Uncertainty quantification in hierarchical vehicular flow models

Kinetic and Related Models, vol. 15, pp. 239

Abstract

We consider kinetic vehicular traffic flow models of BGK type [ 24 ]. 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

   RWTH Aachen University

   Affiliation as printed

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

2. Elisa Iacomini corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

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