Does the past predict the future? The case of delay announcements in service systems

Motivated by the recent interest in making delay announcements in large service systems, such as call centers, we investigate the accuracy of announcing the waiting time of the last customer to enter service (LES). In practice, customers typically respond to delay announcements by either balking or by becoming more or less impatient, and their response alters system performance. We study the accuracy of the LES announcement in single-class, multiserver Markovian queueing models with announcement-dependent customer behavior. We show that, interestingly, even in this stylized setting, the LES announcement may not always be accurate. This motivates the need to study its accuracy carefully and to determine conditions under which it is accurate. Since the direct analysis of the system with customer response is prohibitively difficult, we focus on manyserver, heavy-traffic analysis instead. We consider the quality-and-efficiency-driven and efficiency-driven many-server, heavy-traffic regimes and prove, under both regimes, that the LES prediction is asymptotically accurate if and only if asymptotic fluctuations in the queue length process are small as long as some regulatory conditions apply. This result provides an easy check for the accuracy of LES announcements in practice. We supplement our theoretical results with an extensive simulation study to generate practical managerial insights.