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

Original language | Undefined |
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Pages (from-to) | 43-53 |

Number of pages | 11 |

Journal | Stochastic models |

Volume | 20 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 |

### Keywords

- Queueing
- EWI-17708
- Gaussian sources
- Correlation structure
- IR-70508
- Large deviations asymptotics

## Cite this

Mandjes, M. R. H. (2004). A note on the benefits of buffering.

*Stochastic models*,*20*(1), 43-53. https://doi.org/10.1081/STM-120028390