The Impact of Delay Announcements in Many-Server Queues with Abandonment

Abstract

This paper studies the performance impact of making delay announcements to arriving customers who must wait before starting service in a many-server queue with customer abandonment. The queue is assumed to be invisible to waiting customers, as in most customer contact centers, when contact is made by telephone, e-mail, or instant messaging. Customers who must wait are told upon arrival either the delay of the last customer to enter service or an appropriate average delay. Models for the customer response are proposed. For a rough-cut performance analysis, prior to detailed simulation, two approximations are proposed: (1) the equilibrium delay in a deterministic fluid model, and (2) the equilibrium steady-state delay in a stochastic model with fixed delay announcements. These approximations are shown to be effective in overloaded regimes, where delay announcements are important, by making comparisons with simulations. Within the fluid model framework, conditions are established for the existence and uniqueness of an equilibrium delay, where the actual delay coincides with the announced delay. Multiple equilibria can occur if a key monotonicity condition is violated.

Waiting Patiently: An Empirical Study of Queue Abandonment in an Emergency Department

“…They nd that providing information always either improves throughput or customer utility, but not necessarily both. Similarly, Jouini et al (2009) and Armony et al (2009) both examine the impact of delay announcements on abandonment behavior in multi-server, invisible queues and nd that providing more information can improve system performance with little customer loss. Plambeck and Wang (2012) shows that if customers exhibit time-inconsistent preferences through hyperbolic discounting, then hiding the queue may be welfare maximizing while being suboptimal for the service provider.…”

A Time-Varying Call Center Design via Lagrangian Mechanics

“…Other recent papers within this category include Armony et al [1], Baron and Milner [2], Garnett et al [11], and Zeltyn and Mandelbaum [31], [32]. Each of these papers studies systems with customer abandonment.…”

Queueing models for full-flexible multi-class call centers with real-time anticipated delays

“…An extension of the latter work is addressed by Jouini et al [15]. Other close references include those by Armony et al [4], Guo and Zipkin [12], and references therein. We also refer the reader to Vosz and Witt [25], and Kaminsky and Kaya [17] for work dealing with quoting customer lead times in the context of supply chains.…”

“…Customers would have a patience behavior different from that in the original system (without announcement), depending on the information we provide to them, since the announced time might influence their expectations or perceptions regarding waiting time. We refer the reader to Armony et al [4] and Guo and Zipkin [12] for further details on the subject.…”