Queues with Many Servers and Impatient Customers

Authors:
Avishai Mandelbaum;Petar Momčilović
Affiliations:
Faculty of Industrial Engineering and Management, Technion--Israel Institute of Technology, Haifa 3200, Israel;Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611
Venue:
Mathematics of Operations Research
Year:
2012

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Abstract

The asymptotic many-server queue with abandonments, G/GI/N + GI, is considered in the quality-and efficiency-driven (QED) regime. Here the number of servers and the offered load are related via the square-root rule, as the number of servers increases indefinitely. QED performance entails short waiting times and scarce abandonments (high quality) jointly with high servers' utilization (high efficiency), which is feasible when many servers cater to a single queue. For the G/GI/N + GI queue, we derive diffusion approximations for both its queue-length and virtual-waiting-time processes. Special cases, for which closed-form analysis is provided, are the G/M/N + GI and G/D/N + GI queues, thus expanding and generalizing existing results.