DOI: https://doi.org/10.32515/2664-262X.2019.2(33).161-172
A Fractal Analysis of a Self-similar Traffic Generator Based on a Markov Chain
About the Authors
Г.М Дрєєва, teacher, Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
О.А. Смірнов,Professor, Doctor in Technics (Doctor of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
О.М. Дрєєв, PhD in Technics (Candidate of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
Т.В. Смірнова, PhD in Technics (Candidate of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
Abstract
In this work, we investigate the fractal dimension of the time series, which was obtained using a self-similar traffic generator based on Markov chains with controlled fractal dimension. The subject of the article is a fractal analysis of a self-similar traffic generator based on a Markov chain.
The purpose of the study is to investigate the fractal dimension of the time series, which is obtained using a self-similar traffic generator based on Markov chains with controlled fractal dimension. For this purpose the following problems were solved in the work: on the basis of numerical experiments of determination of fractal dimension of generated numerical sequences, statistically significant changes of fractal properties of numerical sequence on different scales were shown; points out the insufficient development of high-performance algorithms for obtaining self-similar numerical sequences for simulating traffic generation in telecommunication systems and networks; Directions for further studies on the management of the multifractal phenomenon in Markov-based generators are proposed.
Generators of self-similar traffic on Markov circuits differ from their counterparts with lower requirements for the computational power of simulation systems, which improves the performance of imitation modeling of information traffic in telecommunication systems and computer networks, so further development and study of such systems is relevant. On the basis of the simplified metric N (kε), an analytical expression for calculating the fractal dimension of the result of generating a binary number series based on a Markov chain is constructed. The dependence of the fractal dimension on the length of the interval at which the fractal dimension is calculated is made, and the assumption is made of the repetition of the multifractal property on classical metrics, such as dimension calculation based on R/S analysis or Minkowski dimension. In order to verify the assumptions, a numerical experiment was conducted which, with a reliability higher than 99%, confirmed the assumption of multifractal numerical sequence obtained by generators on Markov chains. Work can be continued to develop methods for managing multifractality parameters, or to eliminate multifractality when needed.
Keywords
modeling, traffic, self-similarity, multifractal, computer networks
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References
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Пристатейна бібліографія ГОСТ
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Copyright (c) 2019 Hanna Drieieva, Oleksii Smirnov, Oleksandr Drieiev, Tetiana Smirnova
A Fractal Analysis of a Self-similar Traffic Generator Based on a Markov Chain
About the Authors
Г.М Дрєєва, teacher, Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
О.А. Смірнов,Professor, Doctor in Technics (Doctor of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
О.М. Дрєєв, PhD in Technics (Candidate of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
Т.В. Смірнова, PhD in Technics (Candidate of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine
Abstract
Keywords
Full Text:
PDFReferences
1. Jan W. Kantelhardt Fractal and Multifractal Time Series Institute of Physics, Martin-Luther-University Halle-Wittenberg, 06099 Halle, Germany April 4, 2008 42 p. Retrieved from https://arxiv.org/pdf/0804.0747 [in English].
2. Fontugne, Romain and Abry, Patrice and Fukuda, Akira and Veitch, Darryl and Cho, Kenjiro and Borgnat, Pierre and Wendt, Herwig Scaling in Internet Traffic: a 14 year and 3 day longitudinal study, with multiscale analyses and randomprojections. (2017) IEEE/ACM Transactions on Networking journal, 25 (4). 2152-2165. ISSN 1063-6692. Retrieved from https://ieeexplore.ieee.org/document/7878657 [in English].
3. Lyudmyla Kirichenko, Tamara Radivilova, Vitalii Bulakh Machine Learning in Classification Time Series with Fractal Properties. December 2018. URL: https://www.researchgate.net/publication/ 329973801_Machine_Learning_in_Classification_Time_Series_with_Fractal_Properties [in English].
4. Aleksandrov, P.S.& Pasynkov, B.A. (1973). Vvedenie v teoriju razmernosti [Introduction to the theory of dimension]. Moskow: Science [in Russian].
5. Mackenzie Haffey; Martin Arlitt; Carey Williamson, Modeling, Analysis, and Characterization of Periodic Traffic on a Campus Edge Network. 2018 IEEE 26th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS), pр. 170 – 182, 2018. [in English].
6. Lai Simin, Wan Li, Zeng Xiangjian. (2019). Comparative Analysis of Multi-fractal Data Missing Processing Methods. Applied and Computational Mathematics.,Vol. 8, No. 2, 44-49. doi: 10.11648/j.acm.20190802.14 [in English].
7. Mahdi Barat Zadeh Joveini, Javad Sadri аnd Hoda Alavi Khoushhal. Fractal Modeling of Big Data Networks Conference: International Conference on Pattern Recognition and Artificial Intelligence (ICPRAI 2018) At: Center for Pattern Recognition and Machine Intelligence (CENPARMI), Concordia University, Montreal, Canada, pp. 1-4, 2018. [in English].
8. D. Jiang, L. Huo & Y. Li. (2018). Fine-granularity inference and estimations to network traffic for SDN. PLoS ONE 13(5) Doi.org/10.1371/journal.pone.0194302 [in English].
9. K. Xie, C. Peng, X. Wang, G. Xie & J. Wen (2017). Accurate recovery of internet traffic data under dynamic measurements, in Proc. of INFOCOM’17, pp. 1–9, 2017. [in English].
10. C. Wang, S. T. Maguluri, and T. Javidi Heavy traffic queue length behavior in switches with reconfiguration delay, in Proc. of INFOCOM’17, pp. 1–9, 2017. [in English].
11. G. Xie, K. Xie, J. Huang Wang X, Chen Y and Wen J. Fast low-rank matrix approximation with locality sensitive hashing for quick anomaly detection, in Proc. of INFOCOM’17, pp. 1–9, 2017. [in English].
12. Tatiana Mikhailovna Tatamikova and Oleg Ivanovich Kutuzov, “Evaluation and comparison of classical and fractal queuing systems”, XV International Symposium Problems of Redundancy in Information and Control Systems, pp.155 - 157, 2016. [in English].
13. Michaі Czarkowski, Sylwester Kaczmarek and Maciej Wolff, “Influence of Self -Similar Traffic Type on Perform ance of QoS Routing Algorithms’, INTL Journal of electronics and telecommunications, vol. 62, no. 1, pp. 81-87, 2016 [in English].
14. Lakhmi Priya Das, Sanjay Kumar Patra and Sarojananda Mishra, “Impact of hurst parameter value in self-similarity behaviour of network traffic”, International Journal of Research in Computer and Communication Technology, Vol 5, No 12, pp.631-633, 2016. [in English].
15. K.V. Ushanev, "Imagination models of the mass service system type Pa / M / 1, H2 / M / 1 and studying on their basis the quality of service of traffic with complex structure", Control systems, communication and security. №4, p.217-251, 2015. [in Russian].
16. Kuchuk, G.A., Mozhayev, O.O. & Vorobeyov, O.V. (2006). The method of prediction of fractal traffic. Radio and Computer Systems, No. 6, 181–188. Retrieved from http://nbuv.gov.ua/UJRN/recs_2006_6_34 [in Russian].
17. Kuchuk, G.A., Mozhayev, O.O. & Vorobeyov, O.V. (2007). Traffic prediction for congestion management integrated telecommunications network. Radio-electronic and computer systems, № 8, 261–271. Retrieved from http://nbuv.gov.ua/UJRN/recs_2007_8_48 [in Russian].
18. Kuchuk, G A., Mozhayev, O.O. & Vorobeyov, O.V. (2006). Analiz that model samoponіbnogo traffic. Aerospace and technology, No. 9, 173–180. Retrieved from http: //nbuv.gov.ua/UJRN/aktit_2006_9_35 [in Ukrainian].
19. Smirnov A.A., Kuznetsov A.A., Danilenko D.A.&, Berezovsky A. (2015). «The statistical analysis of a network traffic for the intrusion detection and prevention systems», Telecommunications and Radio Engineering, Vol,74, Issue 1. – Begel House Inc. Р. 61-78. [in English].
20. Smirnov, O., Kuznetsov, A., Kiian, A., Zamula, A., Rudenko, S., Hryhorenko, V., «Variance Analysis of Networks Traffic for Intrusion Detection in Smart Grids», 2019 IEEE 6th International Conference On Energy Smart Systems (2019 IEEE ESS), Kyiv, Ukraine April 17-19, 2019 P. 353-358. [in English].
21. Smirnov, O., Kuznetsov, A., Kavun, S., Babenko, B., Nakisko, O., Kuznetsova, K. (2019). «Malware Correlation Monitoring in Computer Networks of Promising Smart Grids», 2019 IEEE 6th International Conference On Energy Smart Systems (2019 IEEE ESS), Kyiv, Ukraine April 17-19, 2019 P. 347-352 [in English].
22. Kovalenko, A.A., Kuchuk, G. A. & Mozhaev, A. A. (2010). Construction of exponential time scales in the analysis of multiservice network queues. Radio and Computer Systems. No. 7, 257–262. Retrieved from http://nbuv.gov.ua/UJRN/recs_2010_7_52 [in Russian].
23. Dobrovolsky, E.V. & Nechyporuk. O.L. (2005). Modeling of Network Traffic Using Context Methods Scientific Papers ONAS them. O.S. Popova, No. 1, 24-32 [in Russian].