Proof of a fundamental result in self-similar traffic modeling
ACM SIGCOMM Computer Communication Review
Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions
Queueing Systems: Theory and Applications
A most probable path approach to queueing systems with general Gaussian input
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Traffic with an fBm Limit: Convergence of the Stationary Workload Process
Queueing Systems: Theory and Applications
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In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. Let $Q^{(c)}_{X}\equiv\{Q^{(c)}_{X}(t):t\ge0\}$ denote a stationary buffer content process for a fluid queue fed by the centered Gaussian process X≡{X(t):t∈R} with stationary increments, X(0)=0, continuous sample paths and variance function σ2(·). The system is drained at a constant rate c0, so that for any t≥0, $Q^{(c)}_{X}\equiv\{Q_{X}^{(c)}(t):t\ge0\}$ in the regimes c→0 (heavy traffic) and c→∞ (light traffic). We show for both limiting regimes that, under mild regularity conditions on σ, there exists a normalizing function δ(c) such that $Q^{(c)}_{X}(\delta(c)\cdot)/\sigma(\delta(c))$ converges to $Q^{(1)}_{B_{H}}(\cdot)$ in C[0,∞), where BH is a fractional Brownian motion with suitably chosen Hurst parameter H.