Stability analysis in Greenberg’s traffic model

Oscar A. Rosas-Jaimes, Luis A. Quezada-Téllez () and Guillermo Fernández-Anaya ()
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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

International Journal of Modern Physics C (IJMPC), 2017, vol. 28, issue 10, 1-23

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.

Keywords: Greenberg model; traffic fundamental diagrams; dynamical analysis; chaos (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0129183117501303

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