A Note on the Benefits of Buffering

Abstract

Gaussian traffic models are capable of representing a broad variety of correlation structures, ranging from short-range dependent (e.g., Ornstein–Uhlenbeck type) to long-range dependent (e.g., fractional Brownian motion, with Hurst parameter H exceeding ). This note focuses on queues fed by a large number (n) of Gaussian sources, emptied at constant service rate nc. In particular, we consider the probability of exceeding buffer level nb, as a function of b. This probability decaying (asymptotically) exponentially in n, the essential information is contained in the exponential decay rate I(b). The main result of this note describes the duality relation between the shape of I( ⋅ ) and the correlation structure. More specifically, it is shown that the curve I( ⋅ ) is convex at some buffer size b if and only if there are negative correlations on the time scale at which the overflow takes place.

Key Words:

• Queueing
• Gaussian sources
• Correlation structure
• Large deviations asymptotics

Acknowledgments

The author is indebted to Krzysztof De¸bicki (CWI) and Laurent Massoulié (Microsoft Research Cambridge, UK) for valuable discussions.