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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

Information

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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References

Adler, R. J. (1990). An introduction to continuity, extrema and related topics for general Gaussian processes. Institute of Math. Stat. Lecture notes, Hayward, CA.Google Scholar
Adler, R. J., and Samorodnitsky, G. (1987). Tail behaviour for the suprema of Gaussian processes with applications to empirical processes. Ann. Prob. 15, 1339–1351.Google Scholar
Berman, S. M. and Kôno, N. (1989). The maximum of a Gaussian process with non-constant variance: a sharp bound for the distribution tail. Ann. Prob. 17, 632–650.Google Scholar
Brichet, F., Roberts, J., Simonian, A., and Veitch, D. (1997). Heavy traffic analysis of a storage model with long range dependent on/off sources. Queueing Systems 23, 197–215.Google Scholar
Duffield, N. G., and O'Connell, N. (1995). Large deviations and overflow probabilities for the general single-server queue, with applications. Proc. Camb. Phil. Soc. 118, 363–374.Google Scholar
Murray, J. D. (1984). Asymptotic Analysis. Springer, Berlin.Google Scholar
Narayan, O. (1998). Exact asymptotic queue length distribution for fractional Brownian traffic. Adv. Performance Anal. 1, 39–64.Google Scholar
Norros, I. (1994). A storage model with self-similar input. Queueing Systems 16, 387–396.Google Scholar
Norros, I. (1995). On the use of fractional Brownian motion. IEEE Sel. Areas Comm. 13, 953–962.Google Scholar
Norros, I., Simonian, A., Veitch, D., and Virtamo, J. (1995). A Beneš formula for a buffer with fractional Brownian input. In 9th ITC Specialists Seminar '95: Teletraffic Modelling and Measurement.Google Scholar
Samorodnitsky, G., and Taqqu, M. S. (1994). Stable Non-Gaussian Random Processes. Chapman and Hall, London.Google Scholar