Showing papers by "Raul Borsche published in 2012"
TL;DR: In this article, the authors prove the well posedness of mixed problems consisting of a system of ordinary differential equations coupled with systems of balance laws in domains with moving boundaries, where interfaces between the systems are provided by the boundary data and boundary positions.
61 citations
TL;DR: Numerical experiments show similarities and differences of the models, in particular, for the appearance and structure of stop and go waves for highway traffic in dense situations.
Abstract: In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental diagrams are derived from different microscopic and kinetic models. Numerical experiments show similarities and differences of the models, in particular, for the appearance and structure of stop and go waves for highway traffic in dense situations. For all models, but one, phase transitions can appear near bottlenecks depending on the local density and velocity of the flow.
37 citations
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TL;DR: In this article, a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given, in particular for the appearance and structure of stop and go waves for highway traffic in dense situations.
Abstract: In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental diagrams are derived from different microscopic and kinetic models. Numerical experiments show similarities and differences of the models, in particular, for the appearance and structure of stop and go waves for highway traffic in dense situations. For all models, but one, phase transitions can appear near bottlenecks depending on the local density and velocity of the flow.
35 citations
01 Jan 2012
TL;DR: This work combines existing models for car traffic and pedestrian motion to a coupled description taking the mutual interaction into account and extends the flux function of the car traffic by a suitable dependence on the pedestrians on the roads.
Abstract: In urban areas car traffic and pedestrian motion interact in many different situations. For both dynamics separately various models exist. The description of road traffic has a long history and many different models are available. These range from models following a microscopic description [5] to models of a macroscopic viewpoint [1, 3]. For road networks these equations can be combined by suitable coupling conditions [1]. On the other hand similar approaches can be used in order to describe the motion of pedestrians [2, 6, 4]. In the present work we combine existing models for car traffic and pedestrian motion to a coupled description taking the mutual interaction into account. Therefore we extend the flux function of the car traffic by a suitable dependence on the pedestrians on the roads. Similarly influences the traffic density the path of the pedestrians. In several numerical examples we compare different choices of coupling conditions and their influence on the coupled dynamics. Further test cases consider situations of daily experience e.g. like the the crossing of pedestrians at a crosswalk.
TL;DR: In this article, the authors reviewed and considered from the point of view of deriving macroscopic equations for vehicular traffic, including Aw-Rascle equations and Hamilton-Jacobi type traffic equations.
Abstract: Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain situations modified Aw-Rascle equations are obtained. On the other hand, for several choices of kinetic parameters new Hamilton-Jacobi type traffic equations are found. Associated microscopic models are discussed and numerical experiments are presented discussing several situations for highway traffic and comparing the different models.