Uncertainty Quantification in Hierarchical Vehicular Flow Models

2021/08/17 by Michaël Herty, Michael Herty, Herty, Michael +2
Computer Science · Engineering · Mathematics · Social Sciences · #FOS: Mathematics #Numerical Analysis (math.NA) #Traffic Prediction and Management Techniques #Traffic control and management #Transportation Planning and Optimization #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2108.07589

arxiv created 2021/08/17 · openalex publication_date 2021/08/17 · arxiv updated 2021/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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