×

Nonlinear analysis of network traffic. (English) Zbl 0993.90019

Summary: We applied a nonlinear time series analysis approach to the traffic measurements obtained at the input of a medium size local area network. In order to reconstruct the underlying dynamical system, we estimated the correlation length and the embedding dimension of the traffic series. The estimated embedding dimension, based on the Grassberger-Procaccia algorithm, is high. In order to extract the regular part from traffic data and to decrease the system’s dimension, we filtered out a high-frequency, “noisy” part, applying the wavelet filtering. Using the Principal Components Analysis (PCA), we estimated the number of feature components in the traffic series. The reliable values of the correlation length and the embedding dimension provided the application of a layered neural network for identification and reconstruction of the dynamical system. We have found that the trained neural network reproduces the statistical features of real measurements and confirms the PCA result on the dimension of the traffic series.

MSC:

90B20 Traffic problems in operations research
37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
90B18 Communication networks in operations research

Software:

JETNET
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Leland, W.; Taqqu, M.; Willinger, W.; Wilson, D., On the self-similar nature of ethernet traffic (extended version), IEEE/ACM Trans. Network., 2, 1, 1-15 (1994)
[2] Lucas MT, Wrege DE, Dempsey BJ, Weaver AC. Statistical characterization of wide-area self-similar network traffic, University of Virginia Technical Report CS97-04, 1996; October 9; Lucas MT, Wrege DE, Dempsey BJ, Weaver AC. Statistical characterization of wide-area self-similar network traffic, University of Virginia Technical Report CS97-04, 1996; October 9
[3] Crovella, M. E.; Bestavros, A., Self-similarity in world web traffic: evidence and possible causes, IEEE/ACM Trans. Network., 5, 6, 835-846 (1997)
[4] Vishal Misra, Wei-Bo Gong. A hierarchical model for teletraffic. Department of Electrical and Computer Engineering, University of Massachusetts, Amherst MA 01003; 1998; Vishal Misra, Wei-Bo Gong. A hierarchical model for teletraffic. Department of Electrical and Computer Engineering, University of Massachusetts, Amherst MA 01003; 1998
[5] Jon M. Peha. Protocals can make traffic appear self-similar. In: Proceedings of the 1997 IEEA/ACM/SCS Communication Networks and Distributed Systems Modeling and Simulation Conference; Jon M. Peha. Protocals can make traffic appear self-similar. In: Proceedings of the 1997 IEEA/ACM/SCS Communication Networks and Distributed Systems Modeling and Simulation Conference
[6] Jagerman DL, Melamed B, Willinger W, Stochastic modeling of traffic processes. Technical Report; Jagerman DL, Melamed B, Willinger W, Stochastic modeling of traffic processes. Technical Report · Zbl 0871.60085
[7] Tsunyi Tuan, Kihong Park. Multiple time scale congestion control for self-similar network traffic. Network Systems Lab, Department of Computer Sciences, Purdue University, West Lafayette, IN 47907, USA, Preprint submitted to Elsevier Preprint; Tsunyi Tuan, Kihong Park. Multiple time scale congestion control for self-similar network traffic. Network Systems Lab, Department of Computer Sciences, Purdue University, West Lafayette, IN 47907, USA, Preprint submitted to Elsevier Preprint · Zbl 1051.68534
[8] The State University “Dubna”. http://www.uni-dubna.ru; The State University “Dubna”. http://www.uni-dubna.ru
[9] Vasiliev PM, Ivanov VV, Korenkov VV, Kryukov, YuA, Kuptsov SI. System for acquisition, analysis and management of network traffic for segment of the JINR computer network – local network of the Univeristy “Dubna”, JINR Communications, D11-2001-266, JINR, Dubna, Russia, 2001; Vasiliev PM, Ivanov VV, Korenkov VV, Kryukov, YuA, Kuptsov SI. System for acquisition, analysis and management of network traffic for segment of the JINR computer network – local network of the Univeristy “Dubna”, JINR Communications, D11-2001-266, JINR, Dubna, Russia, 2001
[10] Abarbanel, H. D.I., Analysis of observed chaotic data (1996), Springer: Springer New York · Zbl 0875.70114
[11] Kugiumtzis D, Boudourides MA. Chaotic analysis of internet ping data: just a random number generator? Contributed paper on the SOEIS meeting at Bielefeld, 1998; March 27-28; Kugiumtzis D, Boudourides MA. Chaotic analysis of internet ping data: just a random number generator? Contributed paper on the SOEIS meeting at Bielefeld, 1998; March 27-28
[12] Packard, N. H.; Crutchfield, J. P.; Farmer, J. D.; Shaw, R. S., Geometry from a time series, Phys. Rev. Lett., 45, 712 (1980)
[13] Takens, F., Detecting strange attractors in turbulence, (Rand, D.; Young, L. S., Dynamical systems and turbulence. Dynamical systems and turbulence, Lecture Notes in Mathematics, vol. 898 (1981), Springer: Springer Berlin), 366 · Zbl 0513.58032
[14] Broomhead, D. S.; King, G. P., Extracting qualitative dynamics from experimental data, Physica D, 20, 217 (1986) · Zbl 0603.58040
[15] Albano, A. M.; Muench, J.; Schwartz, C.; Mees, A. I.; Rapp, P. E., Singular value decomposition and the Grassberger-Procaccia algorithm, Phys. Rev. A, 38, 3017 (1988)
[16] Grassberger, P.; Procaccia, I., Characterization of strange attractors, Phys. Rev. Lett., 50, 346 (1983)
[17] Cutler, C. D., A theory of correlation dimension for stationary time series, Philos. Trans. R. Soc. Lond. A, 348, 343 (1994) · Zbl 0859.62078
[18] Grassberger, P.; Procaccia, I., Measuring the strangeness of strange attractors, Physica D, 9, 189 (1983) · Zbl 0593.58024
[19] Chui, C. K., (An introduction to wavelets (1992), Academic Press: Academic Press New York), 1-18
[20] Daubechies, I., Wavelets (1992), SIAM: SIAM Philadelphia, PA
[21] Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., (Numerical recipies in C: the art of scientific computing (1988), Cambridge University Press: Cambridge University Press Cambridge), 1992
[22] Preizendorfer, R. W., Principal component analysis in meteorology and oceanography (1988), Elsevier: Elsevier New York
[23] Jolliffe, I. T., Principal component analysis (1986), Springer: Springer New York · Zbl 1011.62064
[24] Jackson, J. E., (A user’s guide to principal component analysis (1992), Wiley: Wiley New York), 26-62
[25] Karhunen K. Uber lineare methoden in der Wahrscheinlichkeitsrechnung, Annales Academiae Scientiarum Fennicae, Series A1: Mathematica-Physica 37, 3-79 (Transl.: RAND corp., Santa Monica, CA, Rep. T-131, 1960); Karhunen K. Uber lineare methoden in der Wahrscheinlichkeitsrechnung, Annales Academiae Scientiarum Fennicae, Series A1: Mathematica-Physica 37, 3-79 (Transl.: RAND corp., Santa Monica, CA, Rep. T-131, 1960)
[26] Loéve, M., Probability theory (1963), Van Nostrand: Van Nostrand New York · Zbl 0108.14202
[27] Haykin, S., Neural networks: a comprehensive foundation (1999), Prentice-Hall: Prentice-Hall Englewood Chiffs, NJ · Zbl 0934.68076
[28] Wasserman, P. D., Neural computing: theory and practice (1989), Van Nostrand Reinhold: Van Nostrand Reinhold New York
[29] Pham, D. T.; Liu, X., Neural networks for identification, prediction and control (1995), Springer: Springer London
[30] C. Peterson, Th. Rongvaldsson, JETNET-3.0 - A versatile artificial neural network package, LU Tp 93-29, 1993; C. Peterson, Th. Rongvaldsson, JETNET-3.0 - A versatile artificial neural network package, LU Tp 93-29, 1993
[31] Oja, E., Data compression, feature extraction, and autoassociation in feedforward neural networks, (Kohonen, T.; Mäkisara, K.; Simula, O.; Kangas, J., Artificial neural networks, vol. 1 (1991), North-Holland: North-Holland Amsterdam), 737-746
[32] Oja, E., Nonlinear PCA: algorithms and applications, (World Congress on Neural Networks, Portland, OR, vol. 2 (1993)), 396
[33] Baldi, P.; Hornik, K., Neural networks and principal component analysis: learning from examples without local minimum, (Neural networks, vol. 1 (1989)), 53-58
[34] Lapedes A, Farber R. Nonlinear signal processing using neural networks: prediction and system modeling. Los Alamos Report LA-UR 87-2662; 1987; Lapedes A, Farber R. Nonlinear signal processing using neural networks: prediction and system modeling. Los Alamos Report LA-UR 87-2662; 1987
[35] Akritas, P.; Antoniou, I.; Ivanov, V. V., Identification and prediction of discrete chaotic maps applying a Chebyshev neural network, Chaos, Solitons & Fractals, 11, 337-344 (2000) · Zbl 1115.68469
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.