Can Customer Arrival Rates Be Modelled by Sine Waves

Customer arrival patterns observed in the real world typically exhibit strong seasonal effects. It is therefore natural to ask: Can a nonhomogeneous Poisson process with a rate that is the simple sum of sinusoids be an adequate description of reality? We empirically investigate this question in two settings of interest to operations scholars: Patient arrivals to an emergency department and customer calls to a call centre. We find that the model is consistent with arrivals data from both settings. Taken together, the flexibility and tractability of the sinusoidal specification suggest that it is a worthy workhorse model for time-varying arrival processes. In fitting the specification to data, surprising pitfalls arise. To bring these issues to the attention of scholars interested in putting the specification to use, we use a real example to illustrate how intuitive estimation approaches can fail spectacularly. To provide researchers with a proper way to perform the estimation, we give a user friendly introduction to a statistical learning technique recently developed for queueing data, and explain intuitively how it addresses these pitfalls.