Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1053.35087
Greenberg, J.M.
(Greenberg, James M.)
Congestion redux. (English)
[J] SIAM J. Appl. Math. 64, No. 4, 1175-1185 (2004). ISSN 0036-1399; ISSN 1095-712X/e

Summary: We analyze a class of second-order traffic models and show that these models support stable oscillatory traveling waves typical of the waves observed on a congested roadway. The basic model has trivial or constant solutions where cars are uniformly spaced and travel at a constant equilibrium velocity that is determined by the car spacing. The stable traveling waves arise because there is an interval of car spacing for which the constant solutions are unstable. These waves consist of a smooth part where both the velocity and spacing between successive cars are increasing functions of a Lagrange mass index. These smooth portions are separated by shock waves that travel at computable negative velocity.

MSC 2000:: *35L60 First-order nonlinear hyperbolic equations
35L65 Conservation laws
90B20 Highway traffic

Keywords: traffic congestion; follow-the-leader; second-order traffic models; shock waves; negative velocity

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]