Resurrection of “second order” models of traffic flow. (English) Zbl 0957.35086

Aw, A.; Rascle, M.

SIAM J. Appl. Math. 60, No. 3, 916-938 (2000).

The authors deal with the 2nd order (two equations) mathematical model of traffic flow and point out drawbacks of currently used models. They change the model by replacing space derivation of the “pressure” with a convective one. The resulting system is strictly hyperbolic, except at the origin. The solution of the Riemann problem is described in details, including the case of the vacuum (i.e. the case of very low traffic). Remarks on the admissibility and stability of the solution are presented. Comparing the solution to the new proposed model with the solution to the older model shows that the older model predicts unrealistic solutions with negative velocities whereas the new model gives a correct answer.

Reviewer: A.Doktor (Praha)

MSC:

35L65	Hyperbolic conservation laws
90B20	Traffic problems in operations research
35L80	Degenerate hyperbolic equations
35Q35	PDEs in connection with fluid mechanics

Keywords:

traffic flow; conservation laws; Riemann problem