Analytical solutions of jam pattern formation on a ring for a class of optimal velocity traffic models

Yuri Borisovich Gaididei, Rainer Berkemer, Jean Guy Caputo, P. L. Christiansen, Atsushi Kawamoto, T. Shiga, Mads Peter Sørensen, Jens Starke

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    Abstract

    A follow-the-leader model of traffic flow on a closed loop is considered in the framework of the extended optimal velocity (OV) model where the driver reacts to both the following and the preceding car. Periodic wave train solutions that describe the formation of traffic congestion patterns are found analytically. Their velocity and amplitude are determined from a perturbation approach based on collective coordinates with the discrete modified Korteweg-de Vries equation as the zero order equation. This contains the standard OV model as a special case. The analytical results are in excellent agreement with numerical solutions.
    Original languageEnglish
    JournalNew Journal of Physics
    Volume11
    Pages (from-to)073012
    ISSN1367-2630
    DOIs
    Publication statusPublished - 2009

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