Establishing Convergence of Infinite-Server Queues with Batch Arrivals to Shot-Noise Processes

• 成果类型: Article
• 署名作者: Daw, Andrew; Fralix, Brian; Pender, Jamol
• 署名单位: University of Southern California; Clemson University; Cornell University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0353
• 发表日期: 2025
• 页码: 2002-2009
• 关键词: fluid queues

摘要

Across domains as diverse as communication channels, computing systems, and public health management, a myriad of real -world queueing systems receive batch arrivals of jobs or customers. In this work, we show that under a natural scaling regime, both the queue -length process and the workload process associated with a properly scaled sequence of infinite -server queueing systems with batch arrivals converge almost surely, uniformly on compact sets, to shot -noise processes. Given the applicability of these models, our relatively direct and accessible methodology may also be of independent interest, where we invoke the Glivenko-Cantelli theorem when the Strong Law of Large Numbers fails to hold for the queue -length batch scaling yet then, exploit the continuity of stationary excess distributions and the classic strong law when the Glivenko-Cantelli theorem fails to hold in the workload batch scaling. These results strengthen a convergence result recently established in the work of de Graaf et al. [de Graaf WF, Scheinhardt WR, Boucherie RJ (2017) Shot -noise fluid queues and infinite -server systems with batch arrivals. Performance Evaluation 116:143-155] in multiple ways, and furthermore, they provide new insight into how the queue -length and workload limits differ from one another.