Nonlinear analysis of wireless LAN traffic

Abstract An understanding of traffic characteristics and accurate traffic models are necessary for the improvement of the capability of wireless networks. In this paper we have analyzed the nonlinear dynamical behavior of several real traffic traces collected from wireless testbeds. We have found strong evidence that the wireless traffic is chaotic from our observations. That is, we found from the correlation dimension, the largest Lyapunov exponent and the principal components for analysis, which are typical indicators of chaotic traffic. This gives us a good theoretical basis for the analysis and modeling of wireless traffic using chaos theory.

[1]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

[2]  L. Glass,et al.  Understanding Nonlinear Dynamics , 1995 .

[3]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[4]  V. V. Ivanov,et al.  Nonlinear analysis of network traffic , 2002 .

[5]  J. Havstad,et al.  Attractor dimension of nonstationary dynamical systems from small data sets. , 1989, Physical review. A, General physics.

[6]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[7]  L. M. Berliner,et al.  Statistics, Probability and Chaos , 1992 .

[8]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[9]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[10]  Richard J. La,et al.  Nonlinear instabilities in TCP-RED , 2004, TNET.

[11]  Andras Veres,et al.  The chaotic nature of TCP congestion control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[12]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[13]  H. Schuster.  Deterministic chaos: An introduction , 1984 .

[14]  A. N. Sharkovskiĭ.  Dynamic systems and turbulence , 1989 .

[15]  Yugeng Xi,et al.  Nonlinear analysis of RED - a comparative study , 2004, Proceedings of the 2004 American Control Conference.

[16]  Upmanu Lall,et al.  Nonlinear Dynamics of the Great Salt Lake: Dimension Estimation , 1996 .

[17]  Walter Willinger,et al.  Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements , 1995 .

[18]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[19]  Victor Firoiu,et al.  A study of active queue management for congestion control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[20]  Wei Zhang,et al.  Chaotic network attractor in packet traffic series , 2004, Comput. Phys. Commun..

[21]  A. Giuliani,et al.  A complexity score derived from principal components analysis of nonlinear order measures , 2001 .

[22]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[23]  Celso Grebogi,et al.  The impact of chaos on science and society , 1997 .