Asymptotic solution of a wide moving jam to a class of higher-order viscous traffic flow models

The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.     

On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flowSur une fermeture des équations de conservation de la masse et l'analyse de la stabilité dans la théorie mathématique de la circulation véhiculaire

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow. To cite this article: V. Coscia, C. R. Mecanique 332 (2004).