Overview on uncertainty quantification in traffic models via intrusive method

TL;DR

This paper reviews how uncertainty quantification is performed across various traffic flow models at microscopic, kinetic, and macroscopic scales using the stochastic Galerkin method, highlighting inter-scale connections and numerical results.

Contribution

It provides a comprehensive overview of applying the stochastic Galerkin method to propagate uncertainties in traffic models across different scales.

Findings

Uncertainty propagation is feasible across microscopic, kinetic, and macroscopic traffic models.

Connections between different scales are established in the stochastic framework.

Numerical simulations demonstrate the effectiveness of the approach.

Abstract

We consider traffic flow models at different scales of observation. Starting from the well known hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models using the stochastic Galerkin approach. Connections between the scales will be presented in the stochastic scenario and numerical simulations will be performed.