A note on the benefits of buffering

M.R.H. Mandjes

5 Citations (Scopus)

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 10.1081/STM-120028390 43-53 11 Stochastic models 20 1 https://doi.org/10.1081/STM-120028390 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. [10.1081/STM-120028390]. https://doi.org/10.1081/STM-120028390
Mandjes, M.R.H. / A note on the benefits of buffering. In: Stochastic models. 2004 ; Vol. 20, No. 1. pp. 43-53.
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Mandjes, MRH 2004, 'A note on the benefits of buffering' 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.

In: Stochastic models, Vol. 20, No. 1, 10.1081/STM-120028390, 2004, p. 43-53.

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 -