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An NHPP {N(t): t ≥ 0} is a counting process such that N(t) is the number of arrivals in the time interval (0, t]; and λ(t), the instantaneous arrival rate at time t, is a nonnegative function of time satisfying the usual Poisson postulates so that the corresponding (cumulative) mean value function is given by ABSTRACTTo 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, constantvariance 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.The rate or mean value function of the NHPP {N(t), t ≥ 0} completely characterizes the probabilistic behavior of the process (Çinlar 1975). Both parametric and nonparametric methods have been developed to estimate the rate or mean value function of the process {N(t) : t ≥ 0} from observed data. This paper focuses on the nonparametric "multiresolution" estimation method of Kuhl, Damerdji, and Wilson (1997) and Kuhl and Wilson (2001), where the target arrival process may exhibit a long-term trend as well as nested cyclic effects that do not necessarily possess the symmetry of sinusoidal oscillations. For example, in developing a largescale simulation model of the organ-procurement and patient-registration processes for liver transplants in the United States, Pritsker et. al (1995) found that the arrival streams of liver donors and liver patients have pronounced long-term trends as well as asymmetric cyclic effects that depend on the time of year, the day of the week, and the hour of the day; see also Pritsker (1998).