Choosing Arrival Process Models for Service Systems: Tests of a Nonhomogeneous Poisson Process

Service systems such as call centers and hospital emergency rooms typically have strongly time-varying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statistical tests with service system data to confirm that an NHPP is actually appropriate, as emphasized by Brown et al. [6]. They suggested a specific statistical test based on the Kolmogorov-Smirnov statistic after exploiting the conditional-uniform property to transform the NHPP into a sequence of i.i.d. random variables uniformly distributed on [0, 1] and then performing a logarithmic transformation of the data. We conduct extensive simulation experiments to study the power of that statistical test and various alternatives. We conclude that the general approach of Brown et al. [6] is excellent, but that an alternative KolmogorovSmirnov test proposed by Lewis [15], exploiting a different transformation due to Durbin [7], consistently has greater power.