ANALYSIS OF GSPN MODELS - Modelling with Generalised Stochastic Petri Nets - page 150

Table 6.14: Comparison of performance figures computed via numerical and
simulation methods for the parallel system of Fig. 6.9

N System Processing Sim.

| TRG | Throughput

Power Time

Num. Sim. Num. Sim.

0.2979 ∓ 0.0137 1.5173 ∓ 0.0179 2 20 0.3011 1.5055 15 sec.

0.8718 ∓ 0.0354 4.4137 ∓ 0.2077 8 825 0.8996 4.4877 23 sec.

1.0008 ∓ 0.0349 4.9494 ∓ 0.2448

20 19481 0.9900 4.9500 27 sec.

1.0402 ∓ 0.0474 5.2243 ∓ 0.2533 50 609076 - - 24 sec.

tions. The size of the reachability set of this model grows quickly according
to the following formula

! !

N + P − 1
P − 1

N + P − 3
P − 1

| TRG(N) | = − (6.48)

where N is the number of customers in the model and P is the number of
places of the net. It thus happens that when 50 customers are in the sys-
tem, the numerical solution becomes practically impossible and simulation
remains the only reasonable analysis technique.
Due to the size of the reachability set in the case of 50 customers, an in-
dependent replication method has been used to obtain interval estimates
that have a 5% precision and a confidence level of 99%. The results are
reported in Table 6.14 where the simulation estimates are shown to cover
the numerical results when the size of the problem allowed the use of both
evaluation methods. Table 6.14 reports also an indication of the time needed
to obtain the simulation estimates that is interesting since it shows that the
cost of simulation does not increase dramatically when the state space ex-
plodes making the numerical solution impossible for both time and space
complexity considerations.