Can Customer Arrival Rates Be Modelled by Sine Waves?
27 Pages Posted: 1 Mar 2018 Last revised: 29 Apr 2018
Date Written: February 16, 2018
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.
Keywords: arrival rate estimation; spectral estimation; nonhomogeneous Poisson process; emergency departments; call centres
JEL Classification: C15, C22, C32, C44, C52, C53
Suggested Citation: Suggested Citation