Graphics Programs Reference
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distribution over the enabled transitions using the expresssion of equation
( 6.16) and selecting the transition via the generation of a random number.
Extending the simulation methodology discussed so far to the case of GSPN
systems with general firing time distributions is quite simple. In this case
firing delay instances for newly enabled transitions are generated with well-
known techniques that are standard in the simulation field [39] and the only
major difference concerns the way of managing the firing delays of transitions
that were enabled in the previous marking and that became disabled due
to the firing of another transition. Two ways of treating these firing delays
need to be implemented, depending on their specific memory policies [ 31] .
Transitions that have been specified with an enabling memory policy have
their remaining firing delays discarded and new firing delay instances are
generated for them when they become enabled again in a new marking.
Transitions that have been specified instead with an age memory policy keep
record of their remaining firing delays by means of proper auxiliary variables.
When they become enabled in a new marking, new firing delay instances are
generated only if their associated auxiliary variables have zero values 1 . In
all the other cases the value of the auxiliary variable is directly interpreted
as the new instance of the firing delay that is used to insert a corresponding
firing event in the event list. The auxiliary variable associated with a timed
transition with age memory policy is set to zero when the transition fires.
The statistical analysis of the simulation output can be performed in the case
of GSPN with the regenerative method [39] , because of the existence of an
underlying CTMC. The only problem may be that of identifying a suitable
regeneration point (marking) that is visited su ciently often during the sim-
ulation run. When the restriction of the negative exponential distribution
of the firing delays is relaxed, the regenerative structure of the associated
stochastic process is maintained only in very special cases [31] and it may
become more convenient to obtain interval estimates for the performance
figures of interest using the independent replication method [ 39] .
6.5.1
Simulation of the example GSPN system
The effectiveness of simulation for the analysis of complex systems can be
demonstrated with the use of the simple parallel processing example of Fig.
6.9, by assuming that a large number of customers are considered in the
system. Table 6.14 summarizes the results of an experiment in which sim-
ulation estimates for the throughput and for the processing power (i.e., the
mean number of tokens in place p 1 ) of the system are compared with the
exact ones computed with numerical methods in the case of small popula-
Some attention must be paid in the case of firing delays with discrete distributions,
since it may happen that several transitions are scheduled to fire at the same time and
an auxiliary variable with zero value does not necesserely means that the corresponding
transition has fired.
1
 
 
 
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