Large scale cross-correlations in Internet traffic

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 5, 2002, Pages 7-

  Barthélemy, Marc ^a   Gondran, Bernard ^b   Guichard, Eric ^c  

^a CEA DIF   (France)

^b TELECOM PARISTECH   (France)

^c ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; INTERNET; MATRIX ALGEBRA; ROUTERS; TELECOMMUNICATION LINKS;

CORRELATION MATRIX; LOGARITHMS; RANDOM MATRIX THEORY (RMT); VOLUME FLOW EXCHANGE;

TELECOMMUNICATION TRAFFIC;

ARTICLE;

EID: 41349093329     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.056110     Document Type: Article

References (36)

1. B.A. Huberman and R.M. Lukose, Science 277, 535 (1997).
2. W.E. Leland, IEEE/ACM Trans. Networking 2, 1 (1994).
3. I. Csabai, J. Phys. A 27, 417 (1994).
4. K. Thompson, G.J. Miller, and R. Wilder, IEEE Network 11, 10 (1997).
5. A. Feldmann, A.C. Gilbert, W. Willinger, and T.G. Kurtz, Comput. Commun. Rev. 28, 5 (1998).
6. M. Takayasu, H. Takayasu, and K. Fukuda, Physica A 277, 248 (2000).
7. For a study on the Internet structure and map, see the Internet Mapping Project: http://www.cs.bell-labs.com/who/ches/map/index.html
8. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999).
9. G. Caldarelli, R. Marchetti, and L. Pietronero, Europhys. Lett. 52, 386 (2000).
10. R. Pastor-Satorras, A. Vasquez, and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001);
11. R. Pastor-SatorrasA. VasquezA. Vespignanie-print cond-mat/0105161.
12. R. Kumar, P. Raghavan, S. Rajalopagan, and A. Tomkins, Proceedings of the 25th VLDB Conference, Edinburgh, 1999, edited by M.P. Atkinson et al. (Morgan Kaufmann, 1999).
13. A. Broder et al., Proceedings of the 9th International WWW Conference, Amsterdam (Elsevier Science, The Netherlands, 2000), pp. 309–320.
14. A.-L. Barabási and R. Albert, Science 286, 509 (1999).
15. L.A. Adamic, Lect. Notes Comput. Sci. 1696, 443 (1999).
16. B.A. Huberman, Science 280, 95 (1998).
17. S. Mossa, Phys. Rev. Lett. 88, 138701 (2002).
18. M. Crovella and A. Bestavros, IEEE/ACM Trans. Networking 5, 835 (1997).
19. W. Willinger, M.S. Taqqu, R. Sherman, and D.V. Wilson, IEEE/ACM Trans. Networking 5, 71 (1997).
20. K. Fukuda, Ph.D. thesis, Keio University, 1999 (unpublished).
21. T. Ohira and R. Sawatari, Phys. Rev. E 58, 193 (1998).
22. M.L. Mehta, Random Matrices (Academic Press, Boston, 1991).
23. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Phys. Rev. Lett. 83, 1467 (1999).
24. V. Plerou, Phys. Rev. Lett. 83, 1471 (1999).
25. M. Barthélemy, B. Gondran, and E. Guichard, Physica A (to be published).
26. M.S. Santhanam and P.K. Patra, Phys. Rev. E 64, 016102 (2001).
27. For a map and more information on this network, see the web page: http://www.renater.fr. For an animated version of flows, see: http://barthes.ens.fr/metrologie/Renater01
28. A. Edelman, SIAM J. Matrix Anal. Appl. 9, 543 (1988), and references therein.
29. H. Bruus and J.-C. Anglés d’Auriac, Europhys. Lett. 35, 321 (1996).
30. F.J. Wegner, Z. Phys. B 36, 209 (1980).
31. B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993).
32. This localization of activity has not to be confused with traffic localization (namely that a subgroup of the network concentrates most of the traffic volume) which was also found for this network 32.
33. V. Plerou, Phys. Rev. E 65, 066126 (2002).
34. C. de Dominicis, Phys. Rev. B 18, 4913 (1978);
35. Phys. Rev. BH. Sompolinsky and A. Zippelius, 25, 6860 (1982);K.H. Fisher and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, 1991).
36. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics Vol. 85 (Addison-Wesley, New York, 1992).