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Exhibit 8.19 Two approaches to arrivals
approaches for simulating the arrivals in a 2 hour period. The range (A1:J25) has
two separate VLOOKUP functions sampling a Poisson with an average arrival rate
of one unit per hour. Why two VLOOKUPs? We have two because one is needed for
each hour in the two hour period. This is the approach we used in Exhibit 8.18. The
approach in range K1:T25 is a single sample which is then multiplied by two. Why
a single sample? In this case we assume that the same value can be used for each
of the two hours. Both approaches collect 250 samples of arrivals for a two hour
The summary statistics in Y27:Z30 show very similar behavior in terms of means
and total arrivals for the 250 samples, approximately a mean of 2.0 and total arrivals
500 for both. Thus, both approaches appear to be similar in some summary statistics.
The difference is seen in the standard deviation for the two VLOOKUP approaches.
The approach with two randomly sample hours, has a lower value, 1.4, than the
approach which used a single VLOOKUP multiplied by two, 2.1. The graph in
Exhibit 8.19 shows the greater dispersion of results for the approach that gener-
ates a single VLOOKUP sample then multiplies by 2. It is far more likely that this
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