Communications in Mathematical Sciences
Volume 11 (2013)
Kinetic derivation of a Hamilton-Jacobi traffic flow model
Pages: 739 – 756
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.
traffic flow, macroscopic equations, kinetic derivation, Hamilton-Jacobi equations
2010 Mathematics Subject Classification
60K15, 76P05, 90B20