A novel approach to the estimation of the Hurst parameter in self-similar traffic

We present a new method to estimate the Hurst parameter of the increment process in network traffic-a process that is assumed to be self-similar. The confidence intervals and biasedness are obtained for the estimates using the new method. This new method is then applied to pseudo-random data and to real traffic data. We compare the performance of the new method to that of the widely-used wavelet method, and demonstrate that the former is much faster and produces much smaller confidence intervals of the Hurst parameter estimate. We believe that the new method can be used as an on-line estimation tool for H and thus be exploited in the new TCP algorithms that exploit the known self-similar and long-range dependent nature of network traffic.

[1]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[3]  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).

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

[5]  Mark E. Crovella,et al.  Effect of traffic self-similarity on network performance , 1997, Other Conferences.

[6]  Mark Crovella,et al.  On the Effec t of Traffic S elf-Similarity on Network Performance , 1997 .

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

[8]  Jennifer C. Hou,et al.  A case for exploiting self-similarity of network traffic in TCP congestion control , 2002, 10th IEEE International Conference on Network Protocols, 2002. Proceedings..

[9]  Vern Paxson,et al.  Fast approximation of self-similar network traffic , 1995, SIGCOMM 1995.

[10]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[11]  Walter Willinger,et al.  Self‐Similar Network Traffic: An Overview , 2002 .

[12]  Matthias Grossglauser,et al.  On the relevance of long-range dependence in network traffic , 1996, SIGCOMM '96.

[13]  Robert Tappan Morris,et al.  Variance of aggregated Web traffic , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

[15]  P. Whittle,et al.  Estimation and information in stationary time series , 1953 .

[16]  W. Willinger,et al.  ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY , 1995 .

[17]  Jonathan R. M. Hosking,et al.  Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series , 1996 .

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