Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

TL;DR

This paper introduces a Boltzmann-type kinetic model that links individual vehicle interactions to overall traffic safety and risk distribution, providing insights into how congestion affects driving risk.

Contribution

It develops a novel kinetic framework connecting microscopic driver interactions to macroscopic risk and traffic flow characteristics.

Findings

Risk correlates with traffic congestion levels.

Model captures free and congested traffic phases.

Provides a probabilistic description of driver interactions.

Abstract

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 distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.