Stability analysis of second-order fluid flow models in a stationary ergodic environment

• 成果类型: Article
• 署名作者: Rabehasaina, L; Sericola, B
• 署名单位: Universite Paris Saclay; Universite de Rennes
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 1449-1473
• 关键词: stochastic-theory; QUEUE

摘要

In this paper, we study the stability of a fluid queue with an infinite-capacity buffer. The input and service rates are governed by a stochastic process, called the environment process, and are allowed to depend on the fluid level in the buffer. The variability of the traffic is modeled by a Brownian motion and a local variance function, which also depends on the fluid level in the buffer. The behavior of this second-order fluid flow model is described by a reflected stochastic differential equation, and, under stationarity and ergodicity assumptions on the environment process, we obtain stability conditions for this general fluid queue.