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Mathematical Problems in Engineering
Volume 2013, Article ID 471963, 7 pages
http://dx.doi.org/10.1155/2013/471963
Research Article

Normality of Ethernet Traffic at Large Time Scales

1School of Finance and Statistics, East China Normal University, No. 500 Dong-Chuan Road, Shanghai 200241, China
2Department of Computer and Information Science, University of Macau, Padre Tomas Pereira Avenue, Taipa, Macau

Received 19 January 2013; Accepted 4 February 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Zhiping Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Transactions on Networking, vol. 2, no. 1, pp. 1–15, 1994. View at Publisher · View at Google Scholar · View at Scopus
  2. D. McDysan, QoS & Traffic Management in IP & ATM Networks, McGraw-Hill, New York, NY, USA, 2000.
  3. P. Abry and D. Veitch, “Wavelet analysis of long-range dependent traffic,” IEEE Transactions on Information Theory, vol. 44, no. 1, pp. 2–15, 1998. View at Publisher · View at Google Scholar
  4. W. Willinger and V. Paxson, “Where mathematics meets the internet,” Notices of the American Mathematical Society, vol. 45, no. 8, pp. 961–970, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Ph. Barbe and W. P. McCormick, “Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution,” Stochastic Processes and Their Applications, vol. 122, no. 4, pp. 1276–1303, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. G. Garroppo, S. Giordano, M. Pagano, and G. Procissi, “Testing α-stable processes in capturing the queuing behavior of broadband teletraffic,” Signal Processing, vol. 82, no. 12, pp. 1861–1872, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Karasaridis and D. Hatzinakos, “Network heavy traffic modeling using α-stable self-similar processes,” IEEE Transactions on Communications, vol. 49, no. 7, pp. 1203–1214, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Terdik and T. Gyires, “Lévy flights and fractal modeling of internet traffic,” IEEE/ACM Transactions on Networking, vol. 17, no. 1, pp. 120–129, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Feldmann, A. C. Gilbert, W. Willinger, and T. G. Kurtz, “The changing nature of network traffic: scaling phenomena,” ACM SIGCOMM Comput Communication Review, vol. 28, no. 2, pp. 5–29, 1998. View at Google Scholar
  10. V. Paxson and S. Floyd, “Wide area traffic: the failure of Poisson modeling,” IEEE/ACM Transactions on Networking, vol. 3, no. 3, pp. 226–244, 1995. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Scherrer, N. Larrieu, P. Owezarski, P. Borgnat, and P. Abry, “Non-Gaussian and long memory statistical characterizations for Internet traffic with anomalies,” IEEE Transactions on Dependable and Secure Computing, vol. 4, no. 1, pp. 56–70, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. http://www.sigcomm.org/ITA/.
  13. P. Borgnat, G. Dewaele, K. Fukuda, P. Abry, and K. Cho, “Seven years and one day: sketching the evolution of internet traffic,” in Proceedings of the 28th Conference on Computer Communications (INFOCOM '09), pp. 711–719, Rio de Janeiro, Brazil, April 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. H. C. Thode, Jr., Testing for Normality, vol. 164 of Statistics: Textbooks and Monographs, Marcel Dekker, New York, NY, USA, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  15. N. Razali and Y. B. Wah, “Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests,” Journal of Statistical Modeling and Analytics, vol. 2, no. 1, pp. 21–33, 2011. View at Google Scholar
  16. D. N. Gujarati, Basic Econometrics, McGraw-Hill, New York, NY, USA, 4th edition, 2002.
  17. G. G. Judge, R. C. Hill, W. E. Griffiths, H. Lütkepohl, and T. C. Lee, Introduction to the Theory and Practice of Econometrics, John Wiley & Sons, New York, NY, USA, 2nd edition, 1988. View at MathSciNet
  18. S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality: complete samples,” Biometrika, vol. 52, no. 3-4, pp. 591–611, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. T. W. Anderson and D. A. Darling, “Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes,” Annals of Mathematical Statistics, vol. 23, pp. 193–212, 1952. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. T. W. Anderson and D. A. Darling, “A test of goodness of fit,” Journal of the American Statistical Association, vol. 49, pp. 765–769, 1954. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. A. Stephens, “EDF statistics for goodness of fit and some comparisons,” Journal of the American Statistical Association, vol. 69, pp. 730–737, 1974. View at Publisher · View at Google Scholar
  22. M. A. Stephens, “Tests based on EDF statistics,” in Goodness-of-Fit Techniques, R. B. d’Agostino and M. A. Stephens, Eds., pp. 97–193, Marcel Dekker, New York, NY, USA, 1986. View at Google Scholar
  23. C. M. Jarque and A. K. Bera, “Efficient tests for normality, homoscedasticity and serial independence of regression residuals,” Economics Letters, vol. 6, no. 3, pp. 255–259, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  24. C. M. Jarque and A. K. Bera, “Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence,” Economics Letters, vol. 7, no. 4, pp. 313–318, 1981. View at Google Scholar
  25. C. Cattani, G. Pierro, and G. Altieri, “Entropy and multifractality for the myeloma multiple TET 2 gene,” Mathematical Problems in Engineering, vol. 2012, Article ID 193761, 14 pages, 2012. View at Google Scholar · View at MathSciNet
  26. C. Cattani, “On the existence of wavelet symmetries in archaea DNA,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 673934, 21 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. C. Toma, “Advanced signal processing and command synthesis for memory-limited complex systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 927821, 13 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  28. E. G. Bakhoum and C. Toma, “Specific mathematical aspects of dynamics generated by coherence functions,” Mathematical Problems in Engineering, vol. 2011, Article ID 436198, 10 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus