Wavelet and Multiscale Analysis of Network Traffic

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 behaviour 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 describe 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]  E. Bacry,et al.  The Multifractal Formalism Revisited with Wavelets , 1994 .

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

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

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

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

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

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

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

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

[10]  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).

[11]  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.

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

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

[14]  Walter Willinger,et al.  On the Self-Similar Nature of Ethernet Traffic ( extended version ) , 1995 .

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

[16]  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).

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

[18]  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).

[19]  Sally Floyd,et al.  Wide-area traffic: the failure of Poisson modeling , 1994 .

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

[21]  C. GilbertAT.  Multiscale analysis and data networks , 1996 .

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

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

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

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

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

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

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

[29]  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).

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

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

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

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