Traffic flow in a spatial network model

  • Michael T. Gastner
Conference paper


A quantity of practical importance in the design of an infrastructure network is the amount of traffic along different parts in the network. Traffic patterns primarily depend on the users’ preference for short paths through the network and spatial constraints for building the necessary connections. Here we study the traffic distribution in a spatial network model which takes both of these considerations into account. Assuming users always travel along the shortest path available, the appropriate measure for traffic flow along the links is a generalization of the usual concept of “edge betweenness”. We find that for networks with a minimal total maintenance cost, a small number of connections must handle a disproportionate amount of traffic. However, if users can travel more directly between different points in the network, the maximum traffic can be greatly reduced.


Short Path Traffic Flow Physical Review Minimum Span Tree User Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Alvarez-Hamelin, José Ignacio, and Nicolas Schabanel, “An internet graph model based on trade-off optimization”, European Physical Journal B 38 (2004), 231–237.ADSCrossRefGoogle Scholar
  2. [2]
    Barrat, Alain, Marc Barthélémy, and Alessandro Vespignani, “The effects of spatial constraints on the evolution of weighted complex networks”, Journal of Statistical Mechanics (2005), P05003.Google Scholar
  3. [3]
    Barthélémy, Marc, “Crossover from scale-free to spatial networks”, Eu-rophysics Letters 63 (2003), 915–921.ADSCrossRefGoogle Scholar
  4. [4]
    Barthélémy, Marc, and Alessandro Flammini, “Optimal traffic networks”, Journal of Statistical Mechanics (2006), L07002.Google Scholar
  5. [5]
    Billheimer, John W., and Paul Gray, “Network design with fixed and variable cost elements”, Transportation Science 7 (1973), 49–74.CrossRefGoogle Scholar
  6. [6]
    Fabrikant, Alex, Elias Koutsoupias, and Christos H. Papadimitriou, “Heuristically optimized trade-offs: A new paradigm for power laws in the internet”, ICALP, vol. 2380 of Lecture Notes in Computer Science, Springer (2002), 110–112.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Flaxman, Abraham D., Alan M. Frieze, and Juan Vera, “A geometric preferential attachment model of networks”, Preprint aflp/Texfiles/NewGeoWeb.pdf (2006).Google Scholar
  8. [8]
    Gastner, Michael T., Spatial Distributions: Density-equalizing map projections, facility location, and two-dimensional networks, PhD thesis University of Michigan, Ann Arbor (2005).Google Scholar
  9. [9]
    Gastner, Michael T., and Mark E. J. Newman, “Shape and efficiency in spatial distribution networks”, Journal of Statistical Mechanics (2006), P01015.Google Scholar
  10. [10]
    Gastner, Michael T., and Mark E. J. Newman, “The spatial structure of networks”, European Physical Journal B 49 (2006), 247–252.ADSGoogle Scholar
  11. [11]
    Girvan, Michelle, and Mark E. J. Newman, “Community structure in social and biological networks”, Proceedings of the National Academy of Sciences in the United States of America 99 (2002), 7821–7826.MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. [12]
    Guimerà, Roger, and Luís A. Nunes Amaral, “Modeling the world-wide airport network”, European Physical Journal B 38 (2004), 381–385.ADSCrossRefGoogle Scholar
  13. [13]
    Kaiser, Marcus, and Claus C. Hilgetag, “Spatial growth of real-world networks”, Physical Review E 69 (2004), 036103.ADSCrossRefGoogle Scholar
  14. [14]
    Los, Marc, and Christian Lardinois, “Combinatorial programming, statistical optimization and the optimal transportation network problem”, Transportation Research-B 16B (1982), 89–124.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Manna, Subhrangshu S., and Parongama Sen, “Modulated scale-free network in Euclidean space”, Physical Review E 66 (2002), 066114.ADSCrossRefGoogle Scholar
  16. [16]
    Newman, Mark E. J., Albert-László Barabási, and Duncan J. Watts eds., The structure and dynamics of networks, Princeton University Press Princeton (2006).zbMATHGoogle Scholar
  17. [17]
    Petermann, Thomas, and Paolo De Los Rios, “Physical realizability of small-world networks”, Physical Review E 73 (2006), 026114.ADSCrossRefGoogle Scholar
  18. [18]
    Rozenfeld, Alejandro F., Reuven Cohen, Daniel ben Avraham, and Shlomo Havlin, “Scale-free networks on lattices”, Physical Review Letters 89 (2002), 218701.ADSCrossRefGoogle Scholar
  19. [19]
    Sen, Parongama, Kinjal Banerjee, and Turbasu Biswas, “Phase transitions in a network with a range-dependent connection probability”, Physical Review E 66 (2002), 037102.ADSCrossRefGoogle Scholar
  20. [20]
    Warren, Christopher R, Leonard M. Sander, and Igor M. Sokolov, “Geography in a scale-free network model”, Physical Review E 66 (2002), 056105.ADSCrossRefGoogle Scholar
  21. [21]
    Xulvi-Brunet, Ramon, and Igor M. Sokolov, “Evolving networks with disadvantaged long-range connections”, Physical Review E 66 (2002), 026118.ADSCrossRefGoogle Scholar
  22. [22]
    Yook, Soon-Hyung, Hawoong Jeong, and Albert-László Barabási, “Modeling the internet’s large-scale topology”, Proceedings of the National Academy of Sciences of the United States of America 99 (2002), 13382–13386.ADSCrossRefGoogle Scholar
  23. [23]
    Youn, Hyejin, Michael T. Gastner, and Hawoong Jeong, “The price of anarchy in transportation networks: efficiency and optimality control”, Preprint physics/0712.1598 (2008).Google Scholar

Copyright information

© Springer 2010

Authors and Affiliations

  • Michael T. Gastner
    • 1
  1. 1.Santa Fe InstituteSanta Fe

Personalised recommendations