# American Institute of Mathematical Sciences

September  2008, 1(3): 437-452. doi: 10.3934/krm.2008.1.437

## On Stop-and-Go waves in dense traffic

 1 RWTH Aachen, Mathematik, Templergraben 55, D-52056 Aachen, Germany 2 University of Victoria, Department of Mathematics and Statistics, PO Box 3045 STN CSC, Victoria, B.C., Canada V8W 3P4, Canada

Received  April 2008 Revised  May 2008 Published  August 2008

From a Vlasov-type kinetic equation with nonlocal braking and acceleration forces, taken as a traffic model for higher densities, we derive macroscopic equations generalizing the second order model of conservation laws suggested by Aw and Rascle [1] and Zhang [19]. The nonlocality remains present in these equations, but more conventional, local equations are derived by using suitable Taylor expansion. A second order model of this type is discussed in some detail and is shown to possess traveling wave solutions that resemble stop-and-go waves in dense traffic. A phase space analysis suggests that inside the class of such traveling waves there are steady solutions that are stable.
Citation: Michael Herty, Reinhard Illner. On Stop-and-Go waves in dense traffic. Kinetic and Related Models, 2008, 1 (3) : 437-452. doi: 10.3934/krm.2008.1.437
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