Invariant states and rates of convergence for a critical fluid model of a processor sharing queue

• 成果类型: Article
• 署名作者: Puha, AL; Williams, RJ
• 署名单位: California State University System; California State University San Marcos; University of California System; University of California San Diego
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000017
• 发表日期: 2004
• 页码: 517-554
• 关键词: space collapse; networks; approximations

摘要

This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches infinity. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of convergence. These results are used in a related work by Gromoll for establishing a heavy traffic diffusion approximation for a processor sharing queue.