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Vehicular traffic through a self-similar sequence of traffic lights

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  • Nagatani, Takashi

Abstract

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time Ts. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x)-x)∝xdf, where df is the fractal dimension of Cantor set. The landscape in the plot of T(x)−x against cycle time Ts shows a self-affine fractal with roughness exponent α=1−df.

Suggested Citation

  • Nagatani, Takashi, 2007. "Vehicular traffic through a self-similar sequence of traffic lights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 381-387.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:381-387
    DOI: 10.1016/j.physa.2007.07.042
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    Cited by:

    1. Li, Xiang & Sun, Jian-Qiao, 2019. "Intersection multi-objective optimization on signal setting and lane assignment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1233-1246.
    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.
    3. Elisabeth Bloder & Georg Jäger, 2021. "Is the Green Wave Really Green? The Risks of Rebound Effects When Implementing “Green” Policies," Sustainability, MDPI, vol. 13(10), pages 1-11, May.

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