Heavy traffic limit for a processor sharing queue with soft deadlines

• 成果类型: Article
• 署名作者: Gromoll, Christian; Kruk, Lukasz
• 署名单位: Stanford University; Maria Curie-Sklodowska University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000014
• 发表日期: 2007
• 页码: 1049-1101
• 关键词: state-space collapse; real-time queues; fluid limit; networks

摘要

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.