Waiting Time Prediction with Invisible Customers

Problem definition: Motivated by technological advances in real-time data collection about customers location in service systems, we study the effect of partial visibility of customers on waiting time prediction. We consider systems where the predictor observes only a subset of the customers interacting with the system while serving all customers indiscriminately. Methodology/results: We formulate a novel model of a partially visible queue and analyze the waiting time prediction problem, deriving a closed-form expression for the optimal prediction. This facilitates quantifying the performance loss of arbitrary prediction methods because of partial visibility and their inherent limitations (i.e., bias and variance). We compare the performance of a wide range of commonly used predictive methods and examine how partial visibility along with other system parameters affects their performance. We further extend these numerical analyses to queueing systems that exhibit characteristics that are common in practice and that were studied in the service operations literature. Managerial implications: Our analysis shows that the phenomenon of invisible customers profoundly impacts the ability to accurately predict waiting times and should, therefore, be considered an important factor in the development of prediction tools. Such tools cannot be effectively deployed if technological barriers or operational limitations prevent a sufficiently high level of data integrity. This work provides specific insights into the effectiveness of various commonly used prediction methods, some of which are shown to be highly sensitive to partial visibility and other queueing systems characteristics. Our findings suggest that machine learning methods that use carefully chosen features offer the most effective generic solution for waiting time prediction in the presence of invisible customers and explain the mechanisms through which partial visibility deteriorates the performance of prediction methods. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0098 .