The Viscosity Solution for Hamilton Jacobi Travel Time Dynamics

Document Type

Article

Publication Date

10-15-2019

Publication Title

IEEE Transactions on Intelligent Transportation Systems

Volume

21

Issue

11

First page number:

4715

Last page number:

4724

Abstract

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

Traffic; Travel time; Shock waves; Lighthill-whitham-richards; LWR; Entropy; Viscosity; Partial differential equation; PDE

Disciplines

Electrical and Computer Engineering | Engineering

Language

English

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