Kinetic derivation of a Hamilton-Jacobi traffic flow model - Borsche, Raul; Kimathi, Mark; Klar, Axel (My University, 2012)
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.
Keywords: Traffic flow; Macroscopic equations; Kinetic derivation; Hamilton-Jacobi equations