Can Customer Arrival Rates Be Modelled by Sine Waves?

27 Pages Posted: 1 Mar 2018 Last revised: 29 Apr 2018

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Donald Lee

Emory University - Goizueta Business School

Haipeng Shen

The University of Hong Kong - Faculty of Business and Economics

Date Written: February 16, 2018

Abstract

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

Chen, Ningyuan and Lee, Donald and Shen, Haipeng, Can Customer Arrival Rates Be Modelled by Sine Waves? (February 16, 2018). Available at SSRN: https://ssrn.com/abstract=3125120 or http://dx.doi.org/10.2139/ssrn.3125120

Ningyuan Chen

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Donald Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Haipeng Shen

The University of Hong Kong - Faculty of Business and Economics ( email )

Hong Kong

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