The analytical approximation (see chapter 2.10.1) is simpler but it is based on the reservation assumption which might be true in some cases and wrong in others. The statistical model may represent most of the important factors but one needs a lot of time to "filter" the random deviations what is not good in the on-line operation.
Testing analytical approximation one compares the estimations of call rates
obtained by the statistical and the reservation models.
A small deviation means that the reservation model is acceptable.
The large deviation means that the improvement of analytical approximation is needed or the statistical model should be used instead of the analytical one.