Networks and Spatial Economics

, Volume 16, Issue 4, pp 997–1018 | Cite as

Population-driven Urban Road Evolution Dynamic Model

  • Fangxia Zhao
  • Jianjun Wu
  • Huijun Sun
  • Ziyou Gao
  • Ronghui Liu


In this paper, we propose a road evolution model by considering the interaction between population distribution and urban road network. In the model, new roads need to be constructed when new zones are built, and existing zones with higher population density have higher probability to connect with new roads. The relative neighborhood graph and a Fermat-Weber location problem are introduced as the connection mechanism to capture the characteristics of road evolution. The simulation experiment is conducted to demonstrate the effects of population on road evolution. Moreover, the topological attributes for the urban road network are evaluated using degree distribution, betweenness centrality, coverage, circuitness and treeness in the experiment. Simulation results show that the distribution of population in the city has a significant influence on the shape of road network, leading to a growing heterogeneous topology.


Road evolution Population distribution Relative neighborhood Fermat-Webber location problem 



This work was partially supported by the National Basic Research Program of China (2012CB725400), NSFC (71271024, 71322102), and the Foundation of State Key Laboratory of Rail Traffic Control and Safety (RCS2015ZZ003).


  1. Alberti M, Waddell P (2000) An integrated urban development and ecological simulation model. Integr Assess 1(3):215–227CrossRefGoogle Scholar
  2. Barthélemy M (2003) Betweenness centrality in large complex networks. Eur Phys J B 38(2):163–168CrossRefGoogle Scholar
  3. Barthélemy M, Flammini A (2008) Modeling Urban Street Patterns. Phys Rev Lett 100(13):138702CrossRefGoogle Scholar
  4. Barthélemy M, Flammini A (2009) Co-evolution of density and topology in a simple model of city formation. Netw Spat Econ 9(3):401–425CrossRefGoogle Scholar
  5. Boyce DE (1984) Urban transportation network-equilibrium and design models: recent achievements and future prospects. Env Plan A 16(1):1445–1474CrossRefGoogle Scholar
  6. Chen A, Zhou Z, Chootinan P, Ryu S, Yang C, Wong SC (2011) Transportation network design problem under uncertainty: a review and new developments. Transp Rev 31(6):743–768CrossRefGoogle Scholar
  7. Courtat T, Gloaguen C (2011) Mathematics and morphogenesis of the cities: a geometrical approach. Phys Rev E 83(3):036106CrossRefGoogle Scholar
  8. Ding Y, Lou Y (1998) Application of fractal theory in the evaluation transportation network. J Shanghai Marit Univ 19(4):7–12Google Scholar
  9. Dorogovtsev SN, Mendes JFF, Samukhin AN (2001) Size-dependent degree distribution of a scale-free growing network. Phys Rev E 63(6):062101CrossRefGoogle Scholar
  10. Ducruet C, Beauguitte L (2014) Spatial science and network science: review and outcomes of a complex relationship. Netw Spat Econ 10(3-4):297–316CrossRefGoogle Scholar
  11. Erath A, Löchl M, Axhausen KW (2009) Graph-theoretical analysis of the swiss road and railway networks over time. Netw Spat Econ 9(3):379–400CrossRefGoogle Scholar
  12. Facchinei F, Pang JS (2003) Finite-dimensional variational inequalities and complementarity problems, vol I. Springer, New YorkGoogle Scholar
  13. Figueiredo L, Machado JAT (2007) Simulation and dynamics of freeway traffic. Nonlinear Dynam 49(4):567–577CrossRefGoogle Scholar
  14. Freeman LC (1997) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41CrossRefGoogle Scholar
  15. Friesz TL (1985) Transportation network equilibrium, design and aggregation: key developments and research opportunities. Transp Res A 19(5-6):413–427CrossRefGoogle Scholar
  16. Haggett P, Chorley R (1969) Network analysis in geography. Edward Arnold, LondonGoogle Scholar
  17. Handy S, Cao X, Mokhtarian P (2005) Correlation or causality between the built environment and travel behavior? Evidence from Northern California. Transp Res D 10(6):427–444CrossRefGoogle Scholar
  18. Hwang FK, Richards DS (1992) Steiner tree problems. Networks 22(10):55–89CrossRefGoogle Scholar
  19. Jaromczyk JW, Toussaint GT (1992) Relative neighborhood graphs and their relatives. IEEE Proc 80(9):1502–1517CrossRefGoogle Scholar
  20. Karger DR, Klein PN, Tarjan RE (1995) A randomized linear-time algorithm to find minimum spanning trees. J ACM 42(2):321–328CrossRefGoogle Scholar
  21. Levinson D (2008) Density and dispersion: the co-development of land use and rail in London. J Econ Geogr 8(1):55–77CrossRefGoogle Scholar
  22. Levinson D, Xie F, Zhu S (2007) The co-evolution of land use and road networks. Proc 17th Int Sympo Transp Traffic Theory 111-126:839–859Google Scholar
  23. Levinson D, Yerra B (2006) Self-organization of transportation networks. Transp Sci 40(2):179–188CrossRefGoogle Scholar
  24. Li TF, Wu JJ, Sun HJ, Gao ZY (2015) Integrated co-evolution model of land use and traffic network design. Netw Spat Econ. doi: 10.1007/s11067-015-9289-3 Google Scholar
  25. Liu HX,Wang DZW (2015) Global optimization method for network design problem with stochastic user equilibrium. Transp Res B 72:20–39Google Scholar
  26. Magnanti TL, Wong RT (1984) Network design and transportation planning: models and algorithms. Transp Sci 18(1):1–55CrossRefGoogle Scholar
  27. Maheshwari P, Khaddar R, Kachroo P, Paz A (2014) Dynamic modeling of performance indices for planning of sustainable transportation systems. Netw Spat Econ. doi: 10.1007/s11067-014-9238-6 Google Scholar
  28. Migdalas A (1995) Bilevel programming in traffic planning: models, methods and challenge. J Globl Optim 7(4):381–405CrossRefGoogle Scholar
  29. Schweitzer F, Ebeling W, Rose H, Weiss O (1997) Optimization of road networks using evolutionary strategies. Evolu Comput 5(4):419–438CrossRefGoogle Scholar
  30. Supowit KJ (1983) The relative neighborhood graph with an application to minimum spanning trees. J ACM 30(3):428–448CrossRefGoogle Scholar
  31. Szeto WY, Jiang Y, Wang DZW, Sumalee A (2013) A sustainable road network design problem with land use transportation interaction over time. Netw Spat Econ. doi: 10.1007/s11067-013-9191-9 Google Scholar
  32. Toussaint GT (1980) The relative neighbourhood graph of a finite planar set. Pattern Recogn 12(4):261–268CrossRefGoogle Scholar
  33. Vardi Y, Zhang CH (2001) A modified Weiszfeld algorithm for the Fermat-Weber location problem. Mathem Program 90(3):559–566CrossRefGoogle Scholar
  34. Wang DZW, Liu HX, Szeto WY (2015) A novel discrete design problem formulation and its global optimization solution algorithm. Transp Res E 79:213–230Google Scholar
  35. Weiszfeld E (1937) Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Math J 43:355–386Google Scholar
  36. Wu JJ, Xu MT, Gao ZY (2013) Coevolution dynamics model of road surface and urban traffic Structure. Nolinear Dynam 73(3):1327–1334CrossRefGoogle Scholar
  37. Xie F, Levinson D (2007) Measuring the structure of road networks. Geogr Anal 39(3):336–356CrossRefGoogle Scholar
  38. Xie F, Levinson D (2009a) Modeling the growth of transportation networks: a comprehensive review. Netw Spat Econ 9(3):291–307CrossRefGoogle Scholar
  39. Xie F, Levinson D (2009b) Topological evolution of surface transportation networks. Comput Environ Urban Syst 33(3):211–223CrossRefGoogle Scholar
  40. Xie F, Levinson D (2011) Evolving transportation networks. SpringerGoogle Scholar
  41. Yamins D, Rasmussen S, Fogel D (2003) Growing urban roads. Netw Spat Econ 3(1):69–85CrossRefGoogle Scholar
  42. Yang H, Huang HJ (1998) Principle of marginal-cost pricing: How does it work in a general road network? Transp Res A 32(1):45–54Google Scholar
  43. Yang H, Bell MGH (1998) Models and algorithms for road network design: a review and some new developments. Transp Rev 18(3):257–278CrossRefGoogle Scholar
  44. Zanjirani FR, Miandoabchi E, Szeto WY, Rashidi H (2013) A review of urban transportation network design problems. Eur J Oper Res 229(2):281–302CrossRefGoogle Scholar
  45. Zhang WY, Guan W, Ma JH, Tian JF (2015) A nonlinear pairwise swapping dynamics to model to selfish rerouting evolutionary game. Netw Spat Econ. doi: 10.1007/s11067-014-9281-3 Google Scholar
  46. Zhao FX, Wu JJ, Sun HJ, Gao ZY (2015) Role of human moving on city spatial evolution. Phys A 419:642–650CrossRefGoogle Scholar
  47. Zhou T, Yan G, Wang BH (2005) Maximal planar networks with large clustering coefficient and power-law degree distribution. Phys Rev E 71(4):046–141CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Fangxia Zhao
    • 1
  • Jianjun Wu
    • 1
  • Huijun Sun
    • 2
  • Ziyou Gao
    • 2
  • Ronghui Liu
    • 3
  1. 1.State Key Laboratory of Rail Traffic Control and SafetyBeijing Jiaotong UniversityBeijingChina
  2. 2.MOE Key Laboratory for Urban Transportation Complex Systems Theory and TechnologyBeijing Jiaotong UniversityBeijingChina
  3. 3.Institute for Transport StudiesUniversity of LeedsLeedsUK

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