Abstract
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.
Citation
Landy Rabehasaina. Bruno Sericola. "Stability analysis of second-order fluid flow models in a stationary ergodic environment." Ann. Appl. Probab. 13 (4) 1449 - 1473, November 2003. https://doi.org/10.1214/aoap/1069786505
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