DISTRIBUTION-VALUED HEAVY-TRAFFIC LIMITS FOR THE G/GI/∞ QUEUE

• 成果类型: Article
• 署名作者: Reed, Josh; Talreja, Rishi
• 署名单位: New York University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1027
• 发表日期: 2015
• 页码: 1420-1474
• 关键词: theorem; Tightness; EQUATIONS; proofs

摘要

We study the G/GI/infinity queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distribution-valued processes. We find that our diffusion limits are tempered distribution-valued Ornstein-Uhlenbeck processes.