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

Mor Armony
Stern School of Business
New York University


Wednesday, March 15, 2006
4:30 - 5:45 PM
Terman Engineering Center, Room 453


Abstract:

In this work we develop methods to study the impact upon aggregate system performance of state-dependent delay announcements to arriving customers in a many-server queue with customer abandonment. We assume that the queue is not visible to waiting customers, as in most customer contact centers, when contact is made by telephone, email or instant messaging. As a function of the announced delay customers may balk or have new abandonment behavior. To perform a rough-cut analysis, prior to a more detailed study, we use a fluid model, which provides an approximate and highly simplified description of large systems in an overloaded regime. In the fluid model, all customers are faced with the same delay and consequently can be given the same delay announcement. At the same time, the time-to-abandon distribution plays a critical role.

We show that the resulting approximate description of aggregate performance is effective by comparing to (1) a numerical algorithm approximating the steady-state performance of an M/GI/s+GI queueing model with a constant delay announcement and (2) simulations with state-dependent announcements. Specifically, customers who cannot enter service immediately are told the delay of the last customer to enter service. Within the fluid-model framework, we find conditions under which there exists a unique equilibrium delay, where the actual delay coincides with the announced delay, and for a natural iteration to converge to that equilibrium delay. We further consider the effect of providing biased delay information, and show how the fluid model can be applied to do further studies.

This is joint work with Nahum Shimkin and Ward Whitt.

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