Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows

• 成果类型: Article
• 署名作者: Zwart, B; Borst, S; Mandjes, M
• 署名单位: Eindhoven University of Technology; Centrum Wiskunde & Informatica (CWI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000161
• 发表日期: 2004
• 页码: 903-957
• 关键词: long-range dependence; buffer-content distributions; m/g/infinity input; large deviations; finite buffer; server queue; probabilities; EQUIVALENCE; models

摘要

We consider a fluid queue fed by multiple On-Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a dominant subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a minimally critical set of On-Off flows with regularly varying On periods. In case the dominant set contains just a single On-Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On-Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reduced-load equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios.