Author : Mahaman Salissou Mahaman Moutari
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (493 download)
Book Synopsis Modélisation mathématique et numérique du trafic automobile by : Mahaman Salissou Mahaman Moutari
Download or read book Modélisation mathématique et numérique du trafic automobile written by Mahaman Salissou Mahaman Moutari and published by . This book was released on 2007 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to simulate in a relevant way vehicular traffic on large road networks, an essential ingredient is using theoretical tools which allow for an adequate modelling of each component of the network. To achieve this goal, several modelling methods exist to date. However, due to some additional constraints, in particular those related to the development of the road networks infrastructures and the increasing concentration of traffic, the investigation of new modelling tools is necessary. In this work, we have introduced some methods and models, which enable a relevant description of the traffic on road networks, by taking into account its specificity through some particular components of the network such as intersections, highway on and off ramps, toll stations, etc.... The presented approaches are expected to be theoretically rigorous, numerically reliable, and computationally efficient. The first approach we have proposed concerns macroscopic models. It is based on the resolution of the Riemann problem whereas the flux at the junction is optimized. Thereafter we have extended this approach to macroscopic multiclass models. The second approach studied in this work is the hybrid modelling. First, we have proposed a hybrid model based on the classical Eulerian-Lagrangian coupling of the Aw & Rascle second order macroscopic model and a class of microscopic models. In a such hybrid model, the interfaces between the coupled models are fixed in eulerian coordinates. Thereby, the interfaces’ functioning is somehow complex and tedious to work out. In order to circumvent this problem, we have proposed a fully lagrangian coupling approach. The novelty of this new hybrid approach is that the interfaces are moving in lagrangian coordinates. This particular property makes the model much simpler than in the previous case and leads to a rigorous and easy computational model. Finally we have proposed a model describing the formation and evolution of traffic jams. This model is derived from the Aw & Rascle second order macroscopic model and based on a realistic formulation of clusters dynamics. We have analysed the solutions to the associated Riemann problem and we have proved the existence of solutions for this model.