Hyper-Erlang Based Model for Network Traffic Approximation

  • Junfeng Wang
  • Hongxia Zhou
  • Fanjiang Xu
  • Lei Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3758)


The long-tailed distribution characterizes many properties of Internet traffic. The property is often modeled by Lognormal distribution, Weibull or Pareto distribution theoretically. However, it hinders us in traffic analysis and evaluation studies directly from these models due to their complex representations and theoretical properties. This paper proposes a Hyper-Erlang Model (Mixed Erlang distribution) for such long-tailed network traffic approximation. It fits network traffic with long-tailed characteristic into a mixed Erlang distribution directly to facilitate our further analysis. Compared with the well-known hyperexponential based method, the mixed Erlang model is more accurate in fitting the tail behavior and also computationally efficient.


Cumulative Distribution Function Expectation Maximization Expectation Maximization Algorithm Tail Behavior Erlang Distribution 
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.
    Leland, W., Taqqu, M., Willinger, W., et al.: On the Self-Similar Nature of Ethernet Traffic (Extended Version). IEEE/ACM Transactions on Networking 2(1), 1–15 (1994)CrossRefGoogle Scholar
  2. 2.
    Paxson, V., Floyd, S.: Wide-Area Traffic: The Failure of Poission Modeling. IEEE/ACM Transactions on Networking 3(3), 226–244 (1995)CrossRefGoogle Scholar
  3. 3.
    Crovella, M.E., Bestavros, A.: Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes. IEEE/ACM Transactions on Networking 5(6), 835–846 (1997)CrossRefGoogle Scholar
  4. 4.
    Arlitt, M., Jin, T.: A workload characterization study of the 1998 World Cup Web site. IEEE Network (Special Issue on Web Performance) 14(3), 30–37 (2000)Google Scholar
  5. 5.
    Mahanti, A., Williamson, C., Eager, D.: Traffic Analysis of a Web Proxy Caching Hierarchy. IEEE Network (Special Issue on Web Performance) 14(3), 16–23 (2000)Google Scholar
  6. 6.
    Kalyanaraman, S., Vandalore, B., Jain, R., et al.: Performance of TCP over ABR with Long-Range Dependent VBR Background Traffic over Terrestrial and Satellite ATM Networks. In: Proceedings of 23rd Annual Conference on Local Computer Networks (LCN 1998), Lowell, MA, October 1998, pp. 70–78 (1998)Google Scholar
  7. 7.
    Ata, S., Murata, M., Miyahara, H.: Analysis of Network Traffic and Its Application to Design of High-speed Routers. IEICE Transactions on Information and Systems E83-D(5), 988–995 (2000)Google Scholar
  8. 8.
    Asaka, T., Ori, K., Yamamoto, H.: Method of Estimating Flow Duration Distribution Using Active Measurements. IEICE Transactions on Communications E86-B(10), 3030–3037 (2003)Google Scholar
  9. 9.
    Downey, A.B.: Evidence for Long-tailed Distributions in the Internet. In: Proceedings of ACM SIGCOMM Internet Measurement Workshop 2001, San Diego, CA, USA (November 2001)Google Scholar
  10. 10.
    Greiner, M., Jobmann, M., Lipsky, L.: The Importance of Power-tail Distributions for Modeling Queueing Systems. Operations Research 47(2) (March-April 1999)Google Scholar
  11. 11.
    Shortle, J.F., Fischer, M.J., Gross, D., et al.: Using the Transform Approximation Method to Analyzed Queues with Heavy-Tailed Service. Journal of Probability and Statistical Science 1(1), 15–27 (2003)Google Scholar
  12. 12.
    Feldamann, A., Whitt, W.: Fitting Mixtures of Exponentials to Long-tailed Distributions to Analyze Network Performance Models. Performance Evaluation 31(3-4), 245–279 (1998)CrossRefGoogle Scholar
  13. 13.
    El Abdouni Khayari, R., Sadre, R., Haverkort, B.R.: Fitting World-wide Web Request Traces with the EM-algorithm. Performance Evaluation 52(2–3), 175–191 (2003)CrossRefGoogle Scholar
  14. 14.
    Riska, A., Diev, V., Smirni, E.: An EM-based technique for approximating long-tailed data sets with PH distributions. Performance Evaluation 55(1-2), 147–164 (2004)CrossRefGoogle Scholar
  15. 15.
    Starobinski, D., Sidi, M.: Modeling and Analysis of Power-Tail Distributions via Classical Teletraffic Methods. Queueing Systems 36(1-3), 243–267 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Bilmes, J.A.: A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixutre and Hidden Markov Models. Technical Report, TR-97-021, International Computer Science Institue, Berkeley CA (April 1998)Google Scholar
  17. 17.
    Kelly, F.: Reversibility and Stochastic Networks. Wiley, New York (June 2004), Google Scholar
  18. 18.
    Klemm, A., Lindemann, C., Lohmann, M.: Modeling IP Traffic Using the Batch Markovian Arrival ProcessGoogle Scholar
  19. 19.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Junfeng Wang
    • 1
  • Hongxia Zhou
    • 2
  • Fanjiang Xu
    • 1
  • Lei Li
    • 1
  1. 1.National Key Laboratory of Integrated Information System Technology, Institute of SoftwareChinese Academy of SciencesBeijingP.R. China
  2. 2.Chongqing Communication InstituteChongqingP.R. China

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