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ABSTRACT

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: (<i>a</i>) 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; <i>(b)</i> fitting a specially formulated polynomial to the transformed responses; <i>(c)</i> performing a likelihood ratio test to determine the degree of the fitted polynomial; and <i>(d)</i> fitting a polynomial of the degree determined in <i>(c)</i> to the original (untransformed) responses. An example demonstrates web-based software that implements this flexible approach to handling complex arrival processes.

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