Stochastic processes for computer network traffic modeling

Computer networks such as local area and wide area networks possess complex characteristics due to the heterogeneous nature of the supported traffic. The network traffic exhibits highly irregular fractal-like structure and long term correlations. Various stochastic processes such as fractional Gaussian noise, multiplicative cascades, linear fractional stable motion have been proposed to model network traffic. These stochastic processes are relatively unheard of in the networking community, until recently. This paper provides a thorough review of these stochastic processes and their application to wireless traffic modeling.

[1]  Laurent E. Calvet,et al.  Multifractality of Deutschemark / Us Dollar Exchange Rates , 1997 .

[2]  J. Lamperti Semi-stable stochastic processes , 1962 .

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

[4]  Anatol Kuczura,et al.  The interrupted poisson process as an overflow process , 1973 .

[5]  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).

[6]  Rudolf H. Riedi,et al.  An introduction to multifractals , 1997 .

[7]  Yannis Viniotis,et al.  Probability and random processes for electrical engineers , 1997 .

[8]  B. Mandelbrot Intermittent turbulence in self-similar cascades : divergence of high moments and dimension of the carrier , 2004 .

[9]  B. Melamed,et al.  Traffic modeling for telecommunications networks , 1994, IEEE Communications Magazine.

[10]  A. Marshak,et al.  Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals , 1994 .

[11]  Piotr Kokoszka,et al.  Fractional ARIMA with stable innovations , 1995 .

[12]  Walter Willinger,et al.  Self-similarity and heavy tails: structural modeling of network traffic , 1998 .

[13]  Edoardo Milotti,et al.  1/f noise: a pedagogical review , 2002, physics/0204033.

[14]  P. A. Blight The Analysis of Time Series: An Introduction , 1991 .

[15]  Gennady Samorodnitsky,et al.  Long range dependence in heavy tailed stochastic processes , 2001 .

[16]  Benoit B. Mandelbrot,et al.  Multifractal measures, especially for the geophysicist , 1989 .

[17]  P. Abry,et al.  SCALE INVARIANT INFINITELY DIVISIBLE CASCADES , 2004 .

[18]  Paul Embrechts,et al.  AN INTRODUCTION TO THE THEORY OF SELF-SIMILAR STOCHASTIC PROCESSES , 2000 .

[19]  Charles-Antoine Gue rin A note on the generalized fractal dimensions of a probability measure , 2001 .

[20]  J. R. M. Hosking,et al.  FRACTIONAL DIFFERENCING MODELING IN HYDROLOGY , 1985 .

[21]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[22]  Reiner Kriesten,et al.  STOCHASTIC SELF-SIMILARITY IN TELETRAFFIC MODELING , 1999 .

[23]  B. Mandelbrot Multifractal measures, especially for the geophysicist , 1989 .

[24]  Patrice Abry,et al.  On non-scale-invariant infinitely divisible cascades , 2005, IEEE Transactions on Information Theory.

[25]  Walter Willinger,et al.  Long-Range Dependence and Data Network Traffic , 2001 .

[26]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[27]  Emmanuel Bacry,et al.  Oscillating singularities on cantor sets: A grand-canonical multifractal formalism , 1997 .

[28]  J. Beran Statistical methods for data with long-range dependence , 1992 .

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

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

[31]  Stephen McLaughlin,et al.  An investigation of the impulsive nature of Ethernet data using stable distributions , 1996 .

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

[33]  Walter Willinger,et al.  Analysis, modeling and generation of self-similar VBR video traffic , 1994, SIGCOMM.

[34]  Murad S. Taqqu,et al.  Theory and applications of long-range dependence , 2003 .

[35]  B. Pesquet-Popescu,et al.  Wavelet based estimators for self-similar /spl alpha/-stable processes , 2000, WCC 2000 - ICSP 2000. 2000 5th International Conference on Signal Processing Proceedings. 16th World Computer Congress 2000.

[36]  David M. Lucantoni,et al.  A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance , 1986, IEEE J. Sel. Areas Commun..

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

[38]  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).

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

[40]  Athina P. Petropulu,et al.  Long-range dependence and heavy-tail modeling for teletraffic data , 2002, IEEE Signal Process. Mag..

[41]  J. Delour,et al.  2 00 0 Modelling fluctuations of financial time series : from cascade process to stochastic volatility model , 2000 .

[42]  R. Adler,et al.  A practical guide to heavy tails: statistical techniques and applications , 1998 .

[43]  Anja Feldmann,et al.  Data networks as cascades: investigating the multifractal nature of Internet WAN traffic , 1998, SIGCOMM '98.

[44]  A. Philippe,et al.  Generators of long-range dependent processes: A survey , 2003 .

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

[46]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[47]  A. Adas,et al.  Traffic models in broadband networks , 1997, IEEE Commun. Mag..

[48]  Rudolf H. Riedi,et al.  This is Printer Multifractal Processes , 1999 .

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

[50]  Laurent E. Calvet,et al.  Large Deviations and the Distribution of Price Changes , 1997 .

[51]  Patrice Abry,et al.  Multifractal analysis and /spl alpha/-stable processes: a methodological contribution , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[52]  Matthew Roughan,et al.  Measuring long-range dependence under changing traffic conditions , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[53]  B.K. Ryu,et al.  Point process approaches to the modeling and analysis of self-similar traffic .I. Model construction , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[54]  Matthias Grossglauser,et al.  On the relevance of long-range dependence in network traffic , 1999, TNET.

[55]  Dimitrios Hatzinakos,et al.  Network heavy traffic modeling using α-stable self-similar processes , 2001, IEEE Trans. Commun..

[56]  M. Taqqu,et al.  Simulation methods for linear fractional stable motion and farima using the fast fourier transform , 2004 .

[57]  E. Bacry,et al.  Modelling fluctuations of financial time series: from cascade process to stochastic volatility model , 2000, cond-mat/0005400.

[58]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[59]  Rudolf H. Riedi,et al.  Multifractal Properties of TCP Traffic: a Numerical Study , 1997 .

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

[61]  J. L. Nolan Stable Distributions. Models for Heavy Tailed Data , 2001 .

[62]  D. Applebaum Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

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

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

[65]  Patrick Flandrin,et al.  On the spectrum of fractional Brownian motions , 1989, IEEE Trans. Inf. Theory.

[66]  Emmanuel Bacry,et al.  THE THERMODYNAMICS OF FRACTALS REVISITED WITH WAVELETS , 1995 .

[67]  A. Oppenheim,et al.  Signal processing with fractals: a wavelet-based approach , 1996 .