Chapter 3

Queues in Service Systems: Customer Abandonment and Diffusion Approximations

J. G. Dai
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, dai@gatech.edu

Shuangchi He
Department of Industrial and Systems Engineering, National University of Singapore, Singapore 117576, heshuangchi@gatech.edu

Abstract
In a service system, the system performance is sensitive to customer abandonment.We focus on G/GI/n+GI parallel-server queues, which serve as a building block to model service systems. Consistent with recent empirical findings, such a queue has a general arrival process (the G) that can be time nonhomogeneous, independent and identically distributed (iid) service times with a general distribution (the first GI), and iid patience times with a general distribution (the +GI). Following the square-root safety staffing rule, companies are able to operate such queues in the quality- and effciency-driven (QED) regime that is characterized by large customer volume, the waiting times being a fraction of the service times, only a small fraction of customers abandoning the queue, and high server utilization. We survey recent results on many-server queues that operate in the QED regime. These results include the sensitivity of patience time distributions and diffusion models as a practical tool for performance analysis.

Keywords: Kingman approximation; heavy traffic; square-root safety staffing; Halfin-Whitt regime; quality- and efficiency-driven regime; piecewise OU process; functional central limit theorem

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Citation information:

Dai J.G., S. He. Queues in service systems: Customer abandonment and diffusion approximations. J. Geunes, ed. INFORMS TutORials in Operations Research, Vol. 8. INFORMS, Hanover, MD, pp. 36--59