On the Accuracy of the Last-To-Enter-Service Delay Announcement: Bridging Theory and Practice
Service providers often share delay information, in the form of delay announcements, with their customers. In practice, simple delay announcements, such as average waiting times or a weighted average of previously delayed customers, are often used. Our goal in this paper is to gain insight into when such announcements perform well. To do so, we compare the accuracies of two announcements: (i) a static announcement which does not exploit information about the current state of the system, and (ii) a dynamic announcement, specifically the last-to-enter-service (LES) announcement, which is equal to the delay of the last customer to have entered service at the time of the announcement. So far, the literature on delay announcements has focused, for the most part, on studying the accuracy of various types of announcements in specific queueing models. As such, the practical validity of various announcements remains intimately tied to the appropriateness of the technical conditions under which these models were studied. In other words, in order to decide whether a type of announcement is appropriate for her system, a manager would need to assess whether a certain queueing model is a good fit for her data. Because this is often difficult to do, we propose a new, practice-driven, approach in this paper. In particular, we propose a novel correlation-based approach which is theoretically appealing because it allows for a comparison of the performances of announcements across different queueing models, including multi-class models with a priority service discipline. It is also practically useful because estimating correlations is much easier than fitting an entire queueing model. Using a combination of queuing-theoretic analysis, real-life data analysis, and simulation, we analyze the performance of static and dynamic announcements, and derive an appropriate weighted average of the two which we demonstrate has a superior performance in both theory and practice.
Bassamboo, Achal. 2018. On the Accuracy of the Last-To-Enter-Service Delay Announcement: Bridging Theory and Practice.