Kinetic and Related Models (KRM)

On Stop-and-Go waves in dense traffic

Pages: 437 - 452, Volume 1, Issue 3, September 2008      doi:10.3934/krm.2008.1.437

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Michael Herty - RWTH Aachen, Mathematik, Templergraben 55, D-52056 Aachen, Germany (email)
Reinhard Illner - University of Victoria, Department of Mathematics and Statistics, PO Box 3045 STN CSC, Victoria, B.C., Canada V8W 3P4, Canada (email)

Abstract: 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:  traffic flow, stop-and-go waves, nonlinear stability, nonlocal equations.
Mathematics Subject Classification:  Primary: 90B20, 34D10; Secondary: 35J15.

Received: April 2008;      Revised: May 2008;      Available Online: August 2008.