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

On Stop-and-Go waves in dense traffic

Michael Herty 1, and  Reinhard Illner 2,

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.
Keywords: nonlinear stability, stop-and-go waves, traffic flow, nonlocal equations..
Mathematics Subject Classification: Primary: 90B20, 34D10; Secondary: 35J1.
Citation: Michael Herty, Reinhard Illner. On Stop-and-Go waves in dense traffic. Kinetic & Related Models, 2008, 1 (3) : 437-452. doi: 10.3934/krm.2008.1.437
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