Related papers: Kinetic derivation of a Hamilton-Jacobi traffic fl…
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…
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…
This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address 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…
Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…
We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic for junctions with diverging lanes. We consider cases with and without directional preferences and present corresponding kinetic coupling…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity…
This work provides a comprehensive analysis on naturalistic driving behavior for highways based on the highD data set. Two thematic fields are considered. First, some macroscopic and microscopic traffic statistics are provided. These…
This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…
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…
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…
Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…
We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic…
Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the…
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…
On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for uni-directional multi-lane freeways is constructed.…