Can customer arrival rates be modelled by sine waves?

Service Science/Stochastic Systems joint special issue

15 Pages Posted: 1 Mar 2018 Last revised: 22 Aug 2023

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto - Rotman School of Management

Ragıp Gürlek

Emory University - Goizueta Business School

Donald K.K. Lee

Emory University - Goizueta Business School; Emory University - Dept of Biostatistics & Bioinformatics

Haipeng Shen

The University of Hong Kong - Faculty of Business and Economics

Date Written: June 1, 2022

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 (NHPP) with a rate function that is the simple sum of sinusoids provide an adequate description of reality? If so, how can the sinusoidal NHPP be used to improve the performance of service systems? We empirically validate that the model is consistent with arrivals data from two settings of great interest in service operations: patient arrivals to an emergency department and customer calls to a bank call centre. This finding provides rigorous justification for the use of the sinusoidal NHPP assumption in many existing queuing models. We also clarify why a sinusoidal NHPP model is more suitable than the standard NHPP when the underlying arrival pattern is aperiodic (e.g., does not follow a weekly cycle). This is illustrated using data from a car dealership, and also via a naturalistic staffing simulation based on the call centre. On the other hand, if the arrival pattern is periodic, we explain why both models should perform comparably. Even then, the sinusoidal NHPP is still necessary for managers to use to verify that the arrival pattern is indeed periodic, a step that is seldom performed in applications. Code for fitting the sinusoidal NHPP to data is provided on GitHub.

Keywords: queues; arrival rate estimation; spectral estimation; Fourier analysis; nonhomogeneous Poisson process; emergency departments; call centres

JEL Classification: C15, C22, C32, C44, C52, C53

Suggested Citation

Chen, Ningyuan and Gürlek, Ragıp and Lee, Donald K.K. and Lee, Donald K.K. and Shen, Haipeng, Can customer arrival rates be modelled by sine waves? (June 1, 2022). Service Science/Stochastic Systems joint special issue, Available at SSRN: https://ssrn.com/abstract=3125120 or http://dx.doi.org/10.2139/ssrn.3125120

Ningyuan Chen

University of Toronto - Rotman School of Management ( email )

Ragıp Gürlek

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Donald K.K. Lee (Contact Author)

Emory University - Goizueta Business School ( email )

1300 Clifton Road
Atlanta, GA 30322-2722
United States

Emory University - Dept of Biostatistics & Bioinformatics ( email )

Atlanta, GA 30322
United States

Haipeng Shen

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

Hong Kong

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
302
Abstract Views
1,824
Rank
189,261
PlumX Metrics