A flexible automated procedure for modeling complex arrival processes

To automate the multiresolution procedure of Kuhl and Wilson for modeling and simulating arrival processes that exhibit long-term trends and nested periodic effects (such as daily, weekly, and monthly cycles), we present a statistical-estimation method that involves the following steps at each resolution level corresponding to a basic cycle: (a) transforming the cumulative relative frequency of arrivals within the cycle (for example, the percentage of all arrivals as a function of the day of the week within the weekly cycle) to obtain a statistical model with normal, constant-variance responses; (b) fitting a specially formulated polynomial to the transformed responses; (c) performing a likelihood ratio test to determine the degree of the fitted polynomial; and (d) fitting a polynomial of the degree determined in (c) to the original (untransformed) responses. An example demonstrates Web-based software that implements this flexible approach to handling complex arrival processes.