### Abstract

Original language | Undefined |
---|---|

Article number | 10.1081/STM-120028390 |

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

*Stochastic models*,

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

}

*Stochastic models*, vol. 20, no. 1, 10.1081/STM-120028390, pp. 43-53. https://doi.org/10.1081/STM-120028390

**A note on the benefits of buffering.** / Mandjes, M.R.H.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A note on the benefits of buffering

AU - Mandjes, M.R.H.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Queueing

KW - EWI-17708

KW - Gaussian sources

KW - Correlation structure

KW - IR-70508

KW - Large deviations asymptotics

U2 - 10.1081/STM-120028390

DO - 10.1081/STM-120028390

M3 - Article

VL - 20

SP - 43

EP - 53

JO - Stochastic models

JF - Stochastic models

SN - 1532-6349

IS - 1

M1 - 10.1081/STM-120028390

ER -