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There is something more fundamental than fundamental diagram

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  • Ni, Daiheng

Abstract

Revealing the inherent relationships among traffic flow characteristics, fundamental diagram has long been regarded as one of the pillars of traffic flow theory since Greenshields seminal work. When it is combined with the law of (mass/vehicle) conservation, dynamic modelling of traffic flow at the macroscopic level such as LWR and others have thrived. This paper shows that fundamental diagram is only a shadow of something more fundamental, i.e., phase diagram, which is originated from first principles of physics. At the microscopic level, traffic flow can be analyzed by examining the relative motion of two vehicles in car following. When the coordinate system is fixed on the leading vehicle, the Hamiltonian of this system can be defined as the total energy of the system. Conservation of total energy is established by incorporating physical entities (vehicles) and non-physical entities (drivers), the latter of which is enabled by the field theory of traffic flow. Consequently, the Hamilton's equations stipulate a vector field that constitutes the phase diagram of the system which, in turn, specifies Hamiltonian flow swirling around some equilibrium points. When focusing on the equilibrium points, the phase diagram reduces to the fundamental diagram, during which process much information is lost. Consequently, the lost information obscures the origin of the equilibrium points and further the fundamental diagram. This research roots traffic flow theory in first principles of physics and offers an example to address the dynamics of similar systems that involve human intelligence.

Suggested Citation

  • Ni, Daiheng, 2025. "There is something more fundamental than fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 195(C).
  • Handle: RePEc:eee:transb:v:195:y:2025:i:c:s0191261525000554
    DOI: 10.1016/j.trb.2025.103206
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    1. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    2. Jin, Wen-Long & Laval, Jorge, 2018. "Bounded acceleration traffic flow models: A unified approach," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 1-18.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. Tilg, Gabriel & Ambühl, Lukas & Batista, Sergio & Menendez, Monica & Busch, Fritz, 2021. "On the application of variational theory to urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 435-456.
    5. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    6. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
    7. Laval, Jorge A. & Leclercq, Ludovic, 2008. "Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 511-522, July.
    8. Mazaré, Pierre-Emmanuel & Dehwah, Ahmad H. & Claudel, Christian G. & Bayen, Alexandre M., 2011. "Analytical and grid-free solutions to the Lighthill–Whitham–Richards traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1727-1748.
    9. Zhang, H. M., 1999. "A mathematical theory of traffic hysteresis," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 1-23, February.
    10. Daganzo, Carlos F., 2002. "A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 131-158, February.
    11. Leich, Andreas & Nippold, Ronald & Schadschneider, Andreas & Wagner, Peter, 2024. "Physical models of traffic safety at crossing streams," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    12. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.
    13. Robert E. Chandler & Robert Herman & Elliott W. Montroll, 1958. "Traffic Dynamics: Studies in Car Following," Operations Research, INFORMS, vol. 6(2), pages 165-184, April.
    14. Laval, Jorge A. & Leclercq, Ludovic, 2013. "The Hamilton–Jacobi partial differential equation and the three representations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 17-30.
    15. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    16. I. Prigogine & F. C. Andrews, 1960. "A Boltzmann-Like Approach for Traffic Flow," Operations Research, INFORMS, vol. 8(6), pages 789-797, December.
    17. Schadschneider, Andreas, 2000. "Statistical physics of traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 101-120.
    18. Lily Elefteriadou, 2014. "An Introduction to Traffic Flow Theory," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-8435-6, April.
    19. Newell, G. F., 2002. "A simplified car-following theory: a lower order model," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 195-205, March.
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