Hybrid stochastic kinetic description of two-dimensional traffic dynamics

TL;DR

This paper develops a two-dimensional kinetic traffic model incorporating lane changes and interactions, deriving a hybrid stochastic equation to analyze and validate traffic flow dynamics with real data comparison.

Contribution

It introduces a novel hybrid stochastic Fokker-Planck-Boltzmann model for 2D traffic flow, accounting for lane changes and uncertainties, with numerical validation.

Findings

Speed-density diagrams match real traffic data.

Model captures lane-changing effects on traffic flow.

Provides estimates of data dispersion in traffic modeling.

Abstract

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 interactions along the same lane and considering that their mathematical description can be done up to some uncertainty in the model parameters, we derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the quasi-invariant interaction limit. By means of suitable numerical methods, precisely structure preserving and direct Monte Carlo schemes, we use this equation to compute theoretical speed-density diagrams of traffic both along and across the lanes, including estimates of the data dispersion, and validate them against real data.