Stability Analysis of Second Order Fluid Flow Models with State-Dependent Parameters
Résumé
We study in this paper the stability of a fluid queue with an infinite capacity buffer. The input and service rates are governed by a general stochastic 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, we obtain stability conditions for this general fluid queue.