Uncertainty Quantification in Hierarchical Vehicular Flow Models

arXiv (Cornell University)

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.

Authors 2

1. Michaël Herty Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templergraben 55 , 52062 Aachen , Germany,

2. Elisa Iacomini Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templergraben 55 , 52062 Aachen , Germany,