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Modélisation mathématique et simulation du trafic routier : analyse statistique de modèles d'insertion et simulation probabiliste d'un modèle cinétique

Abstract : The first part of this thesis is dedicated to the optimization of the lengths of acceleration lanes using microscopic data collected from real traffic. The insertions on the highway junctions can indeed be especially dangerous considering the difference between the speeds on the on ramp merge lane and those on the highway lanes. We develop and analyse some microscopic merging models. We first propose a statistical model based on the logistic regression techniques. Statistical hypothesis tests allow to select the most significant descriptive variables in the merging decision process. A behavioural modelling taking those variables into account is next proposed to better capture the interactions by including some thresholds on the gaps between the merging vehicles and freeway vehicles. The models are validated using real traffic data collected at the SAROT site near Angers. Secondly, traffic simulation at the mesoscopic scale is mostly based on deterministic numerical schemes. However, these methods have a high computational cost. The objective of the second part of this thesis is to present a new method to simulate the Paveri-Fontana kinetic model through a probabilistic approach. We interpret the evolution equation in this model as a Fokker-Planck equation and deduce an approximation based on a system of interacting particles. The algorithmic complexity of this method is optimized. We have performed a numerical comparison between the probabilistic method and a deterministic method on some cases study. The qualitative analysis highlights the benefits of the particle method such as its computation cost and its ability to reproduce some typical traffic effects
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Jyda Mint Moustapha. Modélisation mathématique et simulation du trafic routier : analyse statistique de modèles d'insertion et simulation probabiliste d'un modèle cinétique. Modélisation et simulation. Université Paris-Est, 2014. Français. ⟨NNT : 2014PEST1113⟩. ⟨tel-01144601⟩

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