The Viscosity Solution for Hamilton Jacobi Travel Time Dynamics
IEEE Transactions on Intelligent Transportation Systems
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© 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.
Entropy; LWR; shock waves; Traffic; Travel time; Viscosity
The Viscosity Solution for Hamilton Jacobi Travel Time Dynamics.
IEEE Transactions on Intelligent Transportation Systems, 21(11),