Advertisement

Journal of Network and Systems Management

, Volume 23, Issue 3, pp 709–730 | Cite as

End-to-End Network Traffic Reconstruction Via Network Tomography Based on Compressive Sensing

  • Laisen Nie
  • Dingde Jiang
  • Lei Guo
Article

Abstract

Traffic matrices (TM) represent the volumes of end-to-end network traffic between each of the origin–destination pairs. Accurate estimates of TM are used by network operators to perform network management functions and traffic engineering tasks. Despite a large number of methods devoted to the problem of traffic matrix estimation, the inference of end-to-end network traffic is still a main challenge in the large-scale IP backbone network, due to an ill-posed nature of itself. In this paper, we focus on the problem of end-to-end network traffic reconstruction. Based on the network tomography method, we propose a simple method to estimate end-to-end network traffic from the aggregated data. By analyzing, in depth, the properties of the network tomography method, compressive sensing reconstruction algorithms are put forward to overcome the ill-posed nature of the network tomography model. In this case, to satisfy the technical conditions of compressive sensing, we propose a modified network tomography model. Besides, we give a further discussion that the proposed model follows the constraints of compressive sensing. Finally, we validate our method by real data from the Abilene and GÉANT backbone networks.

Keywords

Traffic matrix estimation Network measurement Convex optimization Statistical inference 

Notes

Acknowledgments

This work was supported in part by the Program for New Century Excellent Talents in University (No. NCET-11-0075) and the Fundamental Research Funds for the Central Universities (Nos. N120804004, N130504003). The authors wish to thank the reviewers for their helpful comments.

References

  1. 1.
    Papagiannaki, K., Taft, N., Lakhina, A.: A distributed approach to measure traffic matrices. In: Proceedings of ACM Internet Measurement Conference, Taormina, Italy, Oct 2004Google Scholar
  2. 2.
    Zhang, Y., Roughan, M., Duffield, N., Greenberg, A.: Fast accurate computation of large-scale IP traffic matrices from link loads. ACM SIGMETRICS Perform. Eval. Rev. 31(3), 206–207 (2003)CrossRefGoogle Scholar
  3. 3.
    Lakhina, A., Papagiannaki, K., Crovella, M., Diot, C., Kolaczyk, E., Taft, N.: Structural analysis of network traffic flows. In: Proceedings of SIGMETRICS 2004, pp. 61–72, 2004Google Scholar
  4. 4.
    Soule, A., Lakhina, A., Taft, N., Papagiannaki, K., Salamatian, K., Nucci, A., Crovella, M., Diot, C.: Traffic matrices: balancing measurements, inference and modeling. In: Proceedings of SIGMETRICS 2005, Banff, Canada, June 2005Google Scholar
  5. 5.
    Zhang, J.: Origin-destination network tomography with Bayesian inversion approach. In: Proceedings of IEEE International Conference on Web Intelligence, pp. 38–44, 2006Google Scholar
  6. 6.
    Zhang, Y., Roughan, M., Willinger, W., Qiu, L.: Spatio-temporal compressive sensing and internet traffic matrices. In: Proceedings of SIGCOMM 2009, pp. 267–278, 2009Google Scholar
  7. 7.
    Loiseau, P., Gonçalves, P., Dewaele, G., Borgnat, P., Abry, P., Primet, P.: Investigating self-similarity and heavy-tailed distributions on a large-scale experimental facility. IEEE/ACM Trans. Networking 18(4), 1261–1274 (2012)CrossRefGoogle Scholar
  8. 8.
    Firooz, M., Roy, S.: Network tomography via compressed sensing. In Proceedings of IEEE GLOBECOM 2010, pp. 1–5, 2010Google Scholar
  9. 9.
    Xu, W., Mallada, E., Tang, A.: Compressive sensing over graph, In Proceedings of INFOCOM 2011, pp. 2087–2095, 2011Google Scholar
  10. 10.
    Fornasier, M., Rauhut, H.: Compressive sensing, handbook of mathematical methods in imaging, pp. 187–228. Springer, New York (2011)CrossRefGoogle Scholar
  11. 11.
    Candès, E.: Compressive sampling. In Proceedings of the International Congress of Mathematicians, 2006Google Scholar
  12. 12.
    Donoho, D.: Compressive sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 54(2), 489–509 (2006)CrossRefGoogle Scholar
  14. 14.
    Candès, E.: The restricted isometry property and its implications for compressed sensing. C.R. Math. 346(9–10), 589–592 (2008)MATHCrossRefGoogle Scholar
  15. 15.
    Do, T., Gan, L., Nguyen, N., Tran, T.: Fast and efficient compressive sensing using structurally random matrices. IEEE Trans. Signal Process. 60(1), 139–154 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Atia, G.: Boolean compressed sensing and noisy group testing. IEEE Trans. Inf. Theory 58(3), 1880–1901 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Tropp, J., Gilbert, A.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Candès, E., Plan, Y.: A probabilistic and RIPless theory of compressed sensing. IEEE Trans. Inf. Theory 57(11), 7235–7254 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.College of Information Science and Engineering, 4th Floor, Computing CentreNortheastern UniversityShenyangPeople’s Republic of China

Personalised recommendations