Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times

• 成果类型: Article
• 署名作者: Schol, Dennis; Vlasiou, Maria; Zwart, Bert
• 署名单位: Eindhoven University of Technology; University of Twente
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1171
• 发表日期: 2022
• 页码: 1335-1364
• 关键词: heavy-traffic limits; Synchronization; samples; sets

摘要

In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as N -> infinity. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.