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Large buffer asymptotics for the queue with fractional Brownian input

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Laurent Massoulie  and
Alain Simonian
Laurent Massoulie*
Affiliation:
Microsoft Research
Alain Simonian*
Affiliation:
France Télécom
*
∗Email address: lmassoul@microsoft.com
∗∗Email address: alain.simonian@francetelecom.fr
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Abstract

In this paper, a strong asymptotic estimate for the queue content distribution of a fluid queue fed by a fractional Brownian input with Hurst parameter H ∊ [1/2,1[is studied. By applying general results on suprema of centred Gaussian processes, in particular, we show that for large x. Explicit formulae for constants κ, γ and L are given in terms of H and system parameters.

Keywords

Fluid queuefractional Brownian inputsupremum of Gaussian processesasymptotics

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 894 - 906
Copyright
Copyright © Applied Probability Trust 1999 

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