ANALYSIS OF GSPN MODELS - Modelling with Generalised Stochastic Petri Nets - page 127

Table 6.7: Specification of the transitions of the SPN of Fig. 6.9

transition rate semantics transition weight priority ECS

T ndata λ infinite-server t start 1 1 1

T par1 µ 1 single-server t syn 1 1 2

T par2 µ 2 single-server t OK α 1 3

T I/O ν single-server t KO β 1 3

T check θ single-server

Table 6.8: Initial marking of the SPN of Fig. 6.9

place initial marking

p 1 2

tokens contained in p 1 is removed, while a token is added in p 2 . Then, in
zero time t start fires, placing one token in p 3 and one token in p 4 . The two
timed transitions T par1 and T par2 are now enabled and their probabilities
of firing depend on their relative speeds. Using equation ( 6.15) , transitions
T par1 and T par2 fire with probabilities:

µ 1
µ 1 + µ 2

µ 2
µ 1 + µ 2

P { T par1 } = P { T par2 } = (6.25)

If T par1 fires first, one token moves from p 3 to p 5 , subsequently T par2 fires
moving one token from p 4 to p 6 and enabling immediate transition t syn .
This transition fires immediately, removing the two tokens from p 5 and p 6
and depositing one token in p 7 . The free-choice conflict is now enabled, and
the two immediate transitions are selected to fire with probabilities:

α
α + β

β
α + β

P { t OK } = P { t KO } = (6.26)

Assume that t OK fires, so that a token is removed from p 7 and a token is put
in p 9 . Now transition T I/O is enabled, and after a delay that lasts on the
average 1/ν units of time, the GSPN system returns to its initial marking,
and its evolution continues.
Of course, many other evolution patterns are possible. Table 6.2.2 shows the
reachability set of the GSPN system of Fig. 6.9. It comprises 38 markings,
whereas the reachability set of the associated PN system (without priority)
comprises 44 states. It must be pointed out that in general the reachability