To Investigate the Hidden Gap between Traffic Flow Fundamental Diagrams and the Derived Microscopic Car Following Models: A Theoretical Analysis

  • Yang YuEmail author
  • Jie Zhu
  • Xiaobo Qu
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 185)


Traffic flow fundamental diagram, or simply speeddensity relationship and/or flowdensity relationship, is the basis of traffic flow theories and road performance studies since it depicts the mathematical relationship among three traffic flow fundamental parametersdensity, speed, and traffic flow. In this paper, through mathematical analyses and simulations, we find that for all existing fundamental diagram models, their derived microscopic car following models do not perform well and cannot reproduce the status of the stable flow described by the corresponding fundamental diagrams. The results indicate that there seems to exist a hidden gap between existing traffic flow fundamental diagrams and the corresponding microscopic car following models. We further discuss about the fundamental causes behind such gap and propose a simple yet incomplete solution at the end of this paper.


  1. 1.
    Greenshields, B., Channing, W., Miller, H.: A study of traffic capacity. In: Highway Research Board Proceedings, 1935, vol. 1935. National Research Council (USA), Highway Research BoardGoogle Scholar
  2. 2.
    Greenberg, H.: An analysis of traffic flow. Oper. Res. 7(1), 79–85 (1959)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Wu, N.: A new approach for modeling of fundamental diagrams. Transp. Res. Part A: Policy Pract. 36(10), 867–884 (2002)Google Scholar
  4. 4.
    Underwood, R.T.: Speed, Volume, and Density Relationship: Quality and Theory of Traffic Flow, (1961), pp. 141–188. Yale Bureau of Highway Traffic, New Haven, Connecticut (2008)Google Scholar
  5. 5.
    Wang, H., Li, J., Chen, Q.-Y., Ni, D.: Logistic modeling of the equilibrium speed–density relationship. Transp. Res. Part A: Policy Pract. 45(6), 554–566 (2011)Google Scholar
  6. 6.
    Wang, H., Ni, D., Chen, Q.Y., Li, J.: Stochastic modeling of the equilibrium speed–density relationship. J. Adv. Transp. 47(1), 126–150 (2013)CrossRefGoogle Scholar
  7. 7.
    Qu, X., Wang, S., Zhang, J.: On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models. Transp. Res. Part B: Methodol. 73, 91–102 (2015)CrossRefGoogle Scholar
  8. 8.
    Qu, X., Zhang, J., Wang, S.: On the stochastic fundamental diagram for freeway traffic: model development, analytical properties, validation, and extensive applications. Transp. Res. Part B: Methodol. 104, 256–271 (2017)CrossRefGoogle Scholar
  9. 9.
    Gipps, P.G.: A behavioural car-following model for computer simulation. Transp. Res. Part B: Methodol. 15(2), 105–111 (1981)CrossRefGoogle Scholar
  10. 10.
    Bando, M., Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51(2), 1035 (1995)CrossRefGoogle Scholar
  11. 11.
    Treiber, M., Hennecke, A., Helbing, D.: Congested traffic states in empirical observations and microscopic simulations. Phy. Rev. E. 62(2), 1805–1824 (2000). Available:
  12. 12.
    Jiang, R., Wu, Q., Zhu, Z.: Full velocity difference model for a car-following theory. Phys. Rev. E 64(1), 017101 (2001)CrossRefGoogle Scholar
  13. 13.
    Panwai, S., Dia, H.: Neural agent car-following models. IEEE Trans. Intell. Transp. Syst. 8(1), 60–70 (2007)CrossRefGoogle Scholar
  14. 14.
    Zhou, M., Qu, X., Li, X.: A recurrent neural network based microscopic car following model to predict traffic oscillation. Transp. Res. Part C: Emerg. Technol 84, 245–264 (2017)CrossRefGoogle Scholar
  15. 15.
    Xu, C., et al.: Potential risk and its influencing factors for separated bicycle paths. Accid. Anal. Prev. 87, 59–67 (2016)CrossRefGoogle Scholar
  16. 16.
    Qu, X., Yu, Y., Zhou, M., Lin, C.-T., Wang, X.: Jointly dampening traffic oscillations and improving energy consumption with electric, connected and automated vehicles: A reinforcement learning based approach. Appl. Energy 257, 114030 (2020)CrossRefGoogle Scholar
  17. 17.
    He, Z., Zheng, L., Guan, W.: A simple nonparametric car-following model driven by field data. Transp. Res. Part B: Methodol. 80, 185–201 (2015)CrossRefGoogle Scholar
  18. 18.
    Chakroborty, P., Kikuchi, S.: Evaluation of the general motors based car-following models and a proposed fuzzy inference model. Transp. Res. Part C: Emerg. Technol. 7(4), 209–235 (1999)CrossRefGoogle Scholar
  19. 19.
    Zhang, J., Qu, X., Wang, S.: Reproducible generation of experimental data sample for calibrating traffic flow fundamental diagram. Transp. Res. Part A: Policy Pract. 111, 41–52 (2018)Google Scholar
  20. 20.
    Helbing, D., Tilch, B.: Generalized force model of traffic dynamics. Phys. Rev. E 58(1), 133 (1998)CrossRefGoogle Scholar
  21. 21.
    Jin, S., Wang, D., Tao, P., Li, P.: Non-lane-based full velocity difference car following model. Phy. A 389(21), 4654–4662 (2010)CrossRefGoogle Scholar
  22. 22.
    Yu, Y., Jiang, R., Qu, X.: A modified full velocity difference model with acceleration and deceleration confinement: Calibrations, validations, and scenario analyses. IEEE Intell. Transp. Syst. Maga. (2019)Google Scholar
  23. 23.
    Kesting, A., Treiber, M., Helbing, D.: Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity. Philos. Trans. Roy. Soc. London A: Math. Phy. Eng. Sci. 368(1928), 4585–4605 (2010)CrossRefGoogle Scholar
  24. 24.
    Zhou, M., Qu, X., Jin, S.: On the impact of cooperative autonomous vehicles in improving freeway merging: a modified intelligent driver model-based approach. IEEE Trans. Intell. Transp. Syst. 18(6), 1422–1428 (2017)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Civil and Environmental EngineeringUniversity of Technology SydneySydneyAustralia
  2. 2.Department of Architecture and Civil EngineeringChalmers University of TechnologyGothenburgSweden

Personalised recommendations