Graphics Programs Reference

In-Depth Information

p
a

N

p
a

N

T
a

T
a

p
q

T
w

p
s

T
s

T
w

p
w

T
s

p
w

p
p

S

(b)

(a)

Figure 9.11: Two further simplifications of the SPN model

pendency on S is embedded into the arc weights and transition rates. This

embedding bears some resemblance to the embedding of the model charac-

teristics into appropriate functions, typical of high-level SPNs
[36]
. Second,

note that servers have disappeared from the model; the server utilization

policy is not obvious, as it is not obvious that servers can perform several

walks in a row. Third, note that we ended up with three transitions and

three places arranged in a circle; that two of the transitions have infinite-

server rates, while the rate of the third one is an infinite-server multiplied

by a function that accounts for the number of servers in the system and the

number of tokens in the transition output place.

Finally, a few words are needed to comment on the numerical results in

Table
9.5,
which report the cardinality of the tangible and vanishing state

spaces of the various GSPN models presented so far, in the case of two

servers (S = 2), for an increasing number of queues.

While a linear growth with N was already achieved with the model in

Fig.
9.7,
that already exhibits a tangible state space cardinality equal to

3N, the reduction of immediate transitions allows the elimination vanishing

markings, so that the cardinality of the state space of the final model equals

3N. This is extraordinarily less than the number of states of the original

simple GSPN model we started with!

Search WWH ::

Custom Search