Non-stationarity and high-order scaling in TCP flow arrivals: a methodological analysis

The last decade has been a very fruitful period in important discoveries in network traffic modeling, uncovering various scaling behaviors. Self-similarity, long-range dependence, multifractal behavior and finally cascades have been studied and convincingly matched to real traffic. The first purpose of this paper is to provide a methodology to go beyond the naive analysis of the second-order wavelet-based estimators of scaling, by performing non-stationarity checks and relying on the information contained in the high-order properties of the wavelet coefficients. Then, we apply this methodology to study the scaling properties of the TCP flow arrivals based on several traffic traces spanning the years from 1993 to early 2002. Our study reveals that the second-order scaling properties of this process describe its dynamics quite well. However, our analysis also provides evidence that high-order scaling in this process appears due to pathological behaviors like rate limitation and non-stationarity.

[1]  kc claffy,et al.  The architecture of CoralReef: an Internet traffic monitoring software suite , 2001 .

[2]  S. Uhlig.  Conservative cascades: an invariant of Internet traffic , 2003, Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (IEEE Cat. No.03EX795).

[3]  Michalis Faloutsos,et al.  A nonstationary Poisson view of Internet traffic , 2004, IEEE INFOCOM 2004.

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

[5]  Trang Dinh.  ON THE EFFECTS OF NON-STATIONARITY IN LONG-RANGE DEPENDENCE TESTS , 1999 .

[6]  Richard G. Baraniuk,et al.  Multiscale nature of network traffic , 2002, IEEE Signal Process. Mag..

[7]  Stéphane Jaffard,et al.  Multifractal formalism for functions part I: results valid for all functions , 1997 .

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

[9]  Kihong Park.  On the effect and control of self-similar network traffic: a simulation perspective , 1997, WSC '97.

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

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

[12]  Anja Feldmann,et al.  Characteristics of TCP Connection Arrivals , 2002 .

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

[14]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1996, SIGMETRICS '96.

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

[16]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[17]  Vern Paxson,et al.  Empirically derived analytic models of wide-area TCP connections , 1994, TNET.

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

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

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

[21]  Steve Romig,et al.  The OSU Flow-tools Package and CISCO NetFlow Logs , 2000, LISA.

[22]  Kihong Park,et al.  On the relationship between file sizes, transport protocols, and self-similar network traffic , 1996, Proceedings of 1996 International Conference on Network Protocols (ICNP-96).

[23]  D. Sornette.  Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools , 2000 .

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

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

[26]  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).

[27]  Patrice Abry,et al.  Does fractal scaling at the IP level depend on TCP flow arrival processes? , 2002, IMW '02.

[28]  Jin Cao,et al.  On the nonstationarity of Internet traffic , 2001, SIGMETRICS '01.

[29]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1997, TNET.

[30]  Richard Baraniuk,et al.  The Multiscale Nature of Network Traffic: Discovery, Analysis, and Modelling , 2003 .

[31]  Anja Feldmann,et al.  Scaling Analysis of Conservative Cascades, with Applications to Network Traffic , 1999, IEEE Trans. Inf. Theory.

[32]  Mischa Schwartz,et al.  ACM SIGCOMM computer communication review , 2001, CCRV.

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

[34]  Steve Uhlig.  3D-LD: a graphical Wavelet-based method for Analyzing Scaling Processes , 2002 .

[35]  Anja Feldmann,et al.  The changing nature of network traffic: scaling phenomena , 1998, CCRV.

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