The Journal of Supercomputing

, Volume 71, Issue 5, pp 1712–1735 | Cite as

Modern network traffic modeling based on binomial multiplicative cascades

  • Jeferson Wilian de Godoy Stênico
  • Lee Luan Ling
Article

Abstract

In this paper we present a new multifractal approach for modern network traffic modeling. The proposed method is based on a novel construction scheme of conservative multiplicative cascades. We show that the proposed model can faithfully capture some main characteristics (scaling function and moment factor) of multifractal processes. For this new network traffic model, we also explicitly derive analytical expressions for the mean and variance of the corresponding network traffic process and show that its autocorrelation function exhibits long-range dependent characteristics. Finally, we evaluate the performance of our model by testing both real wired and wireless traffic traces, comparing the obtained results with those provided by other well-known traffic models reported in the literature. We found that the proposed model is simple and capable of accurately representing network traffic traces with multifractal characteristics.

Keywords

Multiplicative cascades Multifractal processes  Network traffic modeling 

References

  1. 1.
    Leland W, Taqqu M, Willinger W, Wilson D (1994) On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Trans Netw 2(1):1–15Google Scholar
  2. 2.
    Riedi RH, Crouse MS, Ribeiro VJ, Baraniuk RG (1990) A multifractal wavelet model with application to network traffic. IEEE Trans Inf Theory. Special Issue on Multiscale Signal Analysis and Modeling, 45: 992–1018Google Scholar
  3. 3.
    Vieira FHT, Lee LL (2009) Adaptive wavelet based multifractal model applied to the effective bandwidth estimation of network traffic flows. IET Communications. pp 906–919Google Scholar
  4. 4.
    Krishna PM, Gadre VM, Desai UB (2003) Multifractal based network traffic modeling. Kluwer Academic Publishers, Boston, MAGoogle Scholar
  5. 5.
    Xu Z, Wang L, Wang K (2011) A new multifractal model based on multiplicative cascade. Inf Technol J 10:452–456CrossRefGoogle Scholar
  6. 6.
    Peltier R, Véhel JL (1995) Multifractional brownian motion: definition and preliminary results. Technical Report 2695, INRIAGoogle Scholar
  7. 7.
    Vieira FHT, Bianchi GR, Lee LL (2010) A network traffic prediction approach based on multifractal modeling. J High Speed Netw 17(2):83–96Google Scholar
  8. 8.
    Kolmogorov AN (1941) The local structure of turbulence in a compressible liquid for very large Reynolds numbers. CR (Dokl) Acad Sci URSS (NS) 30:301–305Google Scholar
  9. 9.
    Aloud M, Tsang E, Dupuis A, Olsen R (2011) Minimal agent-based model for the origin of trading activity in foreign exchange market. In: Computational intelligence for financial engineering and economics (CIFEr), pp 1–8Google Scholar
  10. 10.
    Paschalis A, Molnar P, Burlando P (2012) Temporal dependence structure in weights in a multiplicative cascade model for precipitation. Water Resour Res 48:W01501CrossRefGoogle Scholar
  11. 11.
    Stephen DG, Anastas JR, Dixon JA (2012) Scaling in cognitive performance reflects multiplicative multifractal cascade dynamics. In: Frontiers in physiology, fractal physiology 3:102. doi: 10.3389/fphys.2012.00102
  12. 12.
    Feldmann A, Gilbert AC, Willinger W (1997) Data networks as cascades: investigating the multifractal nature of internet WAN traffic. Proc. Of 35th Annual Allerton Conf. on communications, control, and computing, pp 269–280Google Scholar
  13. 13.
    Fisher A, Calvet L, Mandelbrot BB (1997) Multifractality of Deutschmark/US dollar exchanges rates. Yale UniversityGoogle Scholar
  14. 14.
    Dang TD, Molnár S, Maricza I (2003) Queuing performance estimation for general multifractal traffic. Int J Commun Syst 16(2):117–136CrossRefMATHGoogle Scholar
  15. 15.
    Mandelbrot BB (1974) Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J Fluid Mech 62:331–358Google Scholar
  16. 16.
    Guivarc’h Y (1987) Remarques sur les solutions d’ une equation fonctionnelle non linéaire de Benoît Mandelbrot. Comptes Rendus (Paris) 305I(139):1987MathSciNetGoogle Scholar
  17. 17.
    Stolojescu-Crisan C, Isar A, Moga S, Lenca P (2013) WiMax traffic analysis and base stations classifications in terms of LRD. Expert Systems 30(4):285–293. doi:10.1111/exsy.12026 CrossRefGoogle Scholar
  18. 18.
    Jizba P, Korbel J (2013) Modeling financial time series: multifractal cascades and Rényi entropy. In: Interdisciplinary symposium on complex systems emergence, complexity and computation. ISCS 2013, vol 8, pp 227–236Google Scholar
  19. 19.
    Seuret S, Lévy-Véhel J (2000) The local holder function of a continuous function. Appl Comput Harmon Anal 13(3):263–276CrossRefGoogle Scholar
  20. 20.
    Beran J (2010) Long-range dependence Wiley interdisciplinary reviews. Comput Stat 2(1):26–35CrossRefMathSciNetGoogle Scholar
  21. 21.
  22. 22.
    Jardosh A, Krishna NR, Kevin CA, Belding E (2014) CRAWDAD Data Set UCSB/IETF-2005 (v. 2005–10-19). out. 2005. http://crawdad.cs.dartmouth.edu/ucsb/ietf2005. Last accessed Mar 2014
  23. 23.
    Falconer K (2003) Fractal geometry: mathematical foundations and applications. Second Edition Wiley; 2 editionGoogle Scholar
  24. 24.
    Véhel JL (2013) Large deviation multifractal analysis of a class of additive processes with correlated non-stationary increments. IEEE/ACM Trans Netw 21(4):1309–1321CrossRefGoogle Scholar
  25. 25.
    Crouse MS, Baraniuk RG, Ribeiro VJ, Riedi RH (2000) Multiscale queueing analysis of long-range dependent traffic. Proc IEEE INFOCOM 2:1026–1035Google Scholar
  26. 26.
  27. 27.
    Pavlov AN, Anishchenko VS (2007) Multifractal analysis of complex signals. Phys Uspekhi 50:819–834CrossRefGoogle Scholar
  28. 28.
    Zhang ZL, Ribeiro VJ, Moon S, Diot C (2003) Small-time scaling behaviors of internet backbone traffic: an empirical study”, INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies 3:1826–1836Google Scholar
  29. 29.
    Karagiannis T, Faloutsos M (2014) SELFIS: A tool for self-similarity and long-range dependence analysis. 1st Workshop on Fractals and Self-Similarity in Data Mining: Issues and Approaches (in KDD) Edmonton, Canada, 2002. SELFIS—Downloaded from http://alumni.cs.ucr.edu/~tkarag/Selfis/Selfis.html. Last accessed Mar 2014

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jeferson Wilian de Godoy Stênico
    • 1
  • Lee Luan Ling
    • 1
  1. 1.School of Electrical and Computer EngineeringState University of Campinas-UnicampCampinasBrazil

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