An Automated Multiresolution Procedure for Modeling Complex Arrival Processes

Abstract

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.

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