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Logistic modeling of the equilibrium speed-density relationship

Author

Listed:
  • Wang, Haizhong
  • Li, Jia
  • Chen, Qian-Yong
  • Ni, Daiheng

Abstract

The fundamental diagram, as the graphical representation of the relationships among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering. Seventy-five years after the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed-density relationship which underlies the fundamental diagram. Observed in these models was a clear path toward two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, this paper presents a family of speed-density models with varying numbers of parameters. All of these models perform satisfactorily and have physically meaningful parameters. In addition, speed variation with traffic density is accounted for; this enables statistical approaches to traffic flow analysis. The results of this paper not only improve our understanding of traffic flow but also provide a sound basis for transportation engineering studies.

Suggested Citation

  • Wang, Haizhong & Li, Jia & Chen, Qian-Yong & Ni, Daiheng, 2011. "Logistic modeling of the equilibrium speed-density relationship," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 554-566, July.
    • Handle: RePEc:eee:transa:v:45:y:2011:i:6:p:554-566
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    References listed on IDEAS

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    1. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
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    Cited by:

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    2. Qu, Xiaobo & Zhang, Jin & Wang, Shuaian, 2017. "On the stochastic fundamental diagram for freeway traffic: Model development, analytical properties, validation, and extensive applications," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 256-271.
    3. Qu, Xiaobo & Wang, Shuaian & Zhang, Jin, 2015. "On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 91-102.
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    5. Zhang, Jin & Qu, Xiaobo & Wang, Shuaian, 2018. "Reproducible generation of experimental data sample for calibrating traffic flow fundamental diagram," Transportation Research Part A: Policy and Practice, Elsevier, vol. 111(C), pages 41-52.
    6. Cheng, Qixiu & Liu, Zhiyuan & Lin, Yuqian & Zhou, Xuesong (Simon), 2021. "An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 246-271.
    7. Guan, Hao & Wang, Hua & Meng, Qiang & Mak, Chin Long, 2023. "Markov chain-based traffic analysis on platooning effect among mixed semi- and fully-autonomous vehicles in a freeway lane," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 176-202.
    8. Niek Baer & Richard J. Boucherie & Jan-Kees C. W. van Ommeren, 2019. "Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic," Transportation Science, INFORMS, vol. 53(2), pages 585-596, March.
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    10. Xingliang Liu & Jian Wang & Tangzhi Liu & Jin Xu, 2021. "Forecasting Spatiotemporal Boundary of Emergency-Event-Based Traffic Congestion in Expressway Network Considering Highway Node Acceptance Capacity," Sustainability, MDPI, vol. 13(21), pages 1-17, November.
    11. Cheng, Qixiu & Lin, Yuqian & Zhou, Xuesong (Simon) & Liu, Zhiyuan, 2024. "Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters," European Journal of Operational Research, Elsevier, vol. 312(1), pages 182-197.

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