There are a lot more roads being built periodically in most of the countries with the advancement of modern society. In order to promote the overall traffic flow quality within different cities, city traffic management has been playing a more and more essential role during the last few decades. In recent years, a significantly increasing attention has been paid to the management of traffic flow in major cities all over the world. In this thesis, we develop a stochastic dynamic model for urban traffic along with physical constraints characteristic of intersections equipped with traffic light. We assume that the incoming traffic to each stream in an intersection is amenable to the Poisson random process with variable intensity (mean). We introduce expressions for traffic throughput, congestion as well as operator's waiting time for the typical intersection in a city and hereafter define an appropriate objective functional. Afterwards, we formulate an optimization problem and propose the sequential (or recursive) algorithm based on the principle of optimality (dynamic programming) due to Bellman. The solution if implemented is expected to improve throughput, reduce congestion, and promote driver's satisfaction. Because the dynamic programming method is computationally quite intensive, we consider the scenario that one unit traffic stream stands for a specific number of vehicles which actually depends on the volume of traffic flow through the intersection. The system is simulated with inputs described by several distinct nonhomogeneous Poisson processes. For example, we apply the typical traffic arrival rate in Canada with morning peak hour at around 7:30 AM and afternoon peak hour at around 4:30 PM whilst it is also applied with morning rush hour at about 8:00 AM and afternoon rush hour at about 6:00 PM like in China. In the meanwhile, we also present a group of numerical results for the traffic arrival rates that have shorter morning peak-hour period but longer afternoon rush hour period. This may occasionally happen when there are some social activities or big events in the afternoon. In addition, another series of experiments are carried out to illustrate the feasibility of the proposed dynamic model based on the traffic arrival rates with only one peak-hour throughout the whole day. The system is simulated with a series of experiments and the optimization problem is solved by dynamic programming based on the proposed algorithm which gives us the optimal feedback control law. More specifically, the results show that both the optimal traffic light timing allocated for each stream and the congestion broadcast level (CBL) of each road segment during each time segment are found. Accordingly, the corresponding optimal cost can be found for any given initial condition. It is reasonably believed that this stochastic dynamic model would be potentially applicable for real time adaptive traffic control system.

In this thesis, we will study issues related to prediction problems and put an emphasis on those arising when recurrent events are involved. First we define the basic concepts of frequentist and Bayesian statistical prediction in the first chapter. In the second chapter, we study frequentist prediction intervals and their associated predictive distributions. We will then present an approach based on asymptotically uniform pivotals that is shown to dominate the plug-in approach under certain conditions. The following three chapters consider the prediction of recurrent events. The third chapter presents different prediction models when these events can be modeled using homogeneous Poisson processes. Amongst these models, those using random effects are shown to possess interesting features. In the fourth chapter, the time homogeneity assumption is relaxed and we present prediction models for non-homogeneous Poisson processes. The behavior of these models is then studied for prediction problems with a finite horizon. In the fifth chapter, we apply the concepts discussed previously to a warranty dataset coming from the automobile industry. The number of processes in this dataset being very large, we focus on methods providing computationally rapid prediction intervals. Finally, we discuss the possibilities of future research in the last chapter.

In this thesis, we will study issues related to prediction problems and put an emphasis on those arising when recurrent events are involved. First we define the basic concepts of frequentist and Bayesian statistical prediction in the first chapter. In the second chapter, we study frequentist prediction intervals and their associated predictive distributions. We will then present an approach based on asymptotically uniform pivotals that is shown to dominate the plug-in approach under certain conditions. The following three chapters consider the prediction of recurrent events. The third chapter presents different prediction models when these events can be modeled using homogeneous Poisson processes. Amongst these models, those using random effects are shown to possess interesting features. In the fourth chapter, the time homogeneity assumption is relaxed and we present prediction models for non-homogeneous Poisson processes. The behavior of these models is then studied for prediction problems with a finite horizon. In the fifth chapter, we apply the concepts discussed previously to a warranty dataset coming from the automobile industry. The number of processes in this dataset being very large, we focus on methods providing computationally rapid prediction intervals. Finally, we discuss the possibilities of future research in the last chapter.

A água de lastro de navios é um dos principais agentes dispersivos de organismos nocivos à saúde humana e ao meio ambiente e normas internacionais exigem que a concentração desses organismos no tanque seja menor que um valor previamente especificado. Por limitações de tempo e custo, esse controle requer o uso de amostragem. Sob a hipótese de que a concentração desses organismos no tanque é homogênea, vários autores têm utilizado a distribuição Poisson para a tomada de decisão com base num teste de hipóteses. Como essa proposta é pouco realista, estendemos os resultados para casos em que a concentração de organismos no tanque é heterogênea utilizando estratificação, processos de Poisson não-homogêneos ou assumindo que ela obedece a uma distribuição Gama, que induz uma distribuição Binomial Negativa para o número de organismos amostrados. Além disso, propomos uma nova abordagem para o problema por meio de técnicas de estimação baseadas na distribuição Binomial Negativa. Para fins de aplicação, implementamos rotinas computacionais no software R / Ballast water is a leading dispersing agent of harmful organisms to human health and to the environment and international standards require that the concentration of these organisms in the tank must be less than a prespecified value. Because of time and cost limitations, this inspection requires the use of sampling. Under the assumption of an homogeneous organism concentration in the tank, several authors have used the Poisson distribution for decision making based on hypothesis testing. Since this proposal is unrealistic, we extend the results for cases in which the organism concentration in the tank is heterogeneous, using stratification, nonhomogeneous Poisson processes or assuming that it follows a Gamma distribution, which induces a Negative Binomial distribution for the number of sampled organisms. Furthermore, we propose a novel approach to the problem through estimation techniques based on the Negative Binomial distribution. For practical applications, we implemented computational routines using the R software

Este trabalho reporta sobre a avaliação da confiabilidade de networks, uma representação analítica para diversos sistemas de engenharia e de comunicação, cujas falhas de seus componentes (links) ocorrem segundo um Processo de Poisson Não Homogêneo. Concluiremos que, na comparação de dois networks com a mesma quantidade de links, as desigualdades estocásticas de seus D-espectros serão preservadas em seus tempos de vidas e a preservação das classes de distribuições do D-espectro para o tempo de vida de um network ocorrerá com restrições na função de risco do Processo de Poisson Não Homogêneo. / This work reports networks reliability evaluation, an analytic representation to several engineering and comunication systems, whose components (links) failures occur according to a Nonhomogeneous Poisson Process. We will conclude that, on comparison of two networks with same number of links, stochastic orders of their D-spectra will be preserved to their lifetimes and distribution classes preservation of network D-spectrum to its lifetime will occur with restrictions in hazard function of Nonhomogeneous Poisson Process.

A água de lastro de navios é um dos principais agentes dispersivos de organismos nocivos à saúde humana e ao meio ambiente e normas internacionais exigem que a concentração desses organismos no tanque seja menor que um valor previamente especificado. Por limitações de tempo e custo, esse controle requer o uso de amostragem. Sob a hipótese de que a concentração desses organismos no tanque é homogênea, vários autores têm utilizado a distribuição Poisson para a tomada de decisão com base num teste de hipóteses. Como essa proposta é pouco realista, estendemos os resultados para casos em que a concentração de organismos no tanque é heterogênea utilizando estratificação, processos de Poisson não-homogêneos ou assumindo que ela obedece a uma distribuição Gama, que induz uma distribuição Binomial Negativa para o número de organismos amostrados. Além disso, propomos uma nova abordagem para o problema por meio de técnicas de estimação baseadas na distribuição Binomial Negativa. Para fins de aplicação, implementamos rotinas computacionais no software R / Ballast water is a leading dispersing agent of harmful organisms to human health and to the environment and international standards require that the concentration of these organisms in the tank must be less than a prespecified value. Because of time and cost limitations, this inspection requires the use of sampling. Under the assumption of an homogeneous organism concentration in the tank, several authors have used the Poisson distribution for decision making based on hypothesis testing. Since this proposal is unrealistic, we extend the results for cases in which the organism concentration in the tank is heterogeneous, using stratification, nonhomogeneous Poisson processes or assuming that it follows a Gamma distribution, which induces a Negative Binomial distribution for the number of sampled organisms. Furthermore, we propose a novel approach to the problem through estimation techniques based on the Negative Binomial distribution. For practical applications, we implemented computational routines using the R software