The Viscosity Solution for Hamilton Jacobi Travel Time Dynamics
Document Type
Article
Publication Date
11-1-2020
Publication Title
IEEE Transactions on Intelligent Transportation Systems
Volume
21
Issue
11
First page number:
4715
Last page number:
4724
Abstract
© 2000-2011 IEEE. Travel time is an important concept in various intelligent transportation system applications. A density-based travel time partial differential equation (PDE) based on the Lighthill-Whitham-Richards (LWR) model, and its dynamics are reviewed. The travel time dynamics are an asymmetric, one-sided coupled system of hyperbolic PDEs. Although the model has been derived previously, and its applications have been proposed, important properties of the solution to the travel time PDE are studied for the first time. The travel time PDE has the form of a Hamilton Jacobi equation. For this type of equation, finding a unique solution that is consistent with reality is accomplished by finding its viscosity solution. The main contribution of this paper is the mathematical development of the method for finding the viscosity solution of the given travel time PDE.
Keywords
Entropy; LWR; shock waves; Traffic; Travel time; Viscosity
Disciplines
Mechanical Engineering
Language
English
Repository Citation
Contreras, S.,
Kachroo, P.
(2020).
The Viscosity Solution for Hamilton Jacobi Travel Time Dynamics.
IEEE Transactions on Intelligent Transportation Systems, 21(11),
4715-4724.
http://dx.doi.org/10.1109/TITS.2019.2946109