Data-Driven Population Tracking in Service Systems

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. We prove general lower bounds on the cumulative loss of any policy and propose relatively simple policies that achieve these lower bounds, up to logarithmic terms. These policies outperform naive tracking policies in many instances. Finally, we characterize the impact of having the ability to periodically inspect the system at a cost. We find that effective population tracking policies take opportunities to reset the population count to accurate estimates to stop the accumulation of error. Without inspections, this is achieved by resetting the population count to zero when a near-empty system is detected based on observing the departure stream. Inspections, although coming at a cost, allow for greater flexibility in the timing of corrections and, hence, improved performance. We demonstrate the performance of our policies using real-world data we collected by installing people-counting sensors at the airport. This paper was accepted by Vivek Farias, data science. Funding: Financial support from the Triangle Impact Challenge 2021 is gratefully acknowledged. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.05152 .