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A Multi-class Vehicular Flow Model for Aggressive Drivers

In: Traffic and Granular Flow '15

Author

Listed:
  • Wilson Marques Jr.

    (Universidade Federal Do Paraná, Departamento de Fisica)

  • Rosa María Velasco

    (Universidad Autónoma Metropolitana, Departamento de Física)

  • Alma Méndez

    (Universidad Autónoma Metropolitana, Departamento de Matemáticas Aplicadas y Sistemas)

Abstract

TheMarques Jr., Wilson kinetic theory approachesVelasco, Rosa María to vehicularMéndez, Alma traffic modelling have given very good results in the understanding of the dynamical phenomena involved [3, 8]. In this work, we deal with the kinetic approach modelling of a traffic situation where there are many classes of aggressive drivers [5]. Their aggressiveness is characterised through their relaxation times. The reduced Paveri-Fontana equation is taken as a starting point to set the model. It contains the usual drift terms and the interactions between drivers of the same class, as well as the corresponding one between different classes. The reference traffic state used in the kinetic treatment is determined by a dimensionless parameter. The balance equations for the density and average speed for each class are obtained through the usual methods in the kinetic theory. In this model, we consider that each class of drivers preserve the corresponding aggressiveness, in such a way that there will be no adaptation effects [6]. It means that the number of drivers in a class is conserved. As preliminary results, we have obtained a closure relation to derive the Euler-like equations for two drivers classes. Some characteristics of the model are explored with the usual methods.

Suggested Citation

  • Wilson Marques Jr. & Rosa María Velasco & Alma Méndez, 2016. "A Multi-class Vehicular Flow Model for Aggressive Drivers," Springer Books, in: Victor L. Knoop & Winnie Daamen (ed.), Traffic and Granular Flow '15, pages 475-482, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-33482-0_60
    DOI: 10.1007/978-3-319-33482-0_60
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