Busy periods of fractional Brownian storage: A large deviations approach

Ilkka Norros

Research output: Contribution to journalArticleScientificpeer-review

Abstract

A storage with constant service rate and fractional Brownian input is considered. It is shown how large deviation asymptotics of the buffer occupancy and the ongoing busy period can be obtained applying a generalized Schilder's theorem. The crucial point of the method is to identify the "most probable path" satisfying some criterion. Whereas this turns out to be very simple in the case of achieving a given buffer occupancy, the case of achiev-ing a given length of the ongoing busy period remains an open problem. Instead, tight bounds are obtained in this latter case.
Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalAdvances in Performance Analysis
Volume2
Issue number1
Publication statusPublished - 1999
MoE publication typeA1 Journal article-refereed

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Busy Period
Large Deviations
Buffer
Fractional
Probable
Open Problems
Path
Theorem

Cite this

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Busy periods of fractional Brownian storage : A large deviations approach. / Norros, Ilkka.

In: Advances in Performance Analysis, Vol. 2, No. 1, 1999, p. 1-19.

Research output: Contribution to journalArticleScientificpeer-review

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AB - A storage with constant service rate and fractional Brownian input is considered. It is shown how large deviation asymptotics of the buffer occupancy and the ongoing busy period can be obtained applying a generalized Schilder's theorem. The crucial point of the method is to identify the "most probable path" satisfying some criterion. Whereas this turns out to be very simple in the case of achieving a given buffer occupancy, the case of achiev-ing a given length of the ongoing busy period remains an open problem. Instead, tight bounds are obtained in this latter case.

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