skip to main content
10.1145/1921168.1921197acmconferencesArticle/Chapter ViewAbstractPublication PagesconextConference Proceedingsconference-collections
research-article

Inferring invisible traffic

Published:30 November 2010Publication History

ABSTRACT

A traffic matrix encompassing the entire Internet would be very valuable. Unfortunately, from any given vantage point in the network, most traffic is invisible. In this paper we describe results that hold some promise for this problem. First, we show a new characterization result: traffic matrices (TMs) typically show very low effective rank. This result refers to TMs that are purely spatial (have no temporal component), over a wide range of spatial granularities. Next, we define an inference problem whose solution allows one to infer invisible TM elements. This problem relies crucially on an atomicity property we define. Finally, we show example solutions of this inference problem via two different methods: regularized regression and matrix completion. The example consists of an AS inferring the amount of invisible traffic passing between other pairs of ASes. Using this example we illustrate the accuracy of the methods as a function of spatial granularity.

References

  1. Akamai Technologies, Inc. The state of the Internet. 4th Quarter, 2009.Google ScholarGoogle Scholar
  2. A. Broido and kc claffy. Analysis of RouteViews BGP data: policy atoms. In Proceedings of Network Related Data Management Workshop (NRDM), Santa Barbara, CA, May 2001.Google ScholarGoogle Scholar
  3. CAIDA. Atom computation scripts. http://www.caida.org/funding/atomized_routing/documents/report1.xml, February 2003.Google ScholarGoogle Scholar
  4. Emmanuel J. Candès and Benjamin Recht. Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6):712--772, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. H. Chang, S. Jamin, Z. Mao, and W. Willinger. An empirical approach to modeling inter-AS traffic matrices. In Proceedings of IMC, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. V. Erramilli, M. Crovella, and N. Taft. An independent-connection model for traffic matrices. In Proceedings of the Internet Measurement Conference, October 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. W. Fang and L. Peterson. Inter-AS traffic patterns and their implications. In Proceedings of GLOBECOM, 1999.Google ScholarGoogle ScholarCross RefCross Ref
  8. A. Feldmann, N. Kammenhuber, O. Maennel, B. Maggs, R. De Prisco, and R. Sundaram. A methodology for estimating interdomain web traffic demand. In Proceedings of IMC, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer, 2nd edition, 2009.Google ScholarGoogle Scholar
  10. R. H. Keshavan, S. Oh, and A. Montanari. Matrix completion from a few entries. http://arxiv.org/abs/0901.3150, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. L. Kleinrock and W. Naylor. On the measured behavior of the ARPANetwork. In AFIPS Conference Proceedings, National Computer Conference, pages 767--780, May 1974. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. A. Lakhina, K. Papagiannaki, M. Crovella, C. Diot, E. D. Kolaczyk, and N. Taft. Structural analysis of network traffic flows. In Proceedings of ACM SIGMETRICS, pages 61--72, June 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot. Traffic matrix estimation: Existing techniques and new directions. In Proceedings of ACM SIGCOMM, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. W. Mühlbauer, S. Uhlig, B. Fu, M. Meulle, and O. Maennel. In search for an appropriate granularity to model routing policies. In Proceedings of ACM SIGCOMM, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. University of Oregon. Route views project. http://www.routeviews.org/, July 2009.Google ScholarGoogle Scholar
  16. M. Roughan. First order characterization of Internet traffic matrices. Invited paper at the 55th Session of the International Statistics Institute, April 2005.Google ScholarGoogle Scholar
  17. J. Wallerich, H. Dreger, A. Feldmann, B. Krishnamurthy, and W. Willinger. A methodology for studying persistency aspects of Internet flows. Computer Communication Review, April 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Z. Wen, W. Yin, and Y. Zhang. Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Technical report, Rice University, 2010.Google ScholarGoogle Scholar
  19. Y. Zhang, M. Roughan, N. Duffield, and A. Greenberg. Fast accurate computation of large-scale IP traffic matrices from link loads. In Proceedings of ACM SIGMETRICS, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Y. Zhang, M. Roughan, C. Lund, and D. Donoho. Estimating point-to-point and point-to-multipoint traffic matrices: An information-theoretic approach. IEEE/ACM Transactions on Networking, 13(5):947960, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Y. Zhang, M. Roughan, W. Willinger, and L. Qiu. Spatio-temporal compressive sensing and Internet traffic matrices. In Proceedings of ACM SIGCOMM, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Inferring invisible traffic

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Conferences
      Co-NEXT '10: Proceedings of the 6th International COnference
      November 2010
      349 pages
      ISBN:9781450304481
      DOI:10.1145/1921168

      Copyright © 2010 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 30 November 2010

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article

      Acceptance Rates

      Overall Acceptance Rate198of789submissions,25%

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader