Heavy traffic limits for some queueing networks

• 成果类型: Article
• 署名作者: Bramson, M; Dai, JG
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/998926987
• 发表日期: 2001
• 页码: 49-90
• 关键词: multiclass queuing-networks; reflecting brownian motions; state-space collapse; STABILITY; orthant; approximations; customers; feedback

摘要

Using a slight modification of the framework of Bramson [7] and Williams [54], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single-station systems operating under first-in-first-out (FIFO), generalized-head-of-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines that operate under first-buffer-first-serve (FBFS) and last-buffer-first-serve (LBFS) service disciplines; the last family consists of certain two-station, five-class networks operating under an SEP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.