GSPN BASICS - Modelling with Generalised Stochastic Petri Nets - page 105

π = 2 π = 3

t read t start r T read t start LAN r T LAN r

p r p read p LAN r

p think p request p db p LAN

K

t think T exec

p write p LAN w

p w

t reaccess t write

π = 2

t start w t start LAN w T LAN w

T write

π = 4

Figure 5.3: The example GSPN model: a modification of the readers &
writers model

The GSPN model comprises 13 places and 13 transitions, five timed and
eight immediate. To simplify the model description, we use mnemonic names
for all transitions and places. The initial parametric marking assigns K to-
kens to place p think to model the fact that K processes are initially assumed
to be executing in their private memories; one token to place p db to indicate
that the database is initially idle; and one token to place p LAN to indicate
that the LAN is initially idle. All other places contain no tokens in the

initial parametric marking.
Transition T exec models the execution phase of processes in their private
memories; it is timed with parameter λ, and has infinite-server semantics.
The average execution time in private memory is assumed to be 1/λ, and
since all executions proceed in parallel the infinite-server semantics is used.
The firing of T exec models the end of the execution phase and the generation
of a database access request that is modelled by a token in place p request .
The free-choice conflict set comprising the two immediate transitions t read
and t write at priority level 2 models the fact that the request for the database
access can be either a read or a write request, so that a token is generated
in either place p r , or p w , respectively. Assuming that 80% of the requests
are read requests, and only 20% are write requests, the weights of t read and
t write are set to 8 and 2, respectively.
The priorities of t start r and t start w are set to 3 and 4, respectively, so
that the write requests have priority over the read requests, and the two
transitions are in different conflict sets. The weights associated with the
two transitions are thus irrelevant (they are set to 1 by default).
Place p write can contain at most one token, and transition T write is timed
with a rate µ w which is the inverse of the average write time; the transition
semantics is single-server. The firing of T write models the end of a database
access for a write and generates a token in place p LAN w .