The U.S. Coast Guard maintains a network structure to connect its nation-wide assets. This paper analyzes and models four highly aggregate traces of the traffic to/from the Coast Guard Data Network ship-shore nodes, so that the models may be used to predict future system demand. These internet traces (polled at 5â 40â intervals) are shown to adhere to a Gaussian distribution upon detrending, which imposes limits to the exponential distribution of higher time-resolution traces. Wavelet estimation of the Hurst-parameter is shown to outperform estimation by another common method (Sample-Variances). The First Differences method of detrending proved problematic to this analysis and is shown to decorrelate AR(1) processes where 0.65< phi1 <1.35 and correlate AR(1) processes with phi1 <-0.25. The Hannan-Rissanen method for estimating (phi,theta) is employed to analyze this series and a one-step ahead forecast is generated. / Master of Science

A utilização de modelos de teletrafego que contemplem caractersticas tais como autossimilaridade e dependencia de longa duraçao tem se mostrado cada vez mais como sendo ponto-chave na correta caracterizaçao do teletrafego Local Area Network (LAN) e Wide Area Network (WAN) [1, 2]. Tal caracterizaçao e necessaria para o monitoramento e controle de teletrafego em redes convergentes [3]. Nesse contexto, a questão da estimaçao precisa do parâmetro de autossimilaridade, denominado de parâmetro de Hurst, torna-se essencial. Entretanto, estudos comprovam que, alem da dependência de longa duraçao, redes WAN podem, não raramente, apresentar caractersticas mistas de dependência de longa e de curta duraçao [4, 5]. Enquanto vasta literatura cientca, tanto teorica como pratica, tem abordado com anco a questão da acuracia de diversos estimadores para o parâmetro de Hurst [6, 7, 8, 9], pouca atenção tem sido dada a questão da estimação deste parâmetro na presenca de dependência de curta duração. O presente trabalho de pesquisa concentrou-se no estudo dos metodos de estimaçao do parametro de Hurst baseados no espectro wavelet, em particular atraves do metodo de Abry-Veitch [10] { baseado na transformada Discrete Wavelet Transform (DWT) { e atraves do espectro obtido atraves da transformada Discrete Wavelet Packet Transform (DWPT). Os resultados baseados no metodo de Abry-Veitch demonstram que, atraves de um ajuste apropriado dos par^ametros de estimaçao, tal metodo permite uma estimaçao robusta na presenca de componentes com dependencia de curta duraçao, mesmo em situaçoes de mudanca de regime de tal componente, caracterstica desejavel para a estimaçao em tempo real do parametro de Hurst. Entretanto, a dispersao consideravel apresentada, em alguns casos, pelas estimativas do metodo de Abry-Veitch, motivou o estudo da utilizaçao do espectro wavelet obtido via transformada DWPT para realizaçao da estimaçao do parametro de Hurst. Os resultados indicam que a utilizaçao de tal transformada gera um espectro wavelet tal que e possvel detectar a presenca ou não de componentes com dependencia de curta duraçao. Ao final, os resultados da pesquisa realizada são sumarizados e utilizados em uma proposta de mecanismo de estimaçao do parametro de Hurst em tempo real, na presenca simultanea de componentes de dependencia de longa e curta duracão. / The use of network trac models that hold self-similar and long-range dependence characteristics have shown to be a key element on the correct characterization of Local Area Network (LAN) and Wide Area Network (WAN) network trac [1, 2]. Such characterization is necessary to monitor and control the network trac in converged networks [3]. In this context, the accurate estimation of the selfsimilarity parameter, named Hurst parameter, is a major issue. However, studies show that, besides the long-range dependence, WAN network trac may, not uncommonly, present mixed long and short-range dependence characteristics [4, 5]. While great part of either theoretical or practical scientic literature has been focused on the issue of Hurst parameter estimator accuracy [6, 7, 8, 9], little attention has been given to the estimation of such parameter in the presence of short-range dependence. This research work has focused on the study of the Hurst parameter estimation methods based on the wavelet spectrum, specially through the Abry-Veitch method [10] { which is based on the Discrete Wavelet Transform (DWT) transform { and through the wavelet spectrum based on the Discrete Wavelet Packet Transform (DWPT) transform. The results based on the Abry-Veitch method show that, through a suitable adjustment of the estimation parameters, such method yields a robust estimation in the presence of short-range dependence components, even in changing conditions of such component, a desirable characteristic for the real-time estimation of the Hurst parameter. However, the signi cant dispersion presented, occasionally, by the Abry-Veitch method estimates motivated the research of the usage of the wavelet spectrum obtained via DWPT transform to estimate the Hurst parameter. The results show that the usage of such transform generates such a wavelet spectrum that it is possible to detect whether short-range dependence components are present, or not, in the analyzed series. At the end, the research results are summarized and used to propose a realtime Hurst parameter estimation mechanism, in the presence of simultaneous long- and short-range dependence components.

A utilização de modelos de teletrafego que contemplem caractersticas tais como autossimilaridade e dependencia de longa duraçao tem se mostrado cada vez mais como sendo ponto-chave na correta caracterizaçao do teletrafego Local Area Network (LAN) e Wide Area Network (WAN) [1, 2]. Tal caracterizaçao e necessaria para o monitoramento e controle de teletrafego em redes convergentes [3]. Nesse contexto, a questão da estimaçao precisa do parâmetro de autossimilaridade, denominado de parâmetro de Hurst, torna-se essencial. Entretanto, estudos comprovam que, alem da dependência de longa duraçao, redes WAN podem, não raramente, apresentar caractersticas mistas de dependência de longa e de curta duraçao [4, 5]. Enquanto vasta literatura cientca, tanto teorica como pratica, tem abordado com anco a questão da acuracia de diversos estimadores para o parâmetro de Hurst [6, 7, 8, 9], pouca atenção tem sido dada a questão da estimação deste parâmetro na presenca de dependência de curta duração. O presente trabalho de pesquisa concentrou-se no estudo dos metodos de estimaçao do parametro de Hurst baseados no espectro wavelet, em particular atraves do metodo de Abry-Veitch [10] { baseado na transformada Discrete Wavelet Transform (DWT) { e atraves do espectro obtido atraves da transformada Discrete Wavelet Packet Transform (DWPT). Os resultados baseados no metodo de Abry-Veitch demonstram que, atraves de um ajuste apropriado dos par^ametros de estimaçao, tal metodo permite uma estimaçao robusta na presenca de componentes com dependencia de curta duraçao, mesmo em situaçoes de mudanca de regime de tal componente, caracterstica desejavel para a estimaçao em tempo real do parametro de Hurst. Entretanto, a dispersao consideravel apresentada, em alguns casos, pelas estimativas do metodo de Abry-Veitch, motivou o estudo da utilizaçao do espectro wavelet obtido via transformada DWPT para realizaçao da estimaçao do parametro de Hurst. Os resultados indicam que a utilizaçao de tal transformada gera um espectro wavelet tal que e possvel detectar a presenca ou não de componentes com dependencia de curta duraçao. Ao final, os resultados da pesquisa realizada são sumarizados e utilizados em uma proposta de mecanismo de estimaçao do parametro de Hurst em tempo real, na presenca simultanea de componentes de dependencia de longa e curta duracão. / The use of network trac models that hold self-similar and long-range dependence characteristics have shown to be a key element on the correct characterization of Local Area Network (LAN) and Wide Area Network (WAN) network trac [1, 2]. Such characterization is necessary to monitor and control the network trac in converged networks [3]. In this context, the accurate estimation of the selfsimilarity parameter, named Hurst parameter, is a major issue. However, studies show that, besides the long-range dependence, WAN network trac may, not uncommonly, present mixed long and short-range dependence characteristics [4, 5]. While great part of either theoretical or practical scientic literature has been focused on the issue of Hurst parameter estimator accuracy [6, 7, 8, 9], little attention has been given to the estimation of such parameter in the presence of short-range dependence. This research work has focused on the study of the Hurst parameter estimation methods based on the wavelet spectrum, specially through the Abry-Veitch method [10] { which is based on the Discrete Wavelet Transform (DWT) transform { and through the wavelet spectrum based on the Discrete Wavelet Packet Transform (DWPT) transform. The results based on the Abry-Veitch method show that, through a suitable adjustment of the estimation parameters, such method yields a robust estimation in the presence of short-range dependence components, even in changing conditions of such component, a desirable characteristic for the real-time estimation of the Hurst parameter. However, the signi cant dispersion presented, occasionally, by the Abry-Veitch method estimates motivated the research of the usage of the wavelet spectrum obtained via DWPT transform to estimate the Hurst parameter. The results show that the usage of such transform generates such a wavelet spectrum that it is possible to detect whether short-range dependence components are present, or not, in the analyzed series. At the end, the research results are summarized and used to propose a realtime Hurst parameter estimation mechanism, in the presence of simultaneous long- and short-range dependence components.

Doctor of Philosophy (PhD) / This thesis mainly builds on the Variance Gamma (VG) model for financial assets over time of Madan & Seneta (1990) and Madan, Carr & Chang (1998), although the model based on the t distribution championed in Heyde & Leonenko (2005) is also given attention. The primary contribution of the thesis is the development of VG models, and the extension of t models, which accommodate a dependence structure in asset price returns. In particular it has become increasingly clear that while returns (log price increments) of historical financial asset time series appear as a reasonable approximation of independent and identically distributed data, squared and absolute returns do not. In fact squared and absolute returns show evidence of being long range dependent through time, with autocorrelation functions that are still significant after 50 to 100 lags. Given this evidence against the assumption of independent returns, it is important that models for financial assets be able to accommodate a dependence structure.

Doctor of Philosophy (PhD) / This thesis mainly builds on the Variance Gamma (VG) model for financial assets over time of Madan & Seneta (1990) and Madan, Carr & Chang (1998), although the model based on the t distribution championed in Heyde & Leonenko (2005) is also given attention. The primary contribution of the thesis is the development of VG models, and the extension of t models, which accommodate a dependence structure in asset price returns. In particular it has become increasingly clear that while returns (log price increments) of historical financial asset time series appear as a reasonable approximation of independent and identically distributed data, squared and absolute returns do not. In fact squared and absolute returns show evidence of being long range dependent through time, with autocorrelation functions that are still significant after 50 to 100 lags. Given this evidence against the assumption of independent returns, it is important that models for financial assets be able to accommodate a dependence structure.

No / Many studies have been conducted to investigate the performance of priority queuing (PQ) systems with constant service capacity. However, due to the time-varying nature of wireless channels in wireless communication networks, the service capacity of queuing systemsmay vary over time. Therefore, it is necessary to investigate the performance of PQ systems in the presence of varying service capacity. In addition, self-similar traffic has been discovered to be a ubiquitous phenomenon in various communication networks, which poses great challenges to performance modelling of scheduling systems due to its fractal-like nature. Therefore, this paper develops a flow-decomposition based approach to performance modelling of PQ systems subject to self-similar traffic and varying service capacity. It specifically proposes an analytical model to investigate queue length distributions of individual traffic flows. The validity and accuracy of the model is demonstrated via extensive simulation experiments.

In der vorliegenden Arbeit wird das Entstehen von Singularitäten an Oberflächen von dünnen Flüssigkeitsfilmen studiert. Unter einer Singularität versteht man hier das plötzliche Aufreißen einer Flüssigkeitsoberfläche an einer Stelle. Nach einer Diskussion physikalischer Phänomene, wird ein 2D Modell zur Beschreibung von Flüssigkeitsfilmen hergeleitet. Dieses Modell beinhaltet u.a. Oberflächenspannung, van der Waals''sche Kräfte und eine Navier-slip Randbedingung (Schlupf-Randbedingung) zwischen Substrat und Flüssigkeit, d.h. die Flüssigkeite haftet nicht an der Grenzfläche zum Substrat. Dieses Phänomen wird vor allen Dingen im Nano- und Mikrometerbereich beobachtet. Dieses Modell wird vereinfacht und man erhält die sogenannte "strong-slip" Gleichung. In dieser Dissertation werden verschiedene Ansätze verfolgt, um die Singularität der Flüssigkeitsoberfläche zu beschreiben. Der Entstehungsprozess der Singularität wird durch die lineare Stabilitätsuntersuchung beschrieben. Da die Linearisierung schnell ihre Gültigkeit verliert, wird das nichtlineare Verhalten der Singularität mit einem numerischen Verfahren beschrieben. Das dazu hier konstruierte Finite-Differenzen-Schema besitzt eine hohe räumliche und zeitliche Genauigkeit. Dadurch können verschiedene Regime, in denen die Singularität eine selbstähnliche Dynamik besitzt, untersucht und beschrieben werden. Im zweiten Teil der Arbeit werden die Gleichungen weiter vereinfacht. Dadurch können qualitative Eigenschaften der Singularitätsentstehung bewiesen werden. Weiterhin kann so eine Verbindung zu Modellen der Ostwald-Reifung hergestellt werden und man gelangt zu ähnlichen mathematischen Aussagen wie für selbstähnliche Vergröberungsprozesse. Insbesondere wird in der Arbeit gezeigt, dass die Singularität nach endlicher Zeit auftritt. Für das vereinfachte Problem werden hinreichende und notwendige Bedingungen für selbstähnliches Verhalten angegeben. / In this thesis we study the formation of surface singularites of thin liquid films, i.e., rupture of thin liquid films. First, important physical phenomena are discussed and a two-dimensional model for thin-film rupture is derived . That model contains surface tension, van der Waals forces between a liquid and a underlying substrate, and a Navier-slip condition. Using the thin-film hypothesis, this model is simplified and one obtains the so-called strong-slip equation. The phenomenon slip, where the velocity of the liquid is non-zero at a fluid-solid interface, is particularly important at microscopic length scales. In this text we study interfacial singularities with various approaches. The creation of a singularity is described by a linear stability analysis. The non-linear behavior is investigated by a numerical analysis. A finite-difference scheme is used to study the non-linear self-similar dynamics of the singularity. In the second part of this thesis the equations are further simplified. This allows to study qualitative properties of the singularity formation. Furthermore, we can establish a correspondence to models for Ostwald rippending and obtain similar mathematical statements as they are known for self-similar coarsening processes. In particular it is shown that rupture happens after a finite time. In addition, necessary and sufficient condition for self-similar rupture are proven.

FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho propomos dois modelos para a geraÃÃo de fraturas em substratos regulares. No primeiro modelo, empregamos iterativamente o conceito de caminho crÃtico para determinar sistematicamente o elemento de menor âcondutividadeâ da rede. Estes elementos sÃo entÃo identificados como âfalhasâ e removidos permanentemente da estrutura atà que uma fratura macroscÃpica destrua a conectividade global da rede. Uma vez detectada, esta fratura à caracterizada topologicamente como uma estrutura auto-similar de dimensÃo fractal Dp &#8776; 1.21. No segundo modelo, empregamos iterativamente o algoritmo de Dijkstra para determinar o caminho mÃnimo em uma paisagem aleatÃria, retirando sistematicamente desta estrutura o elemento de maior energia. Como no modelo anterior, estes elementos sÃo identificados como âfalhasâ atà que um conjunto conecto deles resulte em uma fratura macroscÃpica. A mÃdia realizada sobre vÃrias amostras de fraturas em diferentes tamanhos de substratos revela a presenÃa de uma estrutura auto-similar de dimensÃo fractal Df &#8776; 1.21. A semelhanÃa numÃrica entre os expoentes Dp e Df sugere que os dois modelos pertencem à mesma classe de universalidade. / In this work we propose two models for fracture generation in regular substrates. In the first model, we iteratively apply the concept of critical path to systematically determine the lower âconductivityâ element in the connected spanning network. At each iteration, once these elements are identified as local âcracks &#769; &#769;, they are permanently removed from the structure up to the point in which a macroscopic fracture can destroy the global network connectivity. This fracture is then topologically characterized as self-similar with fractal dimension Dp &#8776; 1.21. In the second model, we employ the algorithm of Dijkstra to determine the minimal path in a random energy landscape and remove its highest energy element. As in the previous model, these elements are considered to be local âcracks &#769; &#769; till a subset of them can be identified as a macroscopic fracture. The average over many samples of fractures calculated for different system sizes reveals the presence of a self-similar structure with fractal dimension Df &#8776; 1.21. The resemblance between the two exponents Dp e Df suggests that the two models belong to the same universality class.

Fractal is a recursively-generated object describing a family of complex shapes that possess an inherent self-similarity in their geometrical structure. When used in antenna engineering, fractal geometries provide multi-band characteristics and lowering resonance frequencies by enhancing the space filling property. Moreover, utilizing fractal arrays, controlling side lobe-levels and radiation patterns can be realized. In this thesis, the performance of Koch curve as antenna is investigated. Since fractals are complex shapes, there is no well&ndash / established for mathematical formulation to obtain the radiation properties and frequency response of Koch Curve antennas directly. The Koch curve antennas became famous since they exhibit better frequency response than their Euclidean counterparts. The effect of the parameters of Koch geometry to antenna performance is studied in this thesis. Moreover, modified Koch geometries are generated to obtain the relation between fractal properties and antenna radiation and frequency characteristics.

The field of the dissertation research is features of computer network packet traffic, the impact of network node features on traffic service, methods of real-time analysis of network traffic features and their application for dynamic prognostication of computer network packet traffic variance. The object of the research is the features of computer network packet traffic, the impact of network node features on computer network traffic service, methods of real-time network traffic features analysis and their application for dynamic prognostication of network traffic variances. The aim of work is to investigate fractal processes in computer networks, grounding on the results obtained to select methods suitable for real-time analysis of network traffic and to work out methods for real-time measurement of self-similarity as well as to apply it for perfection of computer networks service quality. Possibilities for mathematical modelling of network components, computer network packet traffic models and models using service theory instruments have been analysed. The package of network traffic features analysis has been worked out; it was used for analysis, assessment and comparison of methods for computer networks fractality and self-similarity research. For assessment of self-similarity of the network traffic time lines analysis, frequency/wave feature estimates, self-similarity analysis methods based on time line stability parameters estimators and assessed by the chaos theory... [to full text] / Disertacijos tyrimų sritis – kompiuterių tinklo paketinio srauto savybės, tinklo mazgo savybių įtaka srauto aptarnavimui, tinklo srauto savybių realaus laiku analizės metodai ir jų taikymas kompiuterių tinklo srauto kaitos dinaminiam prognozavimui. Tyrimų objektas – kompiuterių tinklo paketinio srauto savybės, tinklo mazgo savybių įtaka paketinio kompiuterių tinklo srauto aptarnavimui, realaus laiko tinklo srauto savybių analizės metodai ir jų taikymas tinklo srauto kaitos dinaminiam prognozavimui. Darbo tikslas – ištirti fraktalinius procesus kompiuterių tinkluose, remiantis gautais rezultatais parinkti metodus, tinkamus tinklo srauto analizei realiu laiku, ir sukurti savastingumo matavimo realiu laiku metodiką bei ją pritaikyti kompiuterių tinklų aptarnavimo kokybei gerinti. Išanalizuotos tinklo komponentų matematinio modeliavimo galimybės, kompiuterių tinklo paketinio srauto modeliai ir modeliai, naudojantys aptarnavimo teorijos instrumentus. Parengtas tinklo srauto savybių analizės paketas, panaudotas kompiuterių tinklų fraktališkumo ir savastingumo tyrimo metodams analizuoti, vertinti ir palyginti. Ištirti paketinio kompiuterių tinklo srauto laiko eilučių analizės, dažninių/banginių savybių įvertinimo, laiko eilutės stabilumo parametrų įverčiais grindžiami bei chaoso teorijos priemonėmis įvertinami savastingumo analizės metodai. Sudarytas tinklo srauto savastingumo realiu laiku analizės paketas, kurį naudojant savastingumo matavimui realiu laiku atrinktas robastinis... [toliau žr. visą tekstą]