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so that the resulting distribution most closely "resembled" the
available data.) We then made 100 independent simulation runs (i.e.,
different random numbers were used for each run, as discussed in Sec.
7.2) of the queueing system using each of the five fitted distributions.
Each of the 500 simulation runs was continued until 1000 delays in queue
were collected. A summary of the results from these simulation runs is
given in Table 6.2. Note in column 2 of the table that the average of
the 100,000 delays is given for each of the service-time distributions.
As we will se in Sec. 6.7. the Weibull distribution actually provides
the best model for the service-time data. Thus, the average delay for
the real system should be close to 4.36 minutes. On the other hand, the
average delays for the normal and lognormal distributions are 6.04 and
7.19 minutes, respectively, corresponding to model output errors of 39
percent and 65 percent. This is particularly surprising for the
lognormal distribution, since it has the same general shape (i.e.,
skewed to the right) as the Weibull distribution. However, it turns out
that the lognormal distribution has a "thicker" right tail, which allows
larger service times and delays to occur. The relative difference
between the "tail probabilities" in column 4 of the table are even more
significant. The choice of probability distributions can evidently have
a large impact on the simulation output and, potentially, on the quality
of the decisions made with the simulation results.
|
Service-time Distribution |
in queue |
in queue |
of delays >= 20 |
Gamma Weibull Lognormal Normal |
4.54 4.36 7.19 6.04 |
4.60 4.41 7.30 6.13 |
0.019 0.013 0.078 0.045 |
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