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Particle Hopping Models and Traffic Flow Theory

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  • Kai Nagel

Abstract

This paper shows how particle hopping models fit into the context of traffic flow theory, that is, it shows connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equation, and particle hopping models. In some cases, these connections are exact and have long been established, but have never been viewed in the context of traffic theory. In other cases, critical behavior of traffic jam clusters can be compared to instabilities in the partial differential equations. Finally, it is shown how all this leads to a consistent picture of traffic jam dynamics.---In consequence, this paper starts building a foundation of a comprehensive dynamic traffic theory, where strengths and weaknesses of different models (fluid-dynamical, car- following, particle hopping) can be compared, and thus allowing to systematically choose the appropriate model for a given question.

Suggested Citation

  • Kai Nagel, 1996. "Particle Hopping Models and Traffic Flow Theory," Working Papers 96-04-015, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:96-04-015
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    Citations

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    Cited by:

    1. Kelly, Terence, 1997. "Driver strategy and traffic system performance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 407-416.
    2. Bhatia, Nikhil & Gupta, Arvind Kumar, 2023. "Role of site-wise dynamic defects in a resource-constrained exclusion process," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Chengbin Peng & Xiaogang Jin & Ka-Chun Wong & Meixia Shi & Pietro Liò, 2012. "Collective Human Mobility Pattern from Taxi Trips in Urban Area," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-8, April.
    4. Zheng, Liang & Jin, Peter J. & Huang, Helai, 2015. "An anisotropic continuum model considering bi-directional information impact," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 36-57.
    5. 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.
    6. Simão, Ricardo, 2021. "Evolution of behaviors in heterogeneous traffic models as driven annealed disorders and its relation to the n-vector model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Zheng, Zuduo, 2014. "Recent developments and research needs in modeling lane changing," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 16-32.
    8. Kok Mun Ng & Mamun Bin Ibne Reaz, 2016. "Platoon Interactions and Real-World Traffic Simulation and Validation Based on the LWR-IM," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-17, January.
    9. Kai Nagel & Peter Wagner & Richard Woesler, 2003. "Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling," Operations Research, INFORMS, vol. 51(5), pages 681-710, October.
    10. Daganzo, Carlos F., 2006. "In traffic flow, cellular automata = kinematic waves," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 396-403, June.
    11. Mu, Rui & Yamamoto, Toshiyuki, 2019. "Analysis of traffic flow with micro-cars with respect to safety and environmental impact," Transportation Research Part A: Policy and Practice, Elsevier, vol. 124(C), pages 217-241.
    12. Salcido, Alejandro & Hernández-Zapata, Ernesto & Carreón-Sierra, Susana, 2018. "Exact results of 1D traffic cellular automata: The low-density behavior of the Fukui–Ishibashi model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 276-287.
    13. Chen, Qun & Wang, Yan, 2015. "Cellular automata (CA) simulation of the interaction of vehicle flows and pedestrian crossings on urban low-grade uncontrolled roads," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 43-57.
    14. X Chen & F B Zhan, 2008. "Agent-based modelling and simulation of urban evacuation: relative effectiveness of simultaneous and staged evacuation strategies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 25-33, January.
    15. 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.
    16. Silver, Grant & Akbarzadeh, Meisam & Estrada, Ernesto, 2018. "Tuned communicability metrics in networks. The case of alternative routes for urban traffic," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 402-413.
    17. Paul Nelson, 2006. "On Driver Anticipation, Two-Regime Flow, Fundamental Diagrams, and Kinematic-Wave Theory," Transportation Science, INFORMS, vol. 40(2), pages 165-178, May.
    18. Blue, Victor J. & Adler, Jeffrey L., 2001. "Cellular automata microsimulation for modeling bi-directional pedestrian walkways," Transportation Research Part B: Methodological, Elsevier, vol. 35(3), pages 293-312, March.

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