Using simulation to study statistical tests for arrival process and service time models for service systems

When fitting queueing models to service system data, it can be helpful to perform statistical tests to confirm that the candidate model is appropriate. The Kolmogorov-Smirnov (KS) test can be used to test whether a sample of interarrival times or service times can be regarded as a sequence of i.i.d. random variables with a continuous cdf, and also to test a nonhomogeneous Poisson Process (NHPP). Using extensive simulation experiments, we study the power of various alternative KS tests based on data transformations. Among available alternative tests, we find the one with the greatest power in testing a NHPP. Furthermore, we devise a new method to test a sequence of i.i.d. random variables with a specified continuous cdf; it first transforms a given sequence to a rate-1 Poisson process (PP) and then applies the existing KS test of a PP. We show that it has greater power than direct KS tests.