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Self-similar behavior of a single vehicle through periodic traffic lights

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  • Nagatani, Takashi

Abstract

We study the dynamical behavior of a single vehicle moving through a sequence of traffic lights on a single-lane highway, where the traffic lights turn on and off periodically with the synchronized or green-wave strategies. The dynamical model of the vehicle controlled by traffic lights is expressed in terms of the nonlinear map. The tour time of the vehicle exhibits a complex behavior, interacting with the sequence of traffic lights. The dynamical behavior of signal traffic at a low density changes at ts=l/v+τ, where l is the distance between the traffic lights, v the mean speed of the vehicle, and τ the delay of traffic light at the green-wave strategy. When the cycle time ts of traffic lights is less than (l/v+τ), the vehicle exhibits the self-similar behavior, while it shows the periodic behavior for ts>(l/v+τ). The characteristics of the self-similar behavior is clarified.

Suggested Citation

  • Nagatani, Takashi, 2005. "Self-similar behavior of a single vehicle through periodic traffic lights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 673-682.
    • Handle: RePEc:eee:phsmap:v:347:y:2005:i:c:p:673-682
    DOI: 10.1016/j.physa.2004.08.007
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    Cited by:

    1. Nagatani, Takashi & Nagai, Ryoichi, 2005. "Chaotic and periodic motions of two competing vehicles controlled by traffic lights," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 245-253.
    2. Yuan, PengCheng & Lin, XuXun, 2017. "How long will the traffic flow time series keep efficacious to forecast the future?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 419-431.

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