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RAND()s, and different values will be returned for each. The single random num-
ber in P9 insures that a single sequence (e.g. CC/Pol/USM) is selected, and then
the IFs sort out the arrival sequence for each client type for that sequence. In this
particular case, the P9 value is 0.914601. See the Selection of Arrival Order table in
the Brain (Exhibit 8.17). The random number 0.914601 is compared to the values
in D22:D28. Since the value falls between 0.90 (D27) and 0.95 (D28), the value 5
is returned in accordance to the lookup procedure. The value 5 indicates a sequence
of USM/Pol/CC, and thus, the condition defaults to 1 and identifies the US Mail
(USM) as the first position in the sequence. Cell I9 returns a 2 for the Police client
(Pol) since it is second in the USM/Pol/CC sequence, etc. Although this may appear
to be very complex logic, if you consider the overall structure of the cell formula,
you can see that the logic is consistent for each of the 6 possible sequences. Finally,
the calculation of Daily Totals is performed in column N by summing all arrival
values. For Day 1, the sum of cells B5, D5, F5, H5, J5, and L5 is 11 arrivals in (N5).
8.5.4 Variation in Approaches to Poisson Arrivals—Consideration
of Modeling Accuracy
Let us consider for a moment other possible options available to generate arrivals
from the Poisson distributions of hourly arrivals. For the 7:00–9:00 time period, I
have chosen a rather direct approach by selecting two randomly sampled values, one
for the hour spanned in 7:00–8:00 and the other for 8:00–9:00. Another approach,
which we briefly mentioned above, is to select a single hourly value and use it for
both hours. This is equivalent to multiplying the single sample value by two. Does it
really matter which approach you select? The answer is yes, it certainly does matter.
The latter approach will have several important results. First, the totals will all be
multiples of 2, due to the multiplication; thus, odd values for arrivals, for example
17 or 23, will not occur. Secondly, and related to the first, the standard deviation of
the arrivals in the latter approach will be greater than that of the former approach.
What are the implications of these results? For the case of no odd values, this may
not be a serious matter if numbers are relatively large, but this may also be a depar-
ture from reality that a modeler may not want to accommodate. In fact, the average
for the arrivals sampled for several days will be similar for both approaches, as long
as the sample size of days is large, for example 250 days. The second outcome is
more problematic. If there is a need for the model analysis to study the variabil-
ity of arrival outcomes, the latter approach has introduced variability that may not
be acceptable or representative of real behavior. By accentuating (multiplying by
two) extreme values, it is possible that larger than realistic extreme values will be
recorded. In our case, this is an important issue, since we want to study the possible
failure to meet extreme demand for daily arrivals.
To demonstrate the differences discussed above, consider the graph in
Exhibit 8.19. In this simple example, the difference between the approaches
becomes clear. The worksheet in Exhibit 8.19 contains two areas with different
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