Open AccessUncertainty quantification in hierarchical vehicular flow models
Author(s) -
Michaël Herty,
Elisa Iacomini
Publication year - 2022
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2022006
Subject(s) - hierarchy , traffic flow (computer networking) , parametric statistics , statistical physics , flow (mathematics) , mathematics , stochastic differential equation , type (biology) , diffusion , microscopic traffic flow model , stochastic modelling , computer science , physics , geometry , statistics , geology , thermodynamics , traffic generation model , paleontology , computer security , economics , market economy
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.