2006 journal article
An automated multiresolution procedure for modeling complex arrival processes
INFORMS JOURNAL ON COMPUTING, 18(1), 3–18.
To automate the multiresolution procedure of Kuhl et al. for modeling and simulating arrival processes that may exhibit a long-term trend, nested periodic phenomena (such as daily and weekly cycles), or both types of effects, we formulate 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 time of day within the daily cycle) to obtain a statistical model with approximately 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 to the original (untransformed) responses a polynomial of the same form as in (b) with the degree determined in (c). A comprehensive experimental performance evaluation involving 100 independent replications of eight selected test processes demonstrates the accuracy and flexibility of the automated multiresolution procedure.