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A mathematical theory of traffic hysteresis

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  • Zhang, H. M.

Abstract

This paper presents a mathematical theory for modeling the hysteresis phenomenon observed in traffic flow. It proposes that acceleration, deceleration and equilibrium flow should be distinguished in obtaining speed-concentration and/or occupancy relationships, such that the phase transitions from one phase to another can be correctly identified. The analysis shows that the speed-concentration curves obtained following this approach are hysteresis loops, as predicted by the theory. The paper also gives a discussion of the general properties of the proposed modeling equations and examines the relationship between traffic hysteresis and stop-start waves observed in traffic flow.

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  • Zhang, H. M., 1999. "A mathematical theory of traffic hysteresis," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 1-23, February.
    • Handle: RePEc:eee:transb:v:33:y:1999:i:1:p:1-23
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    Cited by:

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    3. Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
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    7. Ngoduy, D. & Liu, R., 2007. "Multiclass first-order simulation model to explain non-linear traffic phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 667-682.
    8. Zhang, H. M., 2001. "A note on highway capacity," Transportation Research Part B: Methodological, Elsevier, vol. 35(10), pages 929-937, November.
    9. Saboohi, Y. & Farzaneh, H., 2009. "Model for developing an eco-driving strategy of a passenger vehicle based on the least fuel consumption," Applied Energy, Elsevier, vol. 86(10), pages 1925-1932, October.
    10. Mohammadian, Saeed & Zheng, Zuduo & Haque, Md. Mazharul & Bhaskar, Ashish, 2021. "Performance of continuum models for realworld traffic flows: Comprehensive benchmarking," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 132-167.
    11. Wei, Dali & Liu, Hongchao, 2013. "Analysis of asymmetric driving behavior using a self-learning approach," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 1-14.
    12. Blandin, Sébastien & Argote, Juan & Bayen, Alexandre M. & Work, Daniel B., 2013. "Phase transition model of non-stationary traffic flow: Definition, properties and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 31-55.
    13. Laval, Jorge A., 2011. "Hysteresis in traffic flow revisited: An improved measurement method," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 385-391, February.
    14. Geroliminis, Nikolas & Sun, Jie, 2011. "Hysteresis phenomena of a Macroscopic Fundamental Diagram in freeway networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 966-979, November.
    15. Zhang, H.M. & Kim, T., 2005. "A car-following theory for multiphase vehicular traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 39(5), pages 385-399, June.
    16. Cheng, Harry H. & Shaw, Ben & Palen, Joe & Wang, Zhaoqing & Chen, Bo, 2002. "A Field-Deployable Real-Time Laser-Based Non-Intrusive Detection System for Measurement of True Travel Time on the Highway," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3p71d33t, Institute of Transportation Studies, UC Berkeley.
    17. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.
    18. Wu, Ning, 2002. "A new approach for modeling of Fundamental Diagrams," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(10), pages 867-884, December.
    19. Zheng, Shi-Teng & Jiang, Rui & Tian, Jun-Fang & Zhang, H.M. & Li, Zhen-Hua & Gao, Lan-Da & Jia, Bin, 2021. "Experimental study on properties of lightly congested flow," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 1-19.
    20. Cheng, Harry H. & Shaw, Ben & Palen, Joe & Wang, Zhaoqing & Feng, Ping & Nestinger, Stephen & Chen, Bo, 2004. "Development and Field Testing of Laser Photodiode Array-Based Vehicle Detection Systems," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3hs755vj, Institute of Transportation Studies, UC Berkeley.
    21. Chen, Danjue & Laval, Jorge A. & Ahn, Soyoung & Zheng, Zuduo, 2012. "Microscopic traffic hysteresis in traffic oscillations: A behavioral perspective," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1440-1453.
    22. Yibing Wang & Long Wang & Xianghua Yu & Jingqiu Guo, 2023. "Capacity Drop at Freeway Ramp Merges with Its Replication in Macroscopic and Microscopic Traffic Simulations: A Tutorial Report," Sustainability, MDPI, vol. 15(3), pages 1-27, January.
    23. Mattas, K. & Albano, G. & Donà, R. & He, Y. & Ciuffo, B., 2023. "On the Relationship between Traffic Hysteresis and String Stability of Vehicle Platoons," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    24. Chen, Danjue & Ahn, Soyoung & Laval, Jorge & Zheng, Zuduo, 2014. "On the periodicity of traffic oscillations and capacity drop: The role of driver characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 117-136.
    25. Saifuzzaman, Mohammad & Zheng, Zuduo & Haque, Md. Mazharul & Washington, Simon, 2017. "Understanding the mechanism of traffic hysteresis and traffic oscillations through the change in task difficulty level," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 523-538.

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