A note on the benefits of buffering

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 $\frac{1}{2}$). 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.