Fluid Limits for Longest Remaining Time First Queues

• 成果类型: Article
• 署名作者: Kruk, Lukasz
• 署名单位: Maria Curie-Sklodowska University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0090
• 发表日期: 2024
• 页码: 2271-2294
• 关键词: processing time; PROOF

摘要

A single-server queue with renewal arrivals and generally distributed independent and identically distributed service times is considered. Customers are served using the longest remaining time first scheduling algorithm. In case of a tie, processor sharing is utilized. We introduce a fluid model for the evolution of a measure-valued state descriptor of this queue, and we investigate its properties. We also prove a fluid limit theorem justifying our fluid model as the first-order approximation of the queueing system under consideration.