Data-driven Population Tracking in Large Service Systems

64 Pages Posted: 6 Mar 2024 Last revised: 8 Mar 2024

See all articles by Fernando Bernstein

Fernando Bernstein

Duke University

N. Bora Keskin

Duke University - Fuqua School of Business

Adam Mersereau

University of North Carolina Kenan-Flagler Business School

Morgan Wood

University of North Carolina (UNC) at Chapel Hill - Department of Statistics and Operation Research

Serhan Ziya

Department of Statistics and Operations Research

Date Written: March 4, 2024

Abstract

Motivated by an application at the Raleigh-Durham International Airport, we consider a service system in which a manager aims to track the number of people in the system based only on noisy observations of arrivals and departures over a time horizon. We study two tracking problems in this context. In the busyness tracking problem, the manager seeks to determine whether the system is busy or not, whereas in the population tracking problem, the manager tracks the number of people in the system and accumulates losses as squared errors. We characterize the cumulative losses of various policies in an asymptotic regime in which the time horizon grows large. Through general lower bounds on cumulative loss, we show that any tracking policy must accumulate loss at a greater rate than typical learning problems in the literature. We also propose policies that achieve the cumulative loss rates in the lower bounds, up to logarithmic terms. We find that effective population tracking policies reset the population count to zero when they detect that the system is empty. Finally, we characterize the impact of having the ability to periodically inspect the system at a cost. We demonstrate the performances of our policies using real-world data we collected by installing people-counting sensors at the airport.

Keywords: Service systems, Internet of Things, people counters, data-driven tracking, change-point detection, inspections

Suggested Citation

Bernstein, Fernando and Keskin, N. Bora and Mersereau, Adam and Wood, Morgan and Ziya, Serhan, Data-driven Population Tracking in Large Service Systems (March 4, 2024). Kenan Institute of Private Enterprise Research Paper No. 4748063, Available at SSRN: https://ssrn.com/abstract=4748063 or http://dx.doi.org/10.2139/ssrn.4748063

Fernando Bernstein

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

N. Bora Keskin (Contact Author)

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Durham, NC 27708-0120
United States

HOME PAGE: http://faculty.fuqua.duke.edu/~nk145/

Adam Mersereau

University of North Carolina Kenan-Flagler Business School ( email )

McColl Building
Chapel Hill, NC 27599-3490
United States

Morgan Wood

University of North Carolina (UNC) at Chapel Hill - Department of Statistics and Operation Research ( email )

United States

Serhan Ziya

Department of Statistics and Operations Research ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

HOME PAGE: http://www.unc.edu/~ziya/

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