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Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

Author

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  • Tian, Jun-fang
  • Yuan, Zhen-zhou
  • Treiber, Martin
  • Jia, Bin
  • Zhang, Wen-yi

Abstract

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The anticipation rule takes into account the average space gap of multiple leading vehicles and conveys to the model its three-phase property. Due to the anticipation rule, ASGM can show the transition from free flow to synchronized flow. Due to the slow-to-start rule, ASGM can show the spontaneous wide moving jam emerges in the synchronized flow. Simulations are carried out for periodic and open boundary conditions. Under periodic boundary condition, the fundamental diagram, and the properties of synchronized flow are studied. Under open boundary condition, different congested patterns induced by an on-ramp are analyzed. We found that the ASGM produces the same spatiotemporal dynamics as many of the more complex three-phase models. Due to its simplicity and its close relation to conventional slow-to-start models, this model can shed light on the relation between ‘two-phase’ and three-phase models.

Suggested Citation

  • Tian, Jun-fang & Yuan, Zhen-zhou & Treiber, Martin & Jia, Bin & Zhang, Wen-yi, 2012. "Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3129-3139.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:11:p:3129-3139
    DOI: 10.1016/j.physa.2011.12.067
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    Citations

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    Cited by:

    1. Jiang, Hang & Ma, Yongjian & Jiang, Lin & Chen, Guozhou & Wang, Dongwei, 2018. "Evaluation of the dispersion effect in through movement bicycles at signalized intersection via cellular automata simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 138-147.
    2. Fu, Ding-Jun & Li, Qi-Lang & Jiang, Rui & Wang, Bing-Hong, 2020. "A simple cellular automaton model with dual cruise-control limit in the framework of Kerner’s three-phase traffic theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    3. Zhou, Shirui & Ling, Shuai & Zhu, Chenqiang & Tian, Junfang, 2022. "Cellular automaton model with the multi-anticipative effect to reproduce the empirical findings of Kerner’s three-phase traffic theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    4. Wang, Yan & Peng, Zhongyi & Chen, Qun, 2018. "Simulated interactions of pedestrian crossings and motorized vehicles in residential areas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1046-1060.
    5. Shi, Xiaowei & Li, Xiaopeng, 2021. "Constructing a fundamental diagram for traffic flow with automated vehicles: Methodology and demonstration," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 279-292.
    6. Hu, Xiaojian & Hao, Xiatong & Wang, Han & Su, Ziyi & Zhang, Fang, 2020. "Research on on-street temporary parking effects based on cellular automaton model under the framework of Kerner’s three-phase traffic theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Tian, Junfang & Treiber, Martin & Ma, Shoufeng & Jia, Bin & Zhang, Wenyi, 2015. "Microscopic driving theory with oscillatory congested states: Model and empirical verification," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 138-157.

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