564 RWTH Publication No: 841576        2021       
TITLE Uncertainty Quantification in Hierarchical Vehicular Flow Models
AUTHORS Michael Herty, Elisa Iacomini
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.
KEYWORDS traffic flow, BGK models, stochastic Galerkin, Aw-Rascle-Zhang model, kinetic equations
DOI 10.3934/krm.2022006
PUBLICATION Kinetic and Related Models,2022, Volume 15, Issue 2: 239-256