Data-driven Population Tracking in Large Service Systems

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