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Stability analysis in Greenberg’s traffic model

Author

Listed:
  • Oscar A. Rosas-Jaimes

    (Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Prol. 24 Sur S/N Ciudad Universitaria, San Manuel, 72570 Puebla, México)

  • Luis A. Quezada-Téllez

    (Departamento de Matemáticas Aplicadas y Sistemas, UAM-Unidad Cuajimalpa, Avenida Vasco de Quiroga 4871, Ciudad de México, México)

  • Guillermo Fernández-Anaya

    (Departmento de Física y Matemáticas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Álvaro Obregón, Lomas de Sta. Fe, Cd. de México, México)

Abstract

In this document, Greenberg’s classical traffic model is analyzed by varying the critical velocity vo that appears in it as a parameter. This model is transformed as a discrete expression and manipulated by means of isolating variables such as vehicular density k, flow q and velocity v that appear in the model. So-called fundamental diagrams are obtained by pairing two out of these three variables, and then they are used to support trajectories of iterated processes depicting distinct behaviors of traffic. As it is shown in this paper, those behaviors have monotonous and stable patterns for some range of values of the parameter vo, but they can change to cyclic and stable trajectories when this parameter is modified. If the modifications of that parameter are taken to a higher range of values, then cycles of different periods appear, reaching chaotic trajectories. These behaviors are analyzed from a dynamical approach, proving their stability conditions, and then they are illustrated with simulations in each case.

Suggested Citation

  • Oscar A. Rosas-Jaimes & Luis A. Quezada-Téllez & Guillermo Fernández-Anaya, 2017. "Stability analysis in Greenberg’s traffic model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(10), pages 1-23, October.
    • Handle: RePEc:wsi:ijmpcx:v:28:y:2017:i:10:n:s0129183117501303
    DOI: 10.1142/S0129183117501303
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