Waiting-Time Prediction with Invisible Customers

Abstract

Problem definition: We study the problem of predicting in real time customers' expected waiting time in partially visible service systems. Unlike previous research, in our problem, the predictor only observes a subset of the customers who interact with the system, while all customers are served indiscriminately.

Methodology/results: We apply a theoretical analysis to a novel partially visible parsimonious queueing model that highlights the technical challenges in obtaining an analytical solution in more general systems. Subsequently, we use the solution as an element of a data-driven approach to solve the problem in more general settings. We also conduct extensive numerical experiments using the simulated data of queueing models inspired by the related literature and real data from a large outpatient hospital. The experiments suggest that the approach is robust to a large extent, yet it is also limited when critical data are missing or when the underlying theoretical model is "too far" from the actual system.

Managerial implications: Our work shows that standard methods fail and instead provides practical tools to predict waiting times in partially visible service systems, as well as insights into how much observable data are actually needed to make sufficiently accurate predictions in partially visible queueing systems.

Keywords: waiting time prediction, queues, invisible customers, machine learning.