Queues with Many Servers and Impatient Customers

• 成果类型: Article
• 署名作者: Mandelbaum, Avishai; Momcilovic, Petar
• 署名单位: Technion Israel Institute of Technology; State University System of Florida; University of Florida
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1110.0530
• 发表日期: 2012
• 页码: 41-65
• 关键词: heavy-traffic limits; ABANDONMENT

摘要

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.