ORCIBS Seminar - Fernando Bernstein

We develop a stylized theoretical framework for the problem of dynamically 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 the noisy data from people counters. In the airport, such real-time population tracking can be useful for several operational decisions. For example, when the number of passengers in the TSA area is large, the airport may need to deploy staff to manage the overflow from the designated queueing area. This use suggests an objective that detects when the queue becomes large. Other operational decisions, such as determining the number of security lanes to open or the number of officials to check IDs, rely on having an accurate estimate of the exact number of passengers in the TSA area. 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, each involving a different objective. First, in the binary loss setting, the objective is to track whether the policy correctly detects if the system census is larger or smaller than a threshold. Second, in the squared loss setting, the objective is to minimize the expected magnitude of the estimation error in each period (more precisely, the squared difference between the estimate and the true census in the system). We show that our problem is more challenging than dynamic learning problems typically studied in the bandit literature. In the binary loss setting, we derive a general lower bound on the cumulative expected cost that grows linearly with the time horizon. In the squared loss setting, we prove another general lower bound on cumulative expected cost that is on the order 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 cost. Furthermore, we generalize our analysis to investigate the benefits of augmenting the people counter information with periodic inspections of the true census in the system. Our motivating problem at the airport exemplifies a problem faced in other brick-and-mortar service settings in which – unlike in virtual service settings such as call centers – real-time occupancy information is not readily gathered but noisy signals may be available.