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Zbl 1165.90374
Herty, Michael; Illner, Reinhard
On stop-and-go waves in dense traffic. (English)
[J] Kinet. Relat. Models 1, No. 3, 437-452 (2008). ISSN 1937-5093; ISSN 1937-5077/e

Summary: 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 {\it A. Aw} and {\it M. Rascle} [SIAM J. Appl. Math. 60, No.~3, 916--938 (2000; Zbl 0957.35086)] and {\it H. M. Zhang} [Chin. Ann. Math., Ser. B 26, No.~2, 275--290 (2005; Zbl 1067.17002)]. 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.

MSC 2000:: *90B20 Highway traffic
34D10 Stability perturbations of ODE
35J15 Second order elliptic equations, general

Keywords: traffic flow; stop-and-go waves; nonlinear stability; nonlocal equations

Citations: Zbl 0957.35086; Zbl 1067.17002

Cited in: Zbl 1200.90044

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