On the maximum workload of a queue fed by fractional Brownian motion

• 成果类型: Article
• 署名作者: Zeevi, AJ; Glynn, PW
• 署名单位: Stanford University; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2000
• 页码: 1084-1099
• 关键词: long-range dependence; input; deviations; MODEL

摘要

Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM). When the queue is stable, we prove that the maximum of the workload process observed over an interval of length t grows like gamma (logt)(1/(2-2H)), where H > 1/2 is the self-similarity index (also known as the Hurst parameter) that characterizes the fBM and can be explicitly computed. Consequently, we also have that the typical time required to reach a level b grows like exp{b(2(1-H))}. We also discuss the implication of these results for statistical estimation of the tail probabilities associated with the steady-state workload distribution.