Lagrangian-based Hydrodynamic Model: Freeway Traffic Estimation
Abstract
This paper is concerned with highway traffic estimation using traffic sensing data, in a Lagrangian-based modeling framework. We consider the Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956) in Lagrangian-coordinates, and provide rigorous mathematical results regarding the equivalence of viscosity solutions to the Hamilton-Jacobi equations in Eulerian and Lagrangian coordinates. We derive closed-form solutions to the Lagrangian-based Hamilton-Jacobi equation using the Lax-Hopf formula (Daganzo, 2005; Aubin et al., 2008), and discuss issues of fusing traffic data of various types into the Lagrangian-based H-J equation. A numerical study of the Mobile Century field experiment (Herrera et al., 2009) demonstrates the unique modeling features and insights provided by the Lagrangian-based approach.
Keywords
Cite
@article{arxiv.1211.4619,
title = {Lagrangian-based Hydrodynamic Model: Freeway Traffic Estimation},
author = {Ke Han and Tao Yao and Terry L. Friesz},
journal= {arXiv preprint arXiv:1211.4619},
year = {2012}
}
Comments
17 pages, 7 figures, current version submitted to Transportation Research Part B