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No description available.

Neste trabalho é proposto um método de carregamento incremental dos fluxos veiculares para a estimação de matriz O-D sintética. A principal motivação para o desenvolvimento deste trabalho está na complexidade dos métodos de estimação de matriz sintética pelo método iterativo, que tem conduzido a resultados não satisfatórios. O método de carregamento incremental, ora proposto neste trabalho, pode ser definido como o inverso do método de alocação incremental de viagens aos arcos de uma rede viária. A matriz O-D obtida com este método é o resultado da soma sucessiva das sub-matrizes estimadas através das parcelas dos fluxos observados nos arcos da rede. Este método pode ser aplicado em qualquer tipo de rede viária: congestionada ou não congestionada e com ou sem continuidade de fluxo. Para verificação do desempenho do método foram realizados testes experimentais, nos quais os resultados obtidos foram comparados com os valores observados. O desempenho do método incremental não se mostrou satisfatório. Assim, com o intuito de verificar a sua utilidade como um método alternativo os mesmos dados foram processados através de dois métodos iterativos. Os resultados mostraram que os erros são ainda maiores do que os obtidos pelo método proposto. A principal conclusão deste trabalho é que o método incremental pode ser usado como uma alternativa aos métodos iterativos. / A synthetic O-D matrix estimation method, based on incremental loading of traffic flow, was proposed in this work. This research was motivated because of the complexity of the iterative methods for synthetic matrix estimation that might produce bias accumulation in the results. The referred incremental loading method could be defined as the inverse of the incremental assignment method for trips to links of a traffic network. The O-D matrix is gathered by successively summing the sub-matrices obtained from parts of the traffic flow counted on the links of the traffic network. This method could be applied to any traffic networks: congested or uncongested and with or without volumetric continuity. As a part of verification proceeding, several experimental tests were carried out to evaluate the method performance. In these tests the estimated results were compared with the real values. These results show that the incremental loading method performance was not satisfactory. Thus, aiming to test the utility of the incremental method, a second round of experimental tests was conducted to evaluate two iterative methods. In these second round tests, the results show that theses methods performance was worse those of the incremental method. The main conclusion of this work is that the incremental loading method for synthetic matrices estimation could be used as an alternative to the iterative methods.

Neste trabalho é proposto um método de carregamento incremental dos fluxos veiculares para a estimação de matriz O-D sintética. A principal motivação para o desenvolvimento deste trabalho está na complexidade dos métodos de estimação de matriz sintética pelo método iterativo, que tem conduzido a resultados não satisfatórios. O método de carregamento incremental, ora proposto neste trabalho, pode ser definido como o inverso do método de alocação incremental de viagens aos arcos de uma rede viária. A matriz O-D obtida com este método é o resultado da soma sucessiva das sub-matrizes estimadas através das parcelas dos fluxos observados nos arcos da rede. Este método pode ser aplicado em qualquer tipo de rede viária: congestionada ou não congestionada e com ou sem continuidade de fluxo. Para verificação do desempenho do método foram realizados testes experimentais, nos quais os resultados obtidos foram comparados com os valores observados. O desempenho do método incremental não se mostrou satisfatório. Assim, com o intuito de verificar a sua utilidade como um método alternativo os mesmos dados foram processados através de dois métodos iterativos. Os resultados mostraram que os erros são ainda maiores do que os obtidos pelo método proposto. A principal conclusão deste trabalho é que o método incremental pode ser usado como uma alternativa aos métodos iterativos. / A synthetic O-D matrix estimation method, based on incremental loading of traffic flow, was proposed in this work. This research was motivated because of the complexity of the iterative methods for synthetic matrix estimation that might produce bias accumulation in the results. The referred incremental loading method could be defined as the inverse of the incremental assignment method for trips to links of a traffic network. The O-D matrix is gathered by successively summing the sub-matrices obtained from parts of the traffic flow counted on the links of the traffic network. This method could be applied to any traffic networks: congested or uncongested and with or without volumetric continuity. As a part of verification proceeding, several experimental tests were carried out to evaluate the method performance. In these tests the estimated results were compared with the real values. These results show that the incremental loading method performance was not satisfactory. Thus, aiming to test the utility of the incremental method, a second round of experimental tests was conducted to evaluate two iterative methods. In these second round tests, the results show that theses methods performance was worse those of the incremental method. The main conclusion of this work is that the incremental loading method for synthetic matrices estimation could be used as an alternative to the iterative methods.

Cette thèse est dédiée à l'étude mathématique de quelques modèles de trafic routier congestionné. La notion essentielle est l'équilibre de Wardrop. Elle poursuit des travaux de Carlier et Santambrogio avec des coauteurs. Baillon et Carlier ont étudié le cas de grilles cartésiennes dans $\RR^2$ de plus en plus denses, dans le cadre de la théorie de $\Gamma$-convergence. Trouver l'équilibre de Wardrop revient à résoudre des problèmes de minimisation convexe. Dans le chapitre 2, nous regardons ce qui se passe dans le cas de réseaux généraux, de plus en plus denses, dans $\RR^d$. Des difficultés nouvelles surgissent par rapport au cas initial de réseaux cartésiens et pour les contourner, nous introduisons la notion de courbes généralisées. Des hypothèses structurelles sur ces suites de réseaux discrets sont nécessaires pour s'assurer de la convergence. Cela fait alors apparaître des fonctions qui sont des sortes de distances de Finsler et qui rendent compte de l'anisotropie du réseau. Nous obtenons ainsi des résultats similaires à ceux du cas cartésien. Dans le chapitre 3, nous étudions le modèle continu et en particulier, les problèmes limites. Nous trouvons alors des conditions d'optimalité à travers une formulation duale qui peut être interprétée en termes d'équilibres continus de Wardrop. Cependant, nous travaillons avec des courbes généralisées et nous ne pouvons pas appliquer directement le théorème de Prokhorov, comme cela a été le cas dans \cite{baillon2012discrete, carlier2008optimal}. Pour pouvoir néanmoins l'utiliser, nous considérons une version relaxée du problème limite, avec des mesures d'Young. Dans le chapitre 4, nous nous concentrons sur le cas de long terme, c'est-à-dire, nous fixons uniquement les distributions d'offre et de demande. Comme montré dans \cite{brasco2013congested}, le problème de l'équilibre de Wardrop est équivalent à un problème à la Beckmann et il se réduit à résoudre une EDP elliptique, anisotropique et dégénérée. Nous utilisons la méthode de résolution numérique de Lagrangien augmenté présentée dans \cite{benamou2013augmented} pour proposer des exemples de simulation. Enfin, le chapitre 5 a pour objet l'étude de problèmes de Monge avec comme coût une distance de Finsler. Cela se reformule en des problèmes de flux minimal et une discrétisation de ces problèmes mène à un problème de point-selle. Nous le résolvons alors numériquement, encore grâce à un algorithme de Lagrangien augmenté. / This thesis is devoted to the mathematical analysis of some models of congested road traffic. The essential notion is the Wardrop equilibrium. It continues Carlier and Santambrogio's works with coauthors. With Baillon they studied the case of two-dimensional cartesian networks that become very dense in the framework of $\Gamma$-convergence theory. Finding Wardrop equilibria is equivalent to solve convex minimisation problems.In Chapter 2 we look at what happens in the case of general networks, increasingly dense. New difficulties appear with respect to the original case of cartesian networks. To deal with these difficulties we introduce the concept of generalized curves. Structural assumptions on these sequences of discrete networks are necessary to obtain convergence. Sorts of Finsler distance are used and keep track of anisotropy of the network. We then have similar results to those in the cartesian case.In Chapter 3 we study the continuous model and in particular the limit problems. Then we find optimality conditions through a duale formulation that can be interpreted in terms of continuous Wardrop equilibria. However we work with generalized curves and we cannot directly apply Prokhorov's theorem, as in \cite{baillon2012discrete, carlier2008optimal}. To use it we consider a relaxed version of the limit problem with Young's measures. In Chapter 4 we focus on the long-term case, that is, we fix only the distributions of supply and demand. As shown in \cite{brasco2013congested} the problem of Wardrop equilibria can be reformulated in a problem à la Beckmann and reduced to solve an elliptic anisotropic and degenerated PDE. We use the augmented Lagrangian scheme presented in \cite{benamou2013augmented} to show a few numerical simulation examples. Finally Chapter 5 is devoted to studying Monge problems with as cost a Finsler distance. It leads to minimal flow problems. Discretization of these problems is equivalent to a saddle-point problem. We then solve it numerically again by an augmented Lagrangian algorithm.