相关论文: The Aw-Rascle traffic model: Enskog-type kinetic d…

In this paper, we derive second order hydrodynamic traffic models from kinetic-controlled equations for driver-assist vehicles. At the vehicle level we take into account two main control strategies synthesising the action of adaptive cruise…

We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic…

We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined…

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…

We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle…

Daganzo's criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277-286 (1995)] and Aw and Rascle's proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916-938 (2000)] have…

Traffic flow modeling spans a wide range of mathematical approaches, from microscopic descriptions of individual vehicle dynamics to macroscopic models based on aggregate quantities. A fundamental challenge in macroscopic modeling lies in…

Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in one…

The paper presents a systematic derivation of macroscopic equations for freeway traffic flow from an Enskog-like kinetic approach. The resulting fluid-dynamic traffic equations for the spatial density, average velocity, and velocity…

We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and…

We present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux…

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For an arbitrary large class of initial data and the periodic domain, we prove the existence of global-in-time measure-valued solutions.…

We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…

In this paper, we introduce a traffic flow model based on a microscopic follow-the-leader model, while enforcing maximal constraints on the density and velocity of the flow. The related macroscopic model can be represented in conservative…

Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The…

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…

Traffic waves, the spatiotemporal propagation of congestion, are a key feature of traffic flow. As Adaptive Cruise Control (ACC) systems gain widespread adoption and show promise for improving both efficiency and safety, understanding how…

We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized…

An extended multi-class Aw-Rascle (AR) model with pressure term described as a function of area occupancy defined in form of proportional densities is presented. Two vehicle classes that is; cars and motorcycles are considered based on an…

We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…