The European Physical Journal B

, Volume 38, Issue 2, pp 245–252 | Cite as

Internet’s critical path horizon

  • S. Valverde
  • R. V. SoléEmail author


Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user’s behavior coupled to the network dynamics and it effects should be minimized by choosing appropriate routing strategies. But what are the requirements of routing depth in order to optimize the traffic flow? In this paper we analyse the behavior of Internet traffic with a topologically realistic spatial structure as described in a previous study [S.-H. Yook et al. , Proc. Natl Acad. Sci. USA 99, 13382 (2002)]. The model involves self-regulation of packet generation and different levels of routing depth. It is shown that it reproduces the relevant key, statistical features of Internet’s traffic. Moreover, we also report the existence of a critical path horizon defining a transition from low-efficient traffic to highly efficient flow. This transition is actually a direct consequence of the web’s small world architecture exploited by the routing algorithm. Once routing tables reach the network diameter, the traffic experiences a sudden transition from a low-efficient to a highly-efficient behavior. It is conjectured that routing policies might have spontaneously reached such a compromise in a distributed manner. Internet would thus be operating close to such critical path horizon.


Direct Consequence Spatial Structure Statistical Feature Traffic Flow Network Dynamic 
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.


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  1. 1.
    S.-H. Yook, H. Jeong, A-L. Barabási, Proc. Natl. Acad. Sci. USA 99, 13382, (2002)ADSCrossRefGoogle Scholar
  2. 2.
    B.A. Huberman, R.M. Lukose, Science 277, (1997)Google Scholar
  3. 3.
    N. Wiener, Cybernetics (John Wiley and Sons, New York, 1949)Google Scholar
  4. 4.
    J.H. Cowie, D.M. Nicol, A.T. Ogielski, Comput. Sci. Engin. 1, 42 (1999)CrossRefGoogle Scholar
  5. 5.
    W. Willinger, R. Govindan, S. Jamin, V. Paxson, S. Shenker, PNAS 99 (Suppl. 1), 2573 (2002)CrossRefGoogle Scholar
  6. 6.
    R.V. Solé, S. Valverde, Physica A 289, 595 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    S. Valverde, R.V. Solé, Physica A 312, 636 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    N. Hohn, D. Veitch, P. Abry, ACM/SIGCOMM Internet Measurement Workshop (Marseille, France, 2002) pp. 63-68Google Scholar
  9. 9.
    K. Fukuda, A Study of Phase Transition Phenomena in Internet Traffic, Ph.D. thesis, Keio Univ. (1999)Google Scholar
  10. 10.
    M. Argollo de Menezes, A.-L. Barabási, cond-mat/0306304 (2003)Google Scholar
  11. 11.
    W. Willinger, M.S. Taqqu, R. Sherman, D.V. Wilson, IEEE ACM Trans. on Networking 5, 71 (1997)CrossRefGoogle Scholar
  12. 12.
    H. Fukś, A.T. Lawniczak, adap-org/9909006 (2001)Google Scholar
  13. 13.
    M. Faloutsos, P. Faloutsos, C. Faloutsos, ACM SIGCOMM 29, 251 (1999)CrossRefGoogle Scholar
  14. 14.
    K. Bolding, M.L. Fulgham, L. Snyder, Tech. Rep. CSE-94-02-04 (1994)Google Scholar
  15. 15.
    P.M.B. Vitányi, SIAM J. Comput. 17 4, 659 (1988)CrossRefGoogle Scholar
  16. 16.
    G. Bilardi, F.P. Preparata, CS-93-20, Dept. Comp. Sci., Brown Univ. (1993)Google Scholar
  17. 17.
    B. Waxman, IEEE J. Selec. Areas Commun., SAC-6(9), 1617 (1988)Google Scholar
  18. 18.
    A. Vázquez, R. Pastor-Satorras, A. Vespignani, cond-mat/0206084 (2002)Google Scholar
  19. 19.
    When the link decision is ambiguous (more than one link can be selected) the less visited link until the moment is chosen (this could be implemented by maintaining a counter of the number of packets forwarded through the link)Google Scholar
  20. 20.
    J. Dong Noh, H Rieger, cond-mat/0307719 (2003)Google Scholar
  21. 21.
    K.-I. Goh, B. Kahng, D. Kim, Traffic and Granular Flow ‘01 (Springer, Berlin, 2003)Google Scholar
  22. 22.
    M.E.J. Newman, cond-mat/0309045 (2003)Google Scholar
  23. 23.
    L.C. Freeman, Sociometry 40, 35 (1979)ADSCrossRefGoogle Scholar
  24. 24.
    D.H. Lorenz, A. Orda, D. Raz, Y. Shavitt, TR-2001-17, DIMACS (2001)Google Scholar
  25. 25.
    L.J. Cowen, Proc. of the 10th Annual ACM-SIAM Symp. on Discrete Algorithms (1999)Google Scholar
  26. 26.
    M. Thorup, U. Zwick, Proc. 33th Annual ACM Symposium on Theory of Computing (SPAA), 1-10 (2001)Google Scholar
  27. 27.
    D. Krioukov, K. Fall, X. Yang, cond-mat/0308288 (2003)Google Scholar
  28. 28.
    R. Percacci, A. Vespignani, cond-mat/0209619 (2002)Google Scholar
  29. 29.
    Internet End-to-end Performance Monitoring, Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.ICREA-Complex Systems LabUniversitat Pompeu FabraBarcelonaSpain
  2. 2.Santa Fe InstituteNew MexicoUSA

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