Analysis of a heterogeneous kinetic model for traffic flow

TL;DR

This paper extends a kinetic traffic flow model to multiple vehicle classes with continuous velocities, analyzing its mathematical properties, equilibria, and introducing a new law to improve traffic capacity representation.

Contribution

It introduces a multi-class kinetic model with continuous velocities, analyzes its well-posedness, and proposes a new probability law to better model traffic capacity drops.

Findings

Exact asymptotic distributions with few velocities

Numerical analysis of fundamental diagrams

Attenuation of capacity drop in traffic models

Abstract

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 interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model based on a lattice of speeds because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic.