EURO 2024 Copenhagen
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945. Data-Driven Population Tracking in Large Service Systems

Invited abstract in session MC-40: Advances in Stochastic Modelling and Applied Probability II, stream Advances in Stochastic Modelling and Learning Methods.

Monday, 12:30-14:00
Room: 96 (building: 306)

Authors (first author is the speaker)

1. Fernando Bernstein
Duke University

Abstract

We develop a stylized theoretical framework for the problem of tracking the population in a service system with noisy input and output observations. The motivation for the project is the problem of tracking the population of passengers in the TSA area at an airport in real time using noisy data from people counters. Our goal is to devise and analyze policies that use past people counter data to estimate the population in the system over a finite and discrete time horizon. We evaluate the performance of policies in two distinct settings. In the busyness tracking problem, the objective is to track whether the policy correctly detects if the system census is larger or smaller than a threshold. In the population tracking problem, the objective is to minimize the expected magnitude of the estimation error in each period. We show that our problem is more challenging than dynamic learning problems studied in the bandit literature. In the busyness tracking problem, we derive a general lower bound on the cumulative expected loss that grows linearly with the time horizon. In the population tracking problem, we prove another general lower bound on cumulative expected loss that is on the order of the square of the time horizon. Given this complexity, we develop and analyze policies that achieve the best possible performance in terms of the growth rate of cumulative expected loss. Furthermore, we investigate the benefit of conducting periodic inspections of the true census in the system.

Keywords

Status: accepted

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