Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

The analysis of characteristics of the correlated traffic using wavelet transform

Keywords:

.V. Kartashevskiy – Ph. D. (Eng.), Associate Professor, Department of Software and Management in Technical Systems, Volga State University of Telecommunications and Informatics (Samara) E-mail: ivk@psuti.ru I.A. Blatov – Dr. Sc. (Phys.-Math.), Professor, Head of Department of Higher Mathematics, Volga State University of Telecommunications and Informatics (Samara) E-mail: blatow@mail.ru Yu.A. Gerasimova – Post-graduate Student, Department of Higher Mathematics, Volga State University of Telecommunications and Informatics (Samara) E-mail: gerasimova.ju@yandex.ru


This article is about the analysis of the statistical properties of wavelet transform of the correlated sequence of samples characterizing the cellular network traffic at the access layer. Probability distribution characterizing the inter-arrival times is heavy-tailed. This problem arises in the analysis of the work of any network device that handles the traffic. The article shows that the wavelet transform of the correlated sequence of temporary traffic counts leads to the almost complete absence of correlation in the raw expansion coefficients of the original sequence. The wavelet decomposition causes the probability distribution function of expansion coefficients greatly different from the probability distribution function of the original sequence. The synthesis of the two-dimensional probability distribution function of the original sequence can help to determine the distribution function of expansion coefficients. The synthesis of the two-dimensional probability distribution function of correlated sequences can be accomplished using copulas. The article describes the method for determining a copula parameter for Farlie–Gumbel–Morgenstern copulas characterizing the correlation properties of the original sequence.
References:

 

  1. SHelukhin O.I., Matveev S.B., Pastukhov A.S. EHksperimentalnoe issledovanie samopodobija GPRS-trafika v sotovojj seti svjazi standarta GSM // EHlektrotekhnicheskie i informacionnye kompleksy i sistemy. 2007. № 2. S. 49−55.
  2. Kartashevskijj I.V. Ispolzovanie uravnenija Lindli dlja reshenija zadachi obrabotki korrelirovannogo trafika // EHlektrosvjaz. 2014. № 12. S. 41−42.
  3. Kartashevskiy I.V., Blatov I.A. Gerasimova Y.A. Decreasing correlation in strongly correlated sequences using wavelets // Proceedings of IEEE Conference Problems of Infocommunications Science and Technology (PIC S&T). 13−15 October 2015. Second International Scientific-Practical Conference. P. 18−20.
  4. Dremin I.N., Ivanov O.V., Nechitajjlo V.A. Vejjvlety i ikh ispolzovanie // Uspekhi fizicheskikh nauk. 2001. T. 171. № 5. S. 465−501.
  5. Ventcel E.S. Teorija verojatnostejj. M.: Nauka. 1969. 576 s.
  6. Balakrishnan N., Chin-Diew Lai. Continuous Bivariate Distributions – Springer Dordrecht Heidelberg London New York. 2009. 684 p.
  7. Nelsen R.B. An introduction to copulas. Lecture Notes in Statistics. 2nd edition. New York: Springer. 2006.
  8. Kartashevskijj I.V. Ispolzovanie kopul v statisticheskom analize telekommunikacionnogo trafika // Infokommunikacionnye tekhnologii. 2016. T. 16. № 4. S. 348−355.
  9. Fantaccini D. Modelirovanie mnogomernykh raspredelenijj s ispolzovaniem kopula-funkcijj. III // Prikladnaja ehkonometrika. 2011. № 4(24). S. 100−130.
  10. Gradshtejjn I.S., Ryzhik I.N. Tablicy integralov, summ, rjadov i proizvedenijj. Izd. 5-e. M.: Fizmatgiz. 1971. 1108 s.
  11. Bejjtmen G., EHrdejji A. Vysshie transcendentnye funkcii.T. 2. M.: SMB. 1974. 296 s.
  12. Malakhov A.N. Kumuljantnyjj analiz sluchajjnykh negaussovykh processov i ikh preobrazovanijj. M.: Sov. radio. 1978. 376 s.

 

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio