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

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.

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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

Information

Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1036.60088
MathSciNet: MR2023883
Digital Object Identifier: 10.1214/aoap/1069786505

Subjects:
Primary: 60G35 , 60K25
Secondary: 60H10 , 60H20

Keywords: Brownian motion , Fluid queues , Lindley's equation , reflected stochastic differential equations , stability

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 4 • November 2003
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