Call center data modeling: a queueing science approach based on Markovian arrival process

ABSTRACT

In this paper we analyze the well-known ‘Anonymous bank’ call center dataset from a queueing science viewpoint. For this purpose, fitted distributions for both the inter-arrival and service times as well as for customers patiences are integrated in a simulator to infer quantities of interest related to call centers managerial decisions as waiting times, abandonment rates and queue lengths. In particular, it is shown how a type of Markov renewal process, the Markovian arrival process (MAP), is able to capture some of the characterizing properties of arrivals in a modern call center as overdispersion and positive correlation between arrival counts. The work provides a new inference approach for the MAP based on the count process descriptors and presents new properties concerning the dependence structure of the cumulated number of arrivals in a MAP.

KEYWORDS:

• Call center
• Markovian arrival process
• Lognormal distribution
• overdispersion
• impatient customers
• queueing science

Acknowledgements

The authors acknowledge grants TED2021-130216A-I00 and TED2021-131264B-100 funded by MICIU/AEI/10.13039/501100011033 and by the European Union Next GenerationEU/PRTR. This research has been also part of the I+D+i projects PDC2022-133359, PID2022-137243OB-I00, PID2022-137818OB-I00, US-138117, P18-FR-2369 and FQM-329. The third author also acknowledges the Ministerio de Universidades for funding this research through an Ayuda de Recualificación del Profesorado (Plan de Recuperación, Transformación y Resiliencia, Gobierno de España). Finally, the authors are also thankful to I. Guedj and A. Mandelbaum for organize the site where the data are available at and for providing helpful details for researchers.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2024.2371715

Additional information

Funding

This work was supported by the Junta de Andalucía [US- 138117, P18-FR-2369, FQM-329]; Ministerio de Ciencia e Innovación [MCIN/AEI/10.13039/501100011033].

Notes on contributors

Marcos Gonzalez Bernal

Marcos Gonzalez Bernal received his B.Sc in Mathematics from the Universidad Complutense (Madrid) in 2014, and M.Sc in Statistics. His current research interest covers stochastic processes, point processes, phase-type distributions, Markovian arrival processes and its statistical applications, where he is developing his Ph.D.

Rosa Elvira Lillo

Rosa Elvira Lillo was born in Mérida, Spain 1969. Obtained her B.A. with Honors and her Ph.D. in Mathematics from Universidad Complutense (Madrid) in 1992 and 1996, respectively. She has been an Associate Professor in Universidad Carlos III de Madrid. Since 2010, she is a Professor of Statistics and Operations Research in Universidad Carlos III de Madrid. She has been Vice-Dean for the Degree in Statistics and Business between 2005 and 2015. Currently, she is the director of the Institute UC3M-BS Financial Big Data. In the past, she was visiting professor in The University of Arizona, Tucson. Her research interests include multivariate risk measures, functional data analysis, BMAP processes and their applications in finance and queue networks, stochastic ordering and reliability, GLM models in high dimension and portfolio optimization.

Pepa Ramirez -Cobo

Pepa Ramirez- Cobo She is a professor at the Department of Statistics and Operations Research of the University of Cádiz. She received her B.Sc. in Mathematics, Universidad Autnoma de Madrid, and M.Sc. in Mathematics applied to social sciences, Université Paris-Dauphine. In 2009 she received her Ph.D. (with honors) at Universidad Carlos III de Madrid. Her research has covered Bayesian inference for stochastic processes, statistical applications of wavelets theory, optimization problems in time series, and stochastic modeling in general.