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In a lot of big cities, the traffic network is overloaded, with congestion and unnecessary emissions as consequence. Therefore, different traffic control methods are useful, especially in case of an incident. One key problem for traffic control is traffic prediction and the aim of this thesis is to develop, calibrate and evaluate a route flow model using only observed travel times and travel demand as input. The route flow model was used to calculate the metric link flow destination distribution, that presents to which destinations the travelers on a link are going in percentage.

Traffic State Estimation (TSE) is a vital component in traffic control which requires an accurate viewof the current traffic situation. Since there is no full sensor coverage and the collected measurementsare inflicted with random noise, statistical estimation techniques are necessary to accomplish this.Common methods, which have been used in highway applications for several decades, are state-spacemodels in the form of Kalman Filters and Particle Filters. These methods are forms of BayesianFilters, and rely on transition models to describe the system dynamics, and observation models torelate collected measurements to the current state. Reliable estimation of traffic in urban environmentshas been considered more difficult than in highways owing to the increased complexity.This MsC thesis build upon previous research studying the use of non-parametric Gaussian Processtransition and measurement models in an extended Kalman Filter to achieve short-term TSE. To dothis, models requiring different feature sets are developed and analysed, as well as a hybrid approchcombining non-parametric and parametric models through an analytical mean function based on vehicleconservation law. The data used to train and test the models was collected in a simulated signalizedintersection constructed in SUMO.The presented results show that the proposed method has potential to performing short-term TSE inthis context. A strength in the proposed framework comes from the probabilistic nature of the GaussianProcesses, as it removes the need to manually calibrate the filter parameters of the Kalman Filter. Themean absolute error (MAE) lies between one and five vehicles for estimation of a one hour long dataseries with varying traffic demand. More importantly, the method has desirable characteristics andcaptures short-term fluctuations as well as larger scale demand changes better than a previously proposedmodel using the same underlying framework. In the cases with poorer performance, the methodprovided estimates unrelated to the system dynamics as well as large error bounds. While the causefor this was not determined, several hypotheses are presented and analysed. These results are takento imply that the combination of BF and GP models has potential for short-term TSE in a signalizedintersection, but that more work is necessary to provide reliable algorithms with known bounds. In particular,the relative ease of augmenting an available analytical model, built on conventional knowledgein traffic modelling, with a non-parametric GP is highlighted.

The Aw-Rascle-Zhang (ARZ) model has become a favorable ``second order" macroscopic traffic model, which corrects several shortcomings of the Payne-Whitham (PW) model. The ARZ model possesses a family of flow rate versus density (FD) curves, rather than a single one as in the ``first order" Lighthill-Whitham-Richards (LWR) model. This is more realistic especially during congested traffic state, where the historic fundamental diagram data points are observed to be set-valued. However, the ARZ model also possesses some obvious shortcomings, e.g., it assumes multiple maximum traffic densities which should be a ``property" of road. Instead, we propose a Generalized ARZ (GARZ) model under the generic framework of ``second order" macroscopic models to overcome the drawbacks of the ARZ model. A systematic approach is presented to design generic ``second order" models from historic data, e.g., we construct a family of flow rate curves by fitting with data. Based on the GARZ model, we then propose a phase-transition-like model that allows the flow rate curves to coincide in the free flow regime. The resulting model is called Collapsed GARZ (CGARZ) model. The CGARZ model keeps the flavor of phase transition models in the sense that it assume a single FD function in the free-flow phase. However, one should note that there is no real phase transition in the CGARZ model. To investigate to which extent the new generic ``second order" models (GARZ, CGARZ) improve the prediction accuracy of macroscopic models, we perform a comparison of the proposed models with two types of LWR models and their ``second order" generalizations, given by the ARZ model, via a three-detector problem test. In this test framework, the initial and boundary conditions are derived from real traffic data. In terms of using historic traffic data, a statistical technique, the so-called kernel density estimation, is applied to obtain density and velocity distributions from trajectory data, and a cubic interpolation is employed to formulate boundary condition from single-loop sensor data. Moreover, a relaxation term is added to the momentum equation of selected ``second order" models to address further unrealistic aspects of homogeneous models. Using these inhomogeneous ``second order" models, we study which choices of the relaxation term &tau are realistic. / Mathematics

On étudie dans ce travail des systèmes de lois de conservation hyperboliques. La première partie étudie le temps d'existence des solutions régulières et régulières par morceaux de la dynamique des fluides compressibles. Après avoir présenté l'état de l'art en matière de solutions régulières, on montre une extension d'un théorème de Grassin à des gaz de Van der Waals. On étudie ensuite les solutions ondes de chocs : on poursuit l'approche de T. T. Li pour estimer leur temps d'existence dans le cas isentropique à symétrie sphérique, et l'approche de Whitham afin d'obtenir une équation approchée vérifiée par la surface de discontinuité. Dans une deuxième partie, motivée par la modélisation d'un rond-point en trafic routier, on étudie une extension multi-classe du modèle macroscopique de Lighthill-Whitham-Richards sur une route infinie avec des jonctions. On différencie les véhicules selon leur origine et leur destination et on introduit des conditions aux bords adaptées au niveau des jonctions. On obtient existence et unicité d'une solution au problème de Riemann pour ce modèle. Des simulations numériques attestent que les solutions obtenues existent en temps long. On aborde enfin le problème de Cauchy par la méthode de front tracking. La dernière partie concerne les lois de conservation scalaires. La première question abordée est le contrôle de la variation totale de la solution et la stabilité des solutions faibles entropiques par rapport au flux et à la source. Ce résultat nous permet d'étudier des équations avec flux non-local. Une fois établi leur caractère bien posé, on montre la Gâteaux-différentiabilité du semi-groupe obtenu par rapport aux conditions initiales. / In this work, we study hyperbolic systems of balance laws. The first part is devoted to compressible fluid dynamics, and particularly to the lifespan of smooth or piecewise smooth solutions. After presenting the state of art, we show an extension to more general gases of a theorem by Grassin.We also study shock waves solutions: first, we extend T. T. Li's approach to estimate the time of existence in the isentropic spherical case; second, we develop Whitham's ideas to obtain an approximated equation satisfied by the discontinuity surface. In the second part, we set up a new model for a roundabout. This leads us to study a multi-class extension of the macroscopic Lighthill-Whitham-Richards' model. We study the traffic on an infinite road, with some points of junction. We distinguish vehicles according to their origin and destination and add some boundary conditions at the junctions. We obtain existence and uniqueness of a weak entropy solution for the Riemann problem. As a complement, we provide numerical simulations that exhibit solutions with a long time of existence. Finally, the Cauchy problem is tackled by the front tracking method. In the last part, we are interested in scalar hyperbolic balance laws. The first question addressed is the control of the total variation and the stability of entropy solutions with respect to flow and source. With this result, we can study equations with non-local flow, which do not fit into the framework of classical theorems. We show here that these kinds of equations are well posed and we show the Gâteaux-differentiability with respect to initial conditions, which is important to characterize maxima or minima of a given cost functional.