GSPN BASICS - Modelling with Generalised Stochastic Petri Nets - page 106

Table 5.1: Characteristics of the timed transitions in the example GSPN

model

transition rate semantics

T exec λ infinite-server

T write µ w single-server

T read µ r infinite-server

T LAN r ρ r single-server

T LAN w ρ w single-server

Place p read can contain several tokens, and transition T read is timed with a
rate µ r which is the inverse of the average read time; the transition semantics
is infinite-server since all read accesses proceed in parallel. The firing of T read
models the end of a database access for a read and generates a token in place
p LAN r .
Transitions t start LAN r and t start LAN w have equal priority set to 1, and
thus form a non-free-choice conflict set of immediate transitions. Their
weights are both set to 1, to indicate that the allocation of the LAN to
processes that have just completed a read or write database access is equally
likely. 1
Transitions T LAN r and T LAN w model the data transfer activities on the
LAN after the two types of database access. They are timed with rates ρ r
and ρ w , respectively, and their semantics is single-server, since no more than
one LAN transfer activity can be in progress at a time.
Transitions t think and t reaccess have equal priority set to 1, and form a free-
choice conflict set of immediate transitions. Their weights are set to 9 and 1,
respectively, to indicate that 10% of the time processes immediately reissue
a database access request after completing the previous access, while 90%
of the time processes go back to execute in their private memory.
The characteristics of the five timed transitions are summarized in Table 7.1,
and those of the eight immediate transitions in Table 7.2.
Note that in the GSPN model we have four different priority levels of im-
mediate transitions, which are necessary to guarantee that the underlying
PN model with priority is not confused. Timed transitions have semantics
both of single-server and of infinite-server type. Immediate transitions form

1

With this choice, when processes that have just completed a read and write database
access are waiting, the LAN is allocated with probability 0.5 to one of the processes
that have just completed a read database access, and with probability 0.5 to one of the
processes that have just completed a write database access. If, instead the weights of

transitions t start LAN r and t start LAN w are made equal to the numbers of tokens in

places p LAN r and p LAN w , respectively, the LAN is allocated to any waiting process with

equal probability.