Gaussian and multifractal processes in teletraffic theory

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Mannersalo, Petteri
dc.date.accessioned 2012-02-10T09:27:08Z
dc.date.available 2012-02-10T09:27:08Z
dc.date.issued 2003-04-25
dc.identifier.isbn 951-38-6037-X
dc.identifier.issn 1455-0849
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/2199
dc.description.abstract In this thesis, we consider two classes of stochastic models which both capture some of the essential properties of teletraffic. Teletraffic has two time regimes where profoundly different behavior and characteristics are seen. When traffic traces are observed at coarse resolutions, properties like self-similarity and long-range dependence are visible. In small time-scales, traffic exhibits complex scaling laws with much more spiky bursts than in coarser resolutions. The main part of the thesis is devoted to a large time-scale analysis by considering Gaussian processes and queueing systems with Gaussian input. In order to understand the small time-scale dynamics, first steps are taken towards general multifractal models offering a suitable basis for short time-scale teletraffic modeling. The family of Gaussian processes with stationary increments serves as the traffic model for large time-scales. First, we introduce a fast and accurate simulation algorithm, which can be used to generate long approximate Gaussian traces. Moreover, the algorithm is also modified to run on-the-fly. Then approximate queue length distributions for ordinary, priority and generalized processor sharing queues are derived using a most probable path approach. Simulation studies show that the performance formulae appear to be quite accurate over the full range of buffer levels. Finally, we construct a semi-stationary predictor, which uses a constant variance function and mean rate estimation based on a moving average method. Moreover, we show that measuring the past of a process by geometrically increasing intervals is a good engineering solution and a much better way than equally spaced measurements. We introduce a family of multifractal processes which belongs to the framework of T-martingales and multiplicative chaos introduced by Kahane. The family has many desirable properties like stationarity of increments, concave multifractal spectra and simple construction. We derive, for example, conditions for non-degeneracy, establish a power law for the moments and obtain a formula for the multifractal spectrum. en
dc.format.extent 44, [109]
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher VTT Technical Research Centre of Finland en
dc.publisher VTT fi
dc.relation.ispartofseries VTT publications en
dc.relation.ispartofseries 491 en
dc.relation.haspart Norros, I., Mannersalo, P. and Wang, J. Simulation of fractional Brownian motion with conditionalized random midpoint displacement. Advances in Performance Analysis, 1999. Vol. 2(1), pp. 77-101.
dc.relation.haspart Addie, R., Mannersalo, P. and Norros, I. Performance formulae for queues with Gaussian input. In Proceedings of ITC 16. Edinburgh, UK, 1999. Pp. 1169-1178.
dc.relation.haspart Addie, R., Mannersalo, P. and Norros, I. Most probable paths and performance formulae for buffers with Gaussian input traffic. European Transactions in Telecommunications, 2002. Vol. 13(3), pp. 183-196.
dc.relation.haspart Mannersalo, P. and Norros, I. Approximate formulae for Gaussian priority queues. In Proceedings of ITC 17. Salvador, Brazil, 2001. Pp. 991-1002.
dc.relation.haspart Mannersalo, P. and Norros, I. GPS schedulers and Gaussian traffic. In Proceedings of IEEE Infocom 2002. New York, USA, 2002. Pp. 1660-1667.
dc.relation.haspart Mannersalo, P. and Norros, I. A most probable path approach to queueing systems with general Gaussian input. Computer Networks, 2002. Vol. 40(3), pp. 399-412.
dc.relation.haspart Mannersalo, P. Some notes on prediction of teletraffic. In Proceedings of 15th ITC Specialist Seminar. Würzburg, Germany, 2002. Pp. 220-229.
dc.relation.haspart Mannersalo, P., Norros, I. and Riedi, R. Multifractal products of stochastic processes: construction and some basic properties. Advances in Applied Probability, 2002. Vol. 34(4), pp. 888-903.
dc.subject.other Electrical engineering en
dc.title Gaussian and multifractal processes in teletraffic theory en
dc.type G5 Artikkeliväitöskirja fi
dc.description.version reviewed en
dc.contributor.department Department of Electrical and Communications Engineering en
dc.contributor.department Sähkö- ja tietoliikennetekniikan osasto fi
dc.subject.keyword Gaussian processes en
dc.subject.keyword multifractals en
dc.subject.keyword queueing systems en
dc.subject.keyword performance analysis en
dc.subject.keyword traffic modeling en
dc.identifier.urn urn:nbn:fi:tkk-001692
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en


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