Related papers: Analysis of a heterogeneous kinetic model for traf…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…
We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…
This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the…
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…
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…
In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…
This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date…
In this paper we present a Boltzmann-type kinetic approach to the modelling of road traffic, which includes control strategies at the level of microscopic binary interactions aimed at the mitigation of speed-dependent road risk factors.…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
In this paper we study a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. These minimal microscopic interaction rules lead to complex…
We present large scale and detailed analysis of the microscopic empirical data of the traffic flow, focusing on the non-linear interactions between the vehicles when the traffic is congested. By implementing a "renormalisation" procedure…
We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some…
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…
We study the application of a recently introduced hierarchical description of traffic flow control by driver-assist vehicles to include lane changing dynamics. Lane-dependent feedback control strategies are implemented at the level of…
In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a…
Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a…
In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
We develop a hierarchical description of traffic flow control by means of driver-assist vehicles aimed at the mitigation of speed-dependent road risk factors. Microscopic feedback control strategies are designed at the level of…