Many-Server Heavy-Traffic Limits for Queueing Systems with Perfectly Correlated Service and Patience Times

• 成果类型: Article
• 署名作者: Yu, Lun; Perry, Ohad
• 署名单位: Tsinghua University; Northwestern University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1300
• 发表日期: 2023
• 页码: 1119-1157
• 关键词: Queues

摘要

We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting in queue. Under the usual many-server diffusion scaling, we show that the system is asymptotically equivalent to a system with no abandonment. In particular, the limit is the Halfin-Whitt diffusion for the M/M/n queue when the traffic intensity approaches its critical value 1 from below, and is otherwise a transient diffusion, despite the fact that the prelimit is positive recurrent. To obtain a refined measure of the congestion due to the correlation, we characterize a lower-order fluid (LOF) limit for the case in which the diffusion limit is transient, demonstrating that the queue in this case scales like n(3/4). Under both the diffusion and LOF scalings, we show that the stationary distributions converge weakly to the time-limiting behavior of the corresponding process limit.