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Exact asymptotics for a queue with fractional Brownian input and applications in ATM networks

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Tyrone E. Duncan ,
Yi Yan  and
Peng Yan
Tyrone E. Duncan*
Affiliation:
University of Kansas
Yi Yan*
Affiliation:
Sprint
Peng Yan*
Affiliation:
Ohio State University
*
∗ Postal address: Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA.
∗∗ Postal address: Sprint, Network Design, 7171 W. 95th Street, Overland Park, KS 66212, USA. Email address: [email protected]
∗∗∗ Postal address: Department of Electrical Engineering, Ohio State University, Columbus, OH 43210, USA.
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Abstract

In this paper, a single channel FIFO fluid queue with an infinite buffer space and a long-range dependent input is studied. The input traffic is modeled by an average input rate plus a standard fractional Brownian motion as the fluctuation. Lower and upper bounds are derived for the tail distribution of the transient queue length at time T, which result in a logarithmic characterization of the asymptotic behavior of the tail distribution. Furthermore, the exact asymptotic is also obtained. It is observed that the transient queue length under fractional Brownian input does not suffer from the heavy-tail property as does the steady-state queue length. The results are used to compute the equivalent bandwidth requirement for ATM broadband connections with fractional Brownian traffic feed and finite connection holding time.

Keywords

Fractional Brownian motionlong-range dependent propertyasymptotic behaviorheavy tailequivalent bandwidth

MSC classification

Primary: 60G18: Self-similar processes
Secondary: 60G70: Extreme value theory; extremal processes 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 932 - 945
Copyright
Copyright © by the Applied Probability Trust 2001 

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