Abstract
The research focuses on the analysis of university e-learning network traffic to work out and validate the methods that are most suitable for robust analysis and on-line monitoring of self-similarity. Time series of network traffic analyzed are formed by registering data packets in a node at different regimes of network traffic and different ways of sampling. The results obtained have been processed by Fractan, Selfis programmes and the modules library SSE (Self-similarity Estimator) developed in the paper, which employs the robust analysis methods. The methods implemented in the SSE (Self-similar Estimator) have been tested by computer simulation applying the Janicki and Weron (2000) algorithm for generating random standard stable values. The research results show that the regression method implemented by the software modules library SSE is most applicable to the network traffic analysis. The investigation of traffic in the Siauliai University e-learning network has been shown that the network traffic is self-similar with the Hurst coefficient that changes in the interval [0.53, 0.70], the correspondent stability index changes in the interval [1.43, 1.89], the skewness not observed because the estimated β = 0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abry P, Veitch D (1998) Wavelet analysis of long-range-dependent traffic. IEEE Trans Inf Theory 44(1): 2–15
Belov I, Kabasinskas A, Sakalauskas L (2006) A study of stable models of stock markets. Inf Technol Control 35(1): 34–56
Beran J (1998) Statistics for long-memory processes. Chapman and Hall/CRC, USA
Erramilli A, Narayan O, Willinger W (1996) Experimental queuing analysis with long-range dependent packet traffic. Available at http://www-net.cs.umass.edu/cs691s/narayan96.ps
Fama EF, Roll R (1971) Parameter estimates for symmetric stable distributions. J Am Stat Assoc 66(334): 331–338
Fractan 4.4 (2003) created by Sychev V. Available at http://www.chaostradinggroup.com/download/?module=filesdb3&id=1&fid=3
Gallos LK, Song C, Makse HA (2007) A review of fractality and self-similarity in complex networks. Phys A: Stat Mech Appl 386: 686–691
Guan L, Awan IU, Woodward ME, Wang X (2007) Discrete-time performance analysis of a congestion control mechanism based on RED under multi-class bursty and correlated traffic. J Syst Softw 80(10): 1716–1725
He G, Gao Y, Hou JC, Park K (2004) A case for exploiting self-similarity of network traffic in TCP congestion control. Comput Netw: Int J Comput Telecommun Netw 45(6): 743–766
Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civil Eng 116: 770–799
Janicki A, Weron A (2000) Simulation and chaotic behavior of a-stable stochastic processes. Marcel Dekker, New York
Kabasinskas A, Rachev S, Sakalauskas L, Sun W, Belovas I (2009) Alpha-stable paradigm in financial markets. J Comput Anal Appl 11(4): 641–668
Kaj I (2002) Stochastic modeling in broadband communications systems. SIAM, Philadelphia
Karagiannis T, Faloutsos M, Molle M. (2003) A user-friendly self-similarity analysis tool. ACM SIGCOMM Comput Commun Rev 33(3): 81–93
Kim JS, Goh K, Salvi IG, Oh E, Kahng B, Kim D (2007) Fractality in complex networks: critical and supercritical skeletons. Phys Rev E 75: 016110
Kleinrock L (2002) Creating a mathematical theory of computer networks. Oper Res 50(1): 125–131
Kokoszka PS, Taqqu MS (1996) Parameter estimation for infinite variance fractional ARIMA. Ann Stat 24(5): 1880–1913
Koutrouvelis IA (1981) An iterative procedure for the estimation of the parameters of the stable law. Commun Stat: Simul Comput B10: 17–28
Leland E, Taqqu S, Willinger W, Wilson DW (1994) On the self-similar nature of ethernet traffic. IEEE/ACM Trans Netw 2(1): 1–15
Li M, Lim SC (2008) Modeling network traffic using generalized Cauchy process. Phys A: Stat Mech Appl 387(11): 2584–2594
McCulloch JH (1986) Simple consistent estimators of stable distribution parameters. Commun Stat: Simul Comput 15(4): 1109–1136
Park K, Willinger W (2000) Self-similar network traffic and performance evaluation. Wiley, USA
Petrov VV (2003) To cto vy hotely znat o samopodobnom teletrafike, no stesnialis sprosit. Available at http://teletraffic.ru/public/pdf/Petroff_It%20is%20that%20you%20wanted_2003.pdf
Press SJ (1972) Estimation in univariate and multivariate stable distribution. J Am Stat Assoc 67: 842–846
Rachev ST, Mittnik S (2000) Stable Paretian models in finance. Wiley, Chichester
Ruelle D, Takens F (1971) On the nature of turbulence. Commun Math Phys 20: 167–192
Samorodnitsky G, Taqqu MS (1994) Stable non-Gaussian processes stochastic models with infinite variance. Chapman and Hall, New York
Samorodnitsky G (2006a) Long memory and self-similar processes. Annales de la faculté des sciences de Toulouse Sér. 6 15(1): 107–123
Samorodnitsky G (2006b) Long range dependence. Found Trends Stoch Syst 1(3): 163–257
Selfis 0.1b (2002) created by Karagiannis T. Available at http://www.cs.ucr.edu/~tkarag/Selfis/Selfis.html
Sornette D (2004) Critical phenomena. In: Chaos F (eds) Natural sciences: self-organization and disorder: concepts and tools, (second ed). Springer, Berlin
SSE (2008) created by Kaklauskas L. Available at http://lk.su.lt/index.php?option=com_content&view=article&id=47&Itemid=29
Taqqu MS, Teverovsky V (1998) Estimating long-range dependence in finite and infinite variance series. In: Adler R, Feldman R, Taqqu MS (eds) A practical guide to heavy tails: statistical techniques for analyzing heavy-tailed distributions. Birkhauser, Boston, pp 177–217
Userspace logging daemon. (2009) Available at http://www.netfilter.org
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaklauskas, L., Sakalauskas, L. Study of on-line measurement of traffic self-similarity. Cent Eur J Oper Res 21, 63–84 (2013). https://doi.org/10.1007/s10100-011-0216-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10100-011-0216-5