Approximation of Internet Traffic Measurements in the Trunk Channel by the Sum of Lognormal Distributions
https://doi.org/10.1134/S2304487X19040047
Abstract
Two numerical approaches for approximating measurements of the network traffic recorded in a trunk channel based on the traditional least squares method and the coefficient of determination R2 . To additionally estimate the accuracy of the approximation of the analyzed data by a lognormal distribution, the dynamics of the dependence of the maximum intensity of the network traffic on the size of the aggregation window has been analyzed. A high level of compliance of the observation data with a lognormal law has been achieved in both approaches. At the same time, the accuracy of approximation increases noticeably when additional terms are included in the approximating function. It has been shown that the dependence of the determination coefficient on the size of the aggregation window for the analyzed network packets allows one to control the accuracy of the observation data by a lognormal law.
About the Authors
V. V. Ivanov
CJSC “MPOTC “TECHNOKOMPLEKT”; United Institute for Nuclear Research
Russian Federation
Russian Federation
Valery V. Ivanov
141981
141980
Moscow oblast
Dubna
V. V. Ivanov
United Institute for Nuclear Research; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
Victor V. Ivanov
141980
115409
Moscow oblast
Dubna
Moscow
A. V. Kryanev
United Institute for Nuclear Research; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
141980
115409
Moscow oblast
Dubna
Moscow
I. I. Tatarinov
Kaspersky Lab
Russian Federation
Russian Federation
123060
Moscow
References
1. Zrelov P. V., Ivanov Valery V., Ivanov Victor V., Kryukov Yu. A., Tatarinov I. I., Study of Internet-Traffic Features in the Trunk Channel, Physics of Particles and Nuclei Letters, 2019, vol. 16, no. 3, pp. 289–299.
2. Antoninou I., Ivanov V. V., Ivanov Valery V., and Zrelov P. V., On the Log-Normal Distribution of Net-work Traffic, Physica D, 2002, vol. 167, no. 7, pp. 2–85.
3. Antoninou I., Ivanov V. V., Ivanov Valery V., and Zrelov P. V., Statistical Model of Network Traffic, “Fizika elementarnykh chastits i atomnogo yadra” [Physics of elementary particles and nucleus], 2004, vol. 35, no. 4, pp. 984–1019.
4. Bakhrushin V. E., Metody ocenivaniya kharakteristik nelineynykh statisticheskikh svyazey [Estimation methods of characteristics of nonlinear statistic connections]. Sistemnye technologii, 2011, vol. 73, № 2, pp. 9–14.
5. Ershov E. B., Vybor regressii maksimiziruyuschiy nesneschyonnuyu ocenku koefficienta determinacii [A choice of regression that maximizes unbiased estimate of determination coefficient] // Ayvazyan S. A. Prikladnaya ecometrica. M.: Market DS, 2008, vol. 12, no. 4, pp. 71–83.
6. Berezin I. S., Zhidkov N. P., Metody vychisleniy [Methods of calculations]. Vol. 1, 2. M.: Fizmatgiz, 1962, 464p.
7. Bakhvalov N. S., Zhidkov N. P., Kobel’kov G. M., Chislennye metody [Numerical methods]. Red. by Tikhonov I. N., 2 ed. M.: Fizmatlit: Lab. bazovykh dannykh; SPb.: Nev. dialekt, 2002, 630 p.
8. Gel’fand I. M., Ceytlin M. L., DAN USSR, 1961, vol.137, № 2, pp. 295–98.
9. Ershov E. B., Rasprostranenie koefficienta determinacii na obschiy sluchay lineynoy regressii, ocenivaemoy s pomosch’yu razlichnykh versiy metoda naimen’schikh kvadratov // CEMI RAN Ekonomika i mat. metody. M.: CEMI RAN, 2002, vol. 38, no. 3, pp.107–120.
10. MAWI Working Group Traffic Archive. URL: http://mawi.wide.ad.jp/mawi/
11. Wireshark, May 2014, http://www.wireshark.org
Review
For citations:
Ivanov V.V., Ivanov V.V., Kryanev A.V., Tatarinov I.I. Approximation of Internet Traffic Measurements in the Trunk Channel by the Sum of Lognormal Distributions. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2019;8(4):380-394. (In Russ.) https://doi.org/10.1134/S2304487X19040047
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