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dc.contributor.advisorDuncan, Tyrone E.
dc.contributor.authorJin, Yasong
dc.date.accessioned2008-07-30T22:22:00Z
dc.date.available2008-07-30T22:22:00Z
dc.date.issued2007-12-11
dc.date.submitted2007
dc.identifier.otherhttp://dissertations.umi.com/ku:2300
dc.identifier.urihttp://hdl.handle.net/1808/3993
dc.description.abstractA fractional Brownian queueing model, that is, a fluid model with an input of a fractional Brownian motion, was proposed in the 1990s to capture the self-similarity and long-range dependence observed in Internet traffic. Since then, a Gaussian queueing model, which is a queueing model with an input of a continuous Gaussian process, has received much attention. In this dissertation, a Gaussian queueing model is discussed and the maximum queue length over a time interval [0, t] is analyzed. Under some mild assumptions, it is shown that a limit of the maximum queue length suitably normalized is determined by a suitable function of the asymptotic variance of the Gaussian input. Some Gaussian queueing models, such as a queue with an input of several independent fractional Brownian motions and a queue with an input of an integrated Ornstein-Uhlenbeck process, are discussed as examples. For a fractional Brownian queueing model, the main results extend some related known results in the literature. The results on the maximum queue length provide insights for the occurrence of large excursions, which are also called congestion events, in a queueing process. In the context of a fractional Brownian queueing model the temporal properties of congestion events, such as the duration and the inter-congestion event time, are analyzed. A new method based on a Poisson clumping approximation is proposed to evaluate these properties. By comparing with simulation results, it is illustrated that the proposed methodology produces satisfying results for estimating the temporal properties of congestion events in a fractional Brownian queueing model.
dc.format.extent111 pages
dc.language.isoEN
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.subjectQueue
dc.subjectFractional brownian motion
dc.subjectMaximum queue length
dc.subjectNetwork modeling
dc.titleMaximum Queue Length of a Fluid Model with a Gaussian Input
dc.typeDissertation
dc.contributor.cmtememberHu, Yaozhong
dc.contributor.cmtememberHuang, Weizhang
dc.contributor.cmtememberPasik-Duncan, Bozenna
dc.contributor.cmtememberFrost, Victor S.
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelPH.D.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
kusw.bibid6599202
dc.rights.accessrightsopenAccess


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