AbstractIn this paper we will discuss some aspects of the recent macroscopic models of the second-order proposed by [Aw, A., Rascle, M., 2000. Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics 60 (3), 916–938] and [Zhang, H.M., 2002. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B 36, 275–290]. These models were suggested after the publication of an article written by [Daganzo, C.F., 1995. Requiem for second-order fluid approximations of traffic flow. Transportation Research Part B 29, 277–286] showing that some classical second-order models can exhibit non-physical solutions. It is shown in this note that the ARZ (Aw–Rascle–Zhang) model respects the anisotropic character of traffic flow, that it yields physical solutions, and that vacuum problems can be solved satisfactorily, provided that the fundamental diagram (equilibrium speed–density relationship) is extended in a suitable fashion. It follows that the Riemann problem for the ARZ model with extended fundamental diagram always admits a solution, and that this solution depends continuously on the initial conditions.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    The Aw–Rascle and Zhang’s model: Vacuum problems, existence and regularity of the solutions of the Riemann problem


    Beteiligte:

    Erschienen in:

    Erscheinungsdatum :

    2006-11-01


    Format / Umfang :

    12 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch






    Riemann Problem Resolution and Godunov Scheme for the Aw-Rascle-Zhang Model

    Mammar, S. / Lebacque, J.-P. / Salem, H.H. | British Library Online Contents | 2009


    Improved Numerical Method for Aw-Rascle Type Continuum Traffic Flow Models

    Mohammadian, Saeed / van Wageningen-Kessels, Femke | Transportation Research Record | 2018


    Varying Speed Limit Control of Aw-Rascle-Zhang Traffic Model

    Yu, Huan / Krstic, Miroslav | IEEE | 2018