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Stern School of Business, New York University, 44 West 4th Street, New York, New York 10012
Motivated by practices in customer contact centers, we consider a system that offers two modes of service: real-time and postponed with a delay guarantee. Customers are informed of anticipated delays and select their preferred option of service. The resulting system is a multiclass, multiserver queueing system with state-dependent arrival rates. We propose an estimation scheme for the anticipated real-time delay that is asymptotically correct, and a routing policy that is asymptotically optimal in the sense that it minimizes real-time delay subject to the deadline of the postponed service mode. We also show that our proposed state-dependent scheme performs better than a system in which customers make decisions based on steady-state waiting-time information. Our results are derived using an asymptotic analysis based on "many-server" limits for systems with state-dependent parameters.
Columbia Business School, 409 Uris Hall, 3022 Broadway, New York, New York 10027
marmony{at}stern.nyu.edu
c.maglaras{at}columbia.edu
Subject classifications: service networks; service level guarantees; multiclass queueing systems; call-back option; call centers; Halfin-Whitt regime; real-time delay notification.
History: Received June 2002;
revision received January 2003;
accepted July 2003.
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