# Tra c ﬂow modelling with junctions

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English
22 Pages

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Niveau: Supérieur, Doctorat, Bac+8
Tra?c ﬂow modelling with junctions. Magali Mercier ? September 9, 2008 Abstract Motivated by the modelling of a roundabout, we are led to study the tra?c on a road with points of entry and exit. In this note, we would like to describe the modellisation of a junction and solve the Riemann problem for such a model. More precisely, between each point of discontinuity we use a multi-class extension of the LWR model to describe the evolution of the density of the vehicles, the multi-class' approach being used in order to distinguish the vehicles after their origin and destination. Then, we treat the points of entry and exit thanks to special boundary conditions that give bounds on the ﬂows of the di?erent types of vehicles. In the case of the one-T road we obtain a result of existence and uniqueness. This ﬁrst step allows us to obtain a similar result for the n-T road. We describe these results and also some properties of the obtained solutions, in order to see how long this model is valid. 2000 Mathematics Subject Classiﬁcation: 35L65, 90B20 Key words and phrases: Hyperbolic Systems of Conservation Laws, Continuum tra?c ﬂow model, Riemann problem. 1 Introduction. Tra?c modelling, in particular from a macroscopic point of view has been intensively investi- gated since the seminal paper by Lighthill & Withham [15] and Richards [17], see for example [16], [10].

• rc ?

• let ?1

• ?1 ﬁrst

• tra?c ﬂow

• bardos-leroux-nédélec ones

• distributed

• points periodically

• continuum tra?c

• ?1

Subjects

##### Mercier

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