Uncertainty Quantification in Hierarchical Vehicular Flow Models

TL;DR

This paper extends kinetic vehicular traffic flow models by incorporating stochastic variables to account for uncertainty, analyzing its impact across different model scales and providing theoretical and numerical insights.

Contribution

It introduces a stochastic extension to BGK-type traffic models and studies the effects of uncertainty within the hierarchical modeling framework.

Findings

The stochastic hydrodynamic model can exhibit negative diffusion effects.

Theoretical formulations ensure consistency of stochastic differential equations.

Numerical simulations demonstrate the impact of uncertainty on traffic flow predictions.

Abstract

We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic BGK-model is extended by introducing a parametric stochastic variable to describe possible uncertainty in traffic. The interplay of uncertainty with the given model hierarchy is studied in detail. Theoretical results on consistent formulations of the stochastic differential equations on the hydrodynamic level are given. The effect of the possibly negative diffusion in the stochastic hydrodynamic model is studied and numerical simulations of uncertain traffic situations are presented.