Kinetic derivation of a Hamilton-Jacobi traffic flow model
Abstract
Kinetic models for vehicular traffic are reviewed and considered from the point
of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow
equations leads to different types of equations: in certain situations modified Aw-Rascle equations
are obtained. On the other hand, for several choices of kinetic parameters new Hamilton-Jacobi type
traffic equations are found. Associated microscopic models are discussed and numerical experiments
are presented discussing several situations for highway traffic and comparing the different models.