The heavy-tailed traffic from wireless users, caused by the emerging Internet and multimedia applications, induces extremely dynamic and variable network environment, which can fundamentally change the way in which wireless networks are conceived, designed, and operated. This thesis is concerned with modeling, analysis, and optimization of wireless networks in the presence of heavy tails. First, a novel traffic model is proposed, which captures the inherent relationship between the traffic dynamics and the joint effects of the mobility variability of network users and the spatial correlation in their observed physical phenomenon. Next, the asymptotic delay distribution of wireless users is analyzed under different traffic patterns and spectrum conditions, which reveals the critical conditions under which wireless users can experience heavy-tailed delay with significantly degraded QoS performance. Based on the delay analysis, the fundamental impact of heavy-tailed environment on network stability is studied. Specifically, a new network stability criterion, namely moment stability, is introduced to better characterize the QoS performance in the heavy-tailed environment. Accordingly, a throughput-optimal scheduling algorithm is proposed to maximize network throughput while guaranteeing moment stability. Furthermore, the impact of heavy-tailed spectrum on network connectivity is investigated. Towards this, the necessary conditions on the existence of delay-bounded connectivity are derived. To enhance network connectivity, the mobility-assisted data forwarding scheme is exploited, whose important design parameters, such as critical mobility radius, are derived. Moreover, the latency in wireless mobile networks is analyzed, which exhibits asymptotic linearity in the initial distance between mobile users.

This dissertation is concerned with the tail asymptotics of queueing networks with subexponential service time distributions. Our objective is to investigate the tail characteristics of key performance measures such as cycle times and waiting times on a variety of queueing models which may arise in many applications such as communication and manufacturing systems. First, we focus on a general class of closed feedforward fork and join queueing networks under the assumption that the service time distribution of at least one station is subexponential. Our goal is to derive the tail asymptotics of transient cycle times and waiting times. Furthermore, we argue that under certain conditions the asymptotic tail distributions remain the same for stationary cycle times and waiting times. Finally, we provide numerical experiments in order to understand how fast the convergence of tail probabilities of cycle times and waiting times is to their asymptotic counter parts. Next, we consider closed tandem queues with finite buffers between stations. We assume that at least one station has a subexponential service time distribution. We analyze this system under communication blocking and manufacturing blocking rules. We are interested in the tail asymptotics of transient cycle times and waiting times. Furthermore, we study under which conditions on system parameters a stationary regime exists and the transient results can be generalized to stationary counter parts. Finally, we provide numerical examples to understand the convergence behavior of the tail asymptotics of transient cycle times and waiting times. Finally, we study open tandem queueing networks with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. Finally, we provide numerical examples to investigate the convergence of the tail probabilities of transient response times and waiting times to their asymptotic counter parts.

Thesis (M.S.) -- Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

Orientador: Itamar Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-11T17:15:29Z (GMT). No. of bitstreams: 1 Alves_CleverGama_M.pdf: 6160446 bytes, checksum: 5afa2cd3848388247de70ceee21a3cf8 (MD5) Previous issue date: 2008 / Resumo: O presente trabalho descreve um procedimento de aprovação de um braço de controle de suspensão automotiva sujeito a fadiga de alto ciclo, ao mesmo tempo em que propõe uma sistemática alternativa de validação baseada em conceitos e teorias estatísticas de confiabilidade. Nesse aspecto, a pesquisa não só avalia o procedimento seguido pelo fabricante, como também executa comparações gráfico-analíticas de distribuições probabilísticas (normal, lognormal e Weibull) a fim de caracterizar a massa de dados completos e suspensos obtidos em ensaios acelerados de bancada. Um espaço amostral constituído por quatro observações completas da configuração final da peça e oito da inicial, complementado por doze dados suspensos, foi usado para determinar os parâmetros dos modelos. Essa análise levou à escolha do modelo de Weibull bi-paramétrico para o tempo até a falha para as duas configurações em foco. A estimação final dos parâmetros foi feita pelo método da máxima verossimilhança, o qual superou um método alternativo específico para Weibull na comparação com a distribuição referencial de categoria. Dessa forma, calculou-se o ganho efetivo em confiabilidade conseguido com o esforço adicional de desenvolvimento da peça. O teste de hipóteses de Kruskal-Wallis permitiu concluir que as duas configurações realmente possuem performances de durabilidade diferentes. É notável o ganho em confiabilidade obtido por meio das mudanças que levaram à configuração final: em um universo de um milhão de peças, o número de falhas esperadas aos 30.000 ciclos caiu de 96.384 para 5 partes por milhão / Abstract: This dissertation aims at describing a procedure for approval of a suspension control arm subjected to high-cycle fatigue and, simultaneously, at proposing a validation alternative method based on reliability concepts and statistical theories. In that manner, the research provides not only an assessment of the procedure followed by the manufacturer, but also analytical and graphical comparisons of probabilistic distributions (normal, lognormal, Weibull) in order to characterize the set of complete and suspended data from bench accelerated tests. A sample space comprised by four complete final configuration observations and eight complete primary configuration ones, in addition to twelve suspended figures, was the basis for determining the model parameters. Such an analysis led to choose the bi-parametric Weibull for both focused configurations¿ time to failure. The ultimate estimation of the parameters was performed through the maximum likelihood method, which beat a specific alternative method for Weibull when compared with the referential category distribution. Thus, the effective gain in reliability resulting from the product development additional effort was calculated. The Kruskal-Wallis hypothesis testing guided the conclusion that the two configurations actually have different durability performances. It is impressive the gain in reliability brought by the changes that led towards the final configuration: taking an amount of one million parts into consideration, the expected number of failures at 30,000 cycles dropped from 96,384 to 5 parts per million / Mestrado / Materiais e Processos de Fabricação / Mestre em Engenharia Mecânica

Orientador: Filidor Edilfonso Vilca Labra / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T16:29:00Z (GMT). No. of bitstreams: 1 Romeiro_RenataGuimaraes_M.pdf: 10761224 bytes, checksum: 3606332b6846c959d076e318f1667133 (MD5) Previous issue date: 2014 / Resumo: O modelo de regressão Birnbaum-Saunders de Rieck e Nedelman (1991) tem sido amplamente discutido por vários autores, com aplicações na área de sobrevivência e confiabilidade. Neste trabalho, desenvolvemos um modelo de regressão Birnbaum-Saunders bivariado através do uso da distribuição Senh-Normal proposta por Rieck (1989). Este modelo de regressão pode ser utilizado para analisar logaritmos de tempos de vida de duas unidades correlacionadas, e gera marginais correspondentes aos modelos de regressão Birnbaum-Saunders univariados. Apresentamos um estudo de inferência e análise de diagnóstico para modelo de regressão Birnbaum-Saunders bivariado proposto. Em primeiro lugar, apresentamos os estimadores obtidos através do método dos momentos e de máxima verossimilhança, e a matriz de informação observada de Fisher. Além disso, discutimos testes de hipóteses com base na normalidade assintótica dos estimadores de máxima verossimilhança. Em segundo lugar, desenvolvemos um método de diagnóstico para o modelo de regressão Birnbaum- Saunders bivariado baseado na metodologia de Cook (1986). Finalmente, apresentamos alguns resultados de estudos de simulações e aplicações em dados reais / Abstract: The Birnbaum-Saunders regression model of Rieck and Nedelman (1991) has been extensively discussed by various authors with application in survival and reliability studies. In this work a bivariate Birnbaum-Saunders regression model is developed through the use of Sinh-Normal distribution proposed by Rieck (1989). This bivariate regression model can be used to analyze correlated log-time of two units, it bivariate regression model has its marginal as the Birnbaum- Saunders regression model. For the bivariate Birnbaum-Saunders regression model is discussed some of its properties, in the moment estimation, the maximum likelihood estimation and the observed Fisher information matrix. Hypothesis testing is performed by using the asymptotic normality of the maximum-likelihood estimators. Influence diagnostic methods are developed for this model based on the Cook¿s(1986) approach. Finally, the results of a simulation study as well as an application to a real data set are presented / Mestrado / Estatistica / Mestra em Estatística

Les modèles de frontières sont actuellement très utilisés par beaucoup d’économistes, gestionnaires ou toute personne dite « decision-maker ». Dans ces modèles de frontières, le but du chercheur consiste à attribuer à des unités de production (des firmes, des hôpitaux ou des universités par exemple) une mesure de leur efficacité en terme de production. Ces unités (dénotées DMU-Decision-Making Units) utilisent-elles à bon escient leurs « inputs » et « outputs »? Font-elles usage de tout leur potentiel dans le processus de production? <p>L’ensemble de production est l’ensemble contenant toutes les combinaisons d’inputs et d’outputs qui sont physiquement réalisables dans une économie. De cet ensemble contenant p inputs et q outputs, la notion d’efficacité d ‘une unité de production peut être définie. Celle-ci se définie comme une distance séparant le DMU de la frontière de l’ensemble de production. A partir d’un échantillon de DMUs, le but est de reconstruire cette frontière de production afin de pouvoir y évaluer l’efficacité des DMUs. A cette fin, le chercheur utilise très souvent des méthodes dites « classiques » telles que le « Data Envelopment Analysis » (DEA).<p><p>De nos jours, le statisticien bénéficie de plus en plus de données, ce qui veut également dire qu’il n’a pas l’opportunité de faire attention aux données qui font partie de sa base de données. Il se peut en effet que certaines valeurs aberrantes s’immiscent dans les jeux de données sans que nous y fassions particulièrement attention. En particulier, les modèles de frontières sont extrêmement sensibles aux valeurs aberrantes et peuvent fortement influencer l’inférence qui s’en suit. Pour éviter que certaines données n’entravent une analyse correcte, des méthodes robustes sont utilisées.<p><p>Allier le côté robuste au problème d’évaluation d’efficacité est l’objectif général de cette thèse. Le premier chapitre plante le décor en présentant la littérature existante dans ce domaine. Les quatre chapitres suivants sont organisés sous forme d’articles scientifiques. <p>Le chapitre 2 étudie les propriétés de robustesse d’un estimateur d’efficacité particulier. Cet estimateur mesure la distance entre le DMU analysé et la frontière de production le long d’un chemin hyperbolique passant par l’unité. Ce type de distance très spécifique s’avère très utile pour définir l’efficacité de type directionnel. <p>Le chapitre 3 est l’extension du premier article au cas de l’efficacité directionnelle. Ce type de distance généralise toutes les distances de type linéaires pour évaluer l’efficacité d’un DMU. En plus d’étudier les propriétés de robustesse de l’estimateur d’efficacité de type directionnel, une méthode de détection de valeurs aberrantes est présentée. Celle-ci s’avère très utile afin d’identifier les unités de production influençantes dans cet espace multidimensionnel (dimension p+q). <p>Le chapitre 4 présente les méthodes d’inférence pour les efficacités dans les modèles nonparamétriques de frontière. En particulier, les méthodes de rééchantillonnage comme le bootstrap ou le subsampling s’avère être très utiles. Dans un premier temps, cet article montre comment améliorer l’inférence sur les efficacités grâce au subsampling et prouve qu’il n’est pas suffisant d’utiliser un estimateur d’efficacité robuste dans les méthodes de rééchantillonnage pour avoir une inférence qui soit fiable. C’est pourquoi, dans un second temps, cet article propose une méthode robuste de rééchantillonnage qui est adaptée au problème d’évaluation d’efficacité. <p>Finalement, le dernier chapitre est une application empirique. Plus précisément, cette analyse s’intéresse à l ‘efficacité des universités américaines publiques et privées au niveau de leur recherche. Des méthodes classiques et robustes sont utilisées afin de montrer comment tous les outils étudiés précédemment peuvent s’appliquer en pratique. En particulier, cette étude permet d’étudier l’impact sur l’efficacité des institutions américaines de certaines variables telles que l’enseignement, l’internationalisation ou la collaboration avec le monde de l’industrie.<p> / Doctorat en sciences, Orientation statistique / info:eu-repo/semantics/nonPublished

This thesis is divided in four chapters. The two first chapters introduce a parametric quantile-based estimation method of univariate heavy-tailed distributions and elliptical distributions, respectively. If one is interested in estimating the tail index without imposing a parametric form for the entire distribution function, but only on the tail behaviour, we propose a multivariate Hill estimator for elliptical distributions in chapter three. In the first three chapters we assume an independent and identically distributed setting, and so as a first step to a dependent setting, using quantiles, we prove in the last chapter the asymptotic normality of marginal sample quantiles for stationary processes under the S-mixing condition.<p><p><p>The first chapter introduces a quantile- and simulation-based estimation method, which we call the Method of Simulated Quantiles, or simply MSQ. Since it is based on quantiles, it is a moment-free approach. And since it is based on simulations, we do not need closed form expressions of any function that represents the probability law of the process. Thus, it is useful in case the probability density functions has no closed form or/and moments do not exist. It is based on a vector of functions of quantiles. The principle consists in matching functions of theoretical quantiles, which depend on the parameters of the assumed probability law, with those of empirical quantiles, which depend on the data. Since the theoretical functions of quantiles may not have a closed form expression, we rely on simulations.<p><p><p>The second chapter deals with the estimation of the parameters of elliptical distributions by means of a multivariate extension of MSQ. In this chapter we propose inference for vast dimensional elliptical distributions. Estimation is based on quantiles, which always exist regardless of the thickness of the tails, and testing is based on the geometry of the elliptical family. The multivariate extension of MSQ faces the difficulty of constructing a function of quantiles that is informative about the covariation parameters. We show that the interquartile range of a projection of pairwise random variables onto the 45 degree line is very informative about the covariation.<p><p><p>The third chapter consists in constructing a multivariate tail index estimator. In the univariate case, the most popular estimator for the tail exponent is the Hill estimator introduced by Bruce Hill in 1975. The aim of this chapter is to propose an estimator of the tail index in a multivariate context; more precisely, in the case of regularly varying elliptical distributions. Since, for univariate random variables, our estimator boils down to the Hill estimator, we name it after Bruce Hill. Our estimator is based on the distance between an elliptical probability contour and the exceedance observations. <p><p><p>Finally, the fourth chapter investigates the asymptotic behaviour of the marginal sample quantiles for p-dimensional stationary processes and we obtain the asymptotic normality of the empirical quantile vector. We assume that the processes are S-mixing, a recently introduced and widely applicable notion of dependence. A remarkable property of S-mixing is the fact that it doesn't require any higher order moment assumptions to be verified. Since we are interested in quantiles and processes that are probably heavy-tailed, this is of particular interest.<p> / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Orientador: Caio Lucidius Naberezny Azevedo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:30:15Z (GMT). No. of bitstreams: 1 Silva_AnaRobertadosSantos_M.pdf: 4052475 bytes, checksum: 08fb6f3f7b4ed838df4eea2dbcf06a29 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho desenvolvemos a distribuição beta retangular aumentada em zero e um, bem como um correspondente modelo de regressão beta retangular aumentado em zero e um para analisar dados limitados-aumentados (representados por variáveis aleatórias mistas com suporte limitado), que apresentam valores discrepantes. Desenvolvemos ferramentas de inferência sob as abordagens bayesiana e frequentista. No que diz respeito à inferência bayesiana, devido à impossibilidade de obtenção analítica das posteriores de interesse, utilizou-se algoritmos MCMC. Com relação à estimação frequentista, utilizamos o algoritmo EM. Desenvolvemos técnicas de análise de resíduos, utilizando o resíduo quantil aleatorizado, tanto sob o enfoque frequentista quanto bayesiano. Desenvolvemos, também, medidas de influência, somente sob o enfoque bayesiano, utilizando a medida de Kullback Leibler. Além disso, adaptamos métodos de checagem preditiva à posteriori existentes na literatura, ao nosso modelo, utilizando medidas de discrepância apropriadas. Para a comparação de modelos, utilizamos os critérios usuais na literatura, como AIC, BIC e DIC. Realizamos diversos estudos de simulação, considerando algumas situações de interesse prático, com o intuito de comparar as estimativas bayesianas com as frequentistas, bem como avaliar o comportamento das ferramentas de diagnóstico desenvolvidas. Um conjunto de dados da área psicométrica foi analisado para ilustrar o potencial do ferramental desenvolvido / Abstract: In this work we developed the zero-one augmented rectangular beta distribution, as well as a correspondent zero-one augmented rectangular beta regression model to analyze limited-augmented data (represented by mixed random variables with limited support), which present outliers. We develop inference tools under the Bayesian and frequentist approaches. Regarding to the Bayesian inference, due the impossibility of obtaining analytically the posterior distributions of interest, we used MCMC algorithms. Concerning the frequentist estimation, we use the EM algorithm. We develop techniques of residual analysis, by using the randomized quantile residuals, under both frequentist and Bayesian approaches. We also developed influence measures, only under the Bayesian approach, by using the measure of Kullback Leibler. In addition, we adapt methods of posterior predictive checking available in the literature, to our model, using appropriate discrepancy measures. For model selection, we use the criteria commonly employed in the literature, such as AIC, BIC and DIC. We performed several simulation studies, considering some situations of practical interest, in order to compare the Bayesian and frequentist estimates, as well as to evaluate the behavior of the developed diagnostic tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools / Mestrado / Estatistica / Mestra em Estatística

A compreensão da dependência espacial das propriedades do solo vem sendo cada vez mais requerida por pesquisadores que objetivam melhorar a interpretação dos resultados de experimentos de campo fornecendo, assim, subsídios para novas pesquisas a custos reduzidos. Em geral, variáveis como, por exemplo, o teor de cálcio no solo, estudado neste trabalho, apresentam grande variabilidade impossibilitando, na maioria das vezes, a detecção de reais diferenças estatísticas entre os efeitos de tratamentos. A consideração de amostras georreferenciadas é uma abordagem importante na análise de dados desta natureza, uma vez que amostras mais próximas são mais similares do que as mais distantes e, assim, cada realização desta variável contém informação de sua vizinhança. Neste trabalho, métodos geoestatísticos que baseiam-se na modelagem da dependência espacial, nas pressuposições Gaussianas e nos estimadores de máxima verossimilhança são utilizados para analisar e interpretar a variabilidade do teor de cálcio no solo, resultado de um experimento realizado na Fazenda Angra localizada no Estado do Rio de Janeiro. A área experimental foi dividida em três regiões em função dos diferentes períodos de adubação realizadas. Neste estudo foram utilizados dados do teor de cálcio obtidos das camadas 0-20cm e 20-40cm do solo, de acordo com as coordenadas norte e leste. Modelos lineares mistos, apropriados para estudar dados com esta característica, e que permitem a utilização de diferentes estruturas de covariâncias e a incorporação da região e tendência linear das coordenadas foram usados. As estruturas de covariâncias utilizadas foram: a exponencial e a Matérn. Para estimar e avaliar a variabilidade dos parâmetros utilizaram-se os métodos de máxima verossimilhança, máxima verossimilhança restrita e o perfil de verossimilhança. A identificação da dependência e a predição foram realizadas por meio de variogramas e mapas de krigagem. Além disso, a seleção do modelo adequado foi feita pelo critério de informação de Akaike e o teste da razão de verossimilhanças. Observou-se, quando utilizado o método de máxima verossimilhança, o melhor modelo foi aquele com a covariável região e, com o método de máxima verossimilhança restrita, o modelo com a covariável região e tendência linear nas coordenadas (modelo 2). Com o teor de cálcio, na camada 0-20cm e considerando-se a estrutura de covariância exponencial foram obtidas as menores variâncias nugget e a maior variância espacial (sill - nugget). Com o método de máxima verossimilhança e com o modelo 2 foram observadas variâncias de predição mais precisas. Por meio do perfil de verossimilhança pode-se observar menor variabilidade dos parâmetros dos variogramas ajustados com o modelo 2. Utilizando-se vários modelos e estruturas de covariâncias, deve-se ser criterioso, pois a precisão das estimativas, depende do tamanho da amostra e da especificação do modelo para a média. Os resultados obtidos foram analisados, com a subrotina geoR desenvolvida por Ribeiro Junior & Diggle (2000), e por meio dela pode-se obter estimativas confiáveis para os parâmetros dos diferentes modelos estimados. / The understanding of the spatial dependence of the properties of the soil becomes more and more required by researchers that attempt to improve the interpretation of the results of field experiments supplying subsidies for new researches at reduced costs. In general, variables as, for example, the calcium content in the soil, studied in this work, present great variability disabling, most of the time, the detection of real statistical differences among the treatment effects. The consideration of georeferenced samples is an important approach in the analysis of data of this nature, because closer samples are more similar than the most distant ones and, thus, each realization of this variable contains information of its neighborhood. In this work, geostatistics methods that are based on the modeling of the spatial dependence, under the Gaussian assumptions and the maximum likelihood estimators, are used to analyze and to interpret the variability of calcium content in the soil, obtained from an experiment carried on at Fazenda Angra, located in Rio de Janeiro, Brazil. The experimental area was divided in three areas depending on the different periods of fertilization. In this study, data of the calcium soil content from the layers 0-20cm and 20-40cm, were used, according to the north and east coordinates. Mixed linear models, ideal to study data with this characteristic, and that allow the use of different covariance structures, and the incorporation of the region and linear tendency of the coordinates, were used. The covariance structures were: the exponential and the Matérn. Maximum likelihood, maximum restricted likelihood and the profile of likelihood methods were used to estimate and to evaluate the variability of the parameters. The identification of the dependence and the prediction were realized using variograms and krigging maps. Besides, the selection of the appropriate model was made through the Akaike information criterion and the likelihood ratio test. It was observed that when maximum likelihood method was used the most appropriate model was that with the region covariate and, with the maximum restricted likelihood method, the best model was the one with the region covariate and linear tendency in the coordinates (model 2). With the calcium content, in the layer 0-20cm and considering the exponential covariance structure, the smallest nugget variances and the largest spatial variance (sill - nugget) were obtained. With the maximum likelihood method and with the model 2 more precise prediction variances were observed. Through the profile of likelihood method, smaller variability of the adjusted variogram parameters can be observed with the model 2. With several models and covariance structures being used, one should be very critical, because the precision of the estimates depends on the size of the sample and on the specification of the model for the average. The obtained results were analyzed, with the subroutine geoR developed by Ribeiro Junior & Diggle (2000), and through this subroutine, reliable estimates for the parameters of the different estimated models can be obtained.

published_or_final_version / Statistics / Master / Master of Philosophy