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A Boltzmann-Like Approach for Traffic Flow

Author

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  • I. Prigogine

    (The University Libre of Brussels, Brussels, Belgium)

  • F. C. Andrews

    (The University of California, Berkeley, California)

Abstract

The approach to the traffic-flow problem based on an integral differential equation of the Boltzmann type which has been considered by one of us (I P ) in a recent paper is further developed. The possibility of passing is explicitly introduced into the equation for the velocity distribution function. As in the previous paper, it is shown that at sufficiently high concentration a collective flow process must take place. In order to study more specifically the effects of one car on another, we define reduced n -car distribution functions giving the probability of finding a cluster of n cars all having the same velocity. We derive an equation for the evolution of this distribution function. Study of it yields some information as to the way traffic changes from relatively free flow to completely hindered, “condensed” flow.

Suggested Citation

  • I. Prigogine & F. C. Andrews, 1960. "A Boltzmann-Like Approach for Traffic Flow," Operations Research, INFORMS, vol. 8(6), pages 789-797, December.
    • Handle: RePEc:inm:oropre:v:8:y:1960:i:6:p:789-797
    DOI: 10.1287/opre.8.6.789
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    Cited by:

    1. Minh Sang Pham Do & Ketoma Vix Kemanji & Man Dinh Vinh Nguyen & Tuan Anh Vu & Gerrit Meixner, 2023. "The Action Point Angle of Sight: A Traffic Generation Method for Driving Simulation, as a Small Step to Safe, Sustainable and Smart Cities," Sustainability, MDPI, vol. 15(12), pages 1-27, June.
    2. Klawtanong, Manit & Limkumnerd, Surachate, 2020. "Dissipation of traffic congestion using autonomous-based car-following model with modified optimal velocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
    4. Siqueira, Adriano F. & Peixoto, Carlos J.T. & Wu, Chen & Qian, Wei-Liang, 2016. "Effect of stochastic transition in the fundamental diagram of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 1-13.
    5. Zhu, Chenqiang & Zhong, Shiquan & Li, Guangyu & Ma, Shoufeng, 2017. "New control strategy for the lattice hydrodynamic model of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 445-453.
    6. Wu, Jinchao & Chen, Bokui & Zhang, Kai & Zhou, Jun & Miao, Lixin, 2018. "Ant pheromone route guidance strategy in intelligent transportation systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 591-603.
    7. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    8. Petrosky, T. & Prigogine, I., 1991. "Alternative formulation of classical and quantum dynamics for non-integrable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 146-209.
    9. Petrosky, Tomio Y. & Prigogine, Ilya, 1988. "Poincaré's theorem and unitary transformations for classical and quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(3), pages 439-460.
    10. Maiti, Nandan & Laval, Jorge A. & Chilukuri, Bhargava Rama, 2024. "Universality of area occupancy-based fundamental diagrams in mixed traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    11. André de Palma, 2003. "In Memoriam: Ilya Prigogine (1917–2003)," Transportation Science, INFORMS, vol. 37(3), pages 255-256, August.
    12. Jabari, Saif Eddin, 2016. "Node modeling for congested urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 229-249.
    13. Kaffash, Sepideh & Nguyen, An Truong & Zhu, Joe, 2021. "Big data algorithms and applications in intelligent transportation system: A review and bibliometric analysis," International Journal of Production Economics, Elsevier, vol. 231(C).
    14. 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.
    15. Kang, Chengjun & Qian, Yongsheng & Zeng, Junwei & Wei, Xuting & Zhang, Futao, 2024. "Analysis of stability, energy consumption and CO2 emissions in novel discrete-time car-following model with time delay under V2V environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    16. Paul Nelson & Bryan Raney, 1999. "Objectives and Benchmarks for Kinetic Theories of Vehicular Traffic," Transportation Science, INFORMS, vol. 33(3), pages 298-314, August.
    17. Mendes, G.A. & da Silva, L.R. & Herrmann, H.J., 2012. "Traffic gridlock on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 362-370.
    18. Qian, Wei-Liang & F. Siqueira, Adriano & F. Machado, Romuel & Lin, Kai & Grant, Ted W., 2017. "Dynamical capacity drop in a nonlinear stochastic traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 328-339.

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