Crowded urban traffic: co-evolution among land development, population, roads and vehicle ownership

  • Rong Li
  • Jianjun WuEmail author
  • Hao Liu
  • Ziyou Gao
  • Huijun Sun
  • Rui Ding
  • Tieqiao Tang
Original Paper


Crowded urban traffic is one of mankind’s greatest past, present, and future challenges, attracting interests from urban planning, urban geography, urban economics and other related disciplines. Although these fields provide some insight into the problem, our understanding of the basic laws determining urban traffic systems’ evolutionary trajectory remains limited given that we do not fully understand the general co-evolutionary mechanisms underlying their complex dynamics. Therefore, a better understanding of the dynamics of urban traffic systems is necessary. The evolution of urban traffic systems appears to be accessible through mathematical descriptions, which involves land development, population, road and motor vehicle subsystems. In this paper, a four-level co-evolution dynamics model is developed to capture the growth trajectory of urban traffic systems. Our aim is to determine the driving force of urban traffic growth, the interactions among the studied subsystems, and whether the “disease” of urban crowding can be effectively predicted. Stability analysis indicates that this model is convergent. Taking two typical Chinese cities (Beijing and Shenzhen) as case studies, it is found that this model can be used to capture the observed co-evolution characteristics and to predict the future development of crowded urban traffic, thus benefitting all cities’ planning and control processes.


Crowded urban traffic Co-evolution dynamics model Traffic carrying capacity 



This work is supported by the National Nature Science Foundation of China (71890972/71890970, 71525002,71621001,71771018), the Fundamental Research Funds for the Central Universities (2017YJS117) and the Science and Technology Project of the Jiangxi Department of Education (GJJ161177).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Barthelemy, M., Bordin, P., Berestycki, H., Gribaudi, M.: Self-organization versus top-down planning in the evolution of a city. Sci. Rep. 3, 2153 (2013)CrossRefGoogle Scholar
  2. 2.
    Barthélemy, M., Flammini, A.: Optimal traffic networks. J. Stat. Mech. 50, 561–593 (2006)Google Scholar
  3. 3.
    Barthélemy, M., Flammini, A.: Co-evolution of density and topology in a simple model of city formation. Netw. Spat. Econ. 9, 401–425 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Batty, M.: The size scale and shape of cities. Science 319, 769–771 (2008)CrossRefGoogle Scholar
  5. 5.
    Cohen, J.E.: Population growth and earth’s human carrying capacity. Science 269, 341–346 (1995)CrossRefGoogle Scholar
  6. 6.
    Colak, S., Lima, A., González, M.C.: Understanding congested travel in urban areas. Nat. Commun. 7, 10793 (2016)CrossRefGoogle Scholar
  7. 7.
    Cullinane, S.: The relationship between car ownership and public transport provision: a case study of Hong Kong. Transp. Policy. 9, 29–39 (2002)CrossRefGoogle Scholar
  8. 8.
    Dendrinos, D.S.: Land development and amenities: a predator–prey interaction. Ann. Reg. Sci. 34, 279–292 (2000)CrossRefGoogle Scholar
  9. 9.
    Dendrinos, D.S., Mullally, H.: Evolutionary patterns of urban populations. Geogr. Anal. 13, 328–344 (1981)CrossRefGoogle Scholar
  10. 10.
    Dendrinos, D.S., Mullally, H.: Urban Evolution: Studies in the Mathematical Ecology of Cities. Oxford University Press, New York (1985)Google Scholar
  11. 11.
    Ding, R., Ujang, N., Hamid, H.B., Wu, J.J.: Complex network theory applied to the growth of Kuala Lumpur’s public urban rail transit network. PLoS ONE 10, e0139961 (2015)CrossRefGoogle Scholar
  12. 12.
    Ding, R., Ujang, N., Hamid, H.B., Manan, M.S.A., Li, R., Wu, J.J.: Heuristic urban transportation network design method, a multilayer coevolution approach. Phys. A Stat. Mech. Appl. 479, 71–83 (2017)CrossRefGoogle Scholar
  13. 13.
    Ding, R., Ujang, N., Hamid, H.B., Manan, M.S.A., He, Y., Li, R., Wu, J.J.: Detecting the urban traffic network structure dynamics through the growth and analysis of multi-layer networks. Phys. A Stat. Mech. Appl. 503, 800–817 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Dissanayke, D., Morkawa, T.: Investigating household vehicle ownership, mode choice and trip sharing decisions using a combined revealed/stated preference Nested Logit Model: case study in Bangkok Metropolitan Region. J. Transp. Geogr. 18, 402–410 (2010)CrossRefGoogle Scholar
  15. 15.
    Gao, G., Sun, H.J., Wu, J.J.: Activity-based trip chaining behavior analysis in the network under the parking fee scheme. Transportation (2017).
  16. 16.
    Levinson, D., Xie, F., Zhu, S.J.: The co-evolution of land use and road networks. Transp. Traffic Theory 17, 839–859 (2007)Google Scholar
  17. 17.
    Li, L., Sato, Y., Zhu, H.: Simulating spatial urban expansion based on a physical process. Landsc. Urban Plan. 64, 67–76 (2003)CrossRefGoogle Scholar
  18. 18.
    Li, T.F., Sun, H.J., Wu, J.J., Ge, Y.E.: Optimal toll of new highway in the equilibrium framework of heterogeneous households’ residential location choice. Transp. Res. A Policy Pract. 105, 123–137 (2017)CrossRefGoogle Scholar
  19. 19.
    Li, T.F., Wu, J.J., Sun, H.J., Gao, Z.Y.: Integrated co-evolution model of land use and traffic network design. Netw. Spat. Econ. 16, 579–603 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Long, Y., Han, H., Lai, S.K., Mao, Q.: Urban growth boundaries of the Beijing Metropolitan Area: comparison of simulation and artwork. Cities 31, 337–348 (2013)CrossRefGoogle Scholar
  21. 21.
    Masucci, A.P., Arcaute, E., Wang, J., Hatna, E., Stanilov, K., Batty, M.: Logistic growth and ergodic properties of urban forms (2015). arXiv:1504.07380
  22. 22.
    Matas, A., Raymond, J.: Changes on the structure of car ownership in Spain. Transp. Res. A Policy Pract. 42, 187–202 (2008)CrossRefGoogle Scholar
  23. 23.
    Meyer, P.S., Ausubel, J.H.: Carrying capacity: a model with logistically varying limits. Technol. Forecast. Soc. Change 61, 209–214 (1999)CrossRefGoogle Scholar
  24. 24.
    Murillo, D., Anderies, J.M., Castillo-Chavez, C.: Towards a theoretical model of urban growth. (2017)
  25. 25.
    Nolan, A.: A dynamic analysis of household car ownership. Transp. Res. A Policy Pract. 44, 446–455 (2010)CrossRefGoogle Scholar
  26. 26.
    Potoglou, D., Kanaroglou, P.S.: Modelling car ownership in urban areas: a case study of Hamilton, Canada. J. Transp. Geogr. 16, 42–54 (2008)CrossRefGoogle Scholar
  27. 27.
    Seidl, I., Tisdell, C.A.: Carrying capacity reconsidered: from Malthus’ population theory to cultural carrying capacity. Ecol. Econ. 31, 395–408 (1999)CrossRefGoogle Scholar
  28. 28.
    Strano, E., Nicosia, V., Latora, V., Porta, S., Barthélemy, M.: Elementary processes governing the evolution of road networks. Sci. Rep. 2, 296 (2012)CrossRefGoogle Scholar
  29. 29.
    Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, pp. 141–142. Perseus Books Publishing, Cambridge (1994)Google Scholar
  30. 30.
    Verhulst, P.F.: Notice sur la loi que la population poursuit dans son accroissement (PDF). Correspondance mathématique et physique 10, 113–121 (1838). Retrieved 3 Dec 2014Google Scholar
  31. 31.
    Wang, G.X., Zhou, Z.M., Zhu, S.M., Wang, S.S.: Ordinary Differential Equation, pp. 255–258. Higher Education Press, Beijing (2006). (in Chinese)Google Scholar
  32. 32.
    Wang, H., Yang, X., Wu, J.J, Sun, H.J., Gao, Z.Y.: Metro timetable optimization for minimizing carbon emission and passenger time: a bi-objective integer programming approach. IET Intell Trans Syst.
  33. 33.
    Witten, T.A., Sander, L.M.: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1981 (2010)CrossRefGoogle Scholar
  34. 34.
    Wu, J.J., Xu, M., Gao, Z.Y.: Coevolution dynamics model of road surface and urban traffic structure. Nonlinear Dyn. 73, 1327–1334 (2013)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Wu, J.J., Xu, M., Gao, Z.Y.: Modeling the coevolution of road expansion and urban traffic growth. Adv. Complex Syst. 17, 1–18 (2014)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Wu, J.J., Li, R., Ding, R., Li, T.F., Sun, H.J.: City expansion model based on population diffusion and road growth. Appl. Math. Model. 43, 1–14 (2017)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Xie, F., Levinson, D.: Modeling the growth of transportation networks: a comprehensive review. Netw. Spat. Econ. 9, 291–307 (2009)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Xu, M., Ye, Z., Shan, X.: Modeling, analysis, and simulation of the co-development of road networks and vehicle ownership. Phys. A Stat. Mech. Appl. 442, 417–428 (2016)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Yamins, D., Rasmussen, S., Fogel, D.: Growing urban roads. Netw. Spat. Econ. 3, 69–85 (2003)CrossRefGoogle Scholar
  40. 40.
    Yang, L.Y., Shao, C.F., Liu, Z.L., Nie, W.: A study on mechanism of interactions between urban transportation and land-use. Urban Trans China. 4(4), 21–25 (2006)Google Scholar
  41. 41.
    Yang, S.P., Wu, J.J., Yang, X., Sun, H.J., Gao, Z.Y.: Energyefficient timetable and speed profile optimization with multi-phase speed limits: theoretical analysis and application. Appl. Math. Model. 56, 32–50 (2018)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Zhao, F.X., Sun, H.J., Wu, J.J., Gao, Z.Y., Liu, R.H.: Analysis of road network pattern considering population distribution and central business district. PLoS ONE. 11(3), e0151676 (2016). CrossRefGoogle Scholar
  43. 43.
    Zhao, F.X., Wu, J.J., Sun, H.J., Gao, Z.Y., Liu, R.H.: Population-driven urban road evolution dynamic model. Netw. Spat. Econ. 16, 997–1018 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Rail Traffic Control and SafetyBeijing Jiaotong UniversityBeijingChina
  2. 2.Department of Traffic ManagementJiangxi Police InstituteNanchangChina
  3. 3.Beijing Transportation Information CenterBeijingChina
  4. 4.Faculty of Design and ArchitectureUniversity Putra MalaysiaSerdangMalaysia
  5. 5.School of Transportation Science and Engineering, Beijing Key Laboratory for Cooperative Vehicle Infrastructure Systems and Safety ControlBeihang UniversityBeijingChina

Personalised recommendations