Fluid queues with heavy-tailed M/G/∞ input

• 成果类型: Article
• 署名作者: Borst, S; Zwart, B
• 署名单位: Centrum Wiskunde & Informatica (CWI); Alcatel-Lucent; Lucent Technologies; AT&T; Eindhoven University of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1050.0159
• 发表日期: 2005
• 页码: 852-879
• 关键词: single-server queue; on-off processes; large deviations; asymptotics; distributions; probabilities; multiplexer

摘要

We consider a fluid queue fed by several heterogeneous M/G/infinity input processes with regularly varying session lengths. Under fairly mild assumptions, we derive the exact asymptotic behavior of the stationary workload distribution. In addition, we obtain several asymptotic results for the transient workload distribution, which are applied to obtain a conditional limit theorem for the most probable time to overflow. The results are strongly inspired by the large-deviations idea that overflow is typically due to some minimal combination of extremely long concurrent sessions causing positive drift. The typical configuration of long sessions is identified through a simple integer program, paving the way for the exact computation of the asymptotic workload behavior. The calculations provide crucial insight in the typical overflow scenario.