 or t 2 is actually crucial for the
possibility of reaching the desired markings. In this case the value assigned
by the analyst to w 0 becomes fundamental for the quantitative evaluation
of the model.
Much more intriguing however is the behaviour of the subnet in Fig. 6.7( b)
that differs from that of Fig. 6.7( a) for the simple addition of place p a and
transition t a between transition t 0 and place p 1 . Given the initial marking
M 0 = (p 0 + p 2 ) and the parameters listed in Table 6.6, markings M 1 = p 3
and M 2 = (p 1 + p 4 ) are reached in the case of the subnet of Fig. 6.7( b)
with total probabilities

w 0
(w 0 + α)

w a
(w a + α)

β
(α + β)

P { M 0 ,M 1 } =