The Multiscale Nature of Network Traffic: Discovery, Analysis, and Modelling

The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behavior in tele-traffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in non-stationary environments. In this paper, we overview the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unravelling the mysteries of traffic statistics and dynamics.

[1]  D. V. Lindley,et al.  The theory of queues with a single server , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[3]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[4]  Kathleen S. Meier-Hellstern,et al.  TRAFFIC MODELS FOR ISDN DATA USERS: OFFICE AUTOMATION APPLICATION , 1991 .

[5]  Will E. Leland,et al.  High time-resolution measurement and analysis of LAN traffic: Implications for LAN interconnection , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[6]  Patrick Flandrin,et al.  Wavelet analysis and synthesis of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[7]  A.H. Tewfik,et al.  Correlation structure of the discrete wavelet coefficients of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[8]  I. Daubechies Ten Lectures on Wavelets , 1992 .

[9]  Murad S. Taqqu,et al.  On the Self-Similar Nature of Ethernet Traffic , 1993, SIGCOMM.

[10]  E. Bacry,et al.  The Multifractal Formalism Revisited with Wavelets , 1994 .

[11]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[12]  R. Peltier,et al.  Multifractional Brownian Motion : Definition and Preliminary Results , 1995 .

[13]  Rudolf H. Riedi,et al.  An Improved Multifractal Formalism and Self Similar Measures , 1995 .

[14]  Sally Floyd,et al.  Wide area traffic: the failure of Poisson modeling , 1995, TNET.

[15]  竹中 茂夫 G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance , 1996 .

[16]  B. Castaing,et al.  The temperature of turbulent flows , 1996 .

[17]  Martin Greiner,et al.  Wavelets , 2018, Complex..

[18]  Walter Willinger,et al.  Is Network Traffic Self-Similar or Multifractal? , 1997 .

[19]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.

[20]  J. L. Véhel,et al.  Fractional Brownian motion and data traffic modeling: The other end of the spectrum , 1997 .

[21]  Alain Arneodo,et al.  Experimental analysis of self-similarity and random cascade processes : Application to fully developed turbulence data , 1997 .

[22]  Patrice Abry,et al.  Wavelet Analysis of Long-Range-Dependent Traffic , 1998, IEEE Trans. Inf. Theory.

[23]  S. Mallat A wavelet tour of signal processing , 1998 .

[24]  Patrice Abry,et al.  A Wavelet-Based Joint Estimator of the Parameters of Long-Range Dependence , 1999, IEEE Trans. Inf. Theory.

[25]  Richard G. Baraniuk,et al.  A Multifractal Wavelet Model with Application to Network Traffic , 1999, IEEE Trans. Inf. Theory.

[26]  Anja Feldmann,et al.  Dynamics of IP traffic: a study of the role of variability and the impact of control , 1999, SIGCOMM '99.

[27]  Walter Willinger,et al.  Self-Similar Network Traffic and Performance Evaluation , 2000 .

[28]  D. Veitch,et al.  Infinitely divisible cascade analysis of network traffic data , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[29]  Richard G. Baraniuk,et al.  Multiscale queuing analysis of long-range-dependent network traffic , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[30]  Shriram Sarvotham,et al.  The Auckland data set : an access link observed , 2000 .

[31]  Richard G. Baraniuk,et al.  Multifractal Cross-Traffic Estimation , 2000 .

[32]  Iraj Saniee,et al.  Performance impacts of multi-scaling in wide area TCP/IP traffic , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[33]  L. Huang,et al.  Statistical scaling analysis of TCP/IP data using cascades , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[34]  Anna C. Gilbert,et al.  Multiscale Analysis and Data Networks , 2001 .

[35]  Patrice Abry,et al.  A statistical test for the time constancy of scaling exponents , 2001, IEEE Trans. Signal Process..

[36]  Patrice Abry,et al.  Wavelets for the Analysis, Estimation, and Synthesis of Scaling Data , 2002 .

[37]  R. Riedi,et al.  Multifractal products of stochastic processes: construction and some basic properties , 2002, Advances in Applied Probability.