The KIPS Transactions:PartC (정보처리학회논문지C)

Korea Information Processing Society (한국정보처리학회)
권호 표지
DOI QR코드

DOI QR Code

Algorithmic Generation of Self-Similar Network Traffic Based on SRA

SRA 알고리즘을 이용한 Self-Similar 네트워크 Traffic의 생성

  • 정해덕 (한국성서대학교 정보과학부) ;
  • 이종숙 (한국과학기술정보연구원 슈퍼컴퓨팅센터그리드연구실)
  • Published : 2005.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

It is generally accepted that self-similar (or fractal) Processes may provide better models for teletraffic in modem computer networks than Poisson processes. f this is not taken into account, it can lead to inaccurate conclusions about performance of computer networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A generator of pseudo-random self similar sequences, based on the SRA (successive random addition) method, is implemented and analysed in this paper. Properties of this generator were experimentally studied in the sense of its statistical accuracy and the time required to produce sequences of a given (long) length. This generator shows acceptable level of accuracy of the output data (in the sense of relative accuracy of the Hurst parameter) and is fast. The theoretical algorithmic complexity is O(n).

최근의 컴퓨터 네트워크에서 teletraffic의 양상은 Poisson 프로세스보다 self-similar 프로세스에 의해서 더 잘 반영된다. 이는 컴퓨터 네트워크의 teletraffic에 관련하여 self-similar한 성질을 고려하지 않는다면, 컴퓨터 네트워크의 성능에 관한 결과는 부정확 할 수밖에 없다는 의미가 된다. 따라서, 통신 네트워크에 관한 시뮬레이션을 수행하기 위한 매우 중요한 요소 중에 하나는 충분히 긴 self-similar한 sequence를 얼마나 잘 생성하느냐의 문제이다. 본 논문에서는 SRA (successive random addition) 방법을 이용한 pseudo-random self-similar sequence 생성기를 구현 및 분석하였다. 본 pseudo-random self-similar sequence 생성기의 성질을 매우 긴 sequence를 생성하는데 요구되는 통계적인 정확도와 생성시간에 대해서 분석하였다. 본 논문에서 제안한 SRA 방법을 이용한 pseudo-random self-similar sequence 생성기의 성능은 Hurst 변수의 상대적인 정확도로 보았을 때, 그리고 sequence의 생성시간을 고려했을 때에 적합함을 보였다. 이 생성기의 이론적 complexity는 n개의 난수를 발생하는데 O(n)이 요구된다.

Keywords

References

  1. J. Beran, 'Statistical Methods for Data with Long Range Dependence,' Statistical Science, VoI.7(4), pp.404-427, 1992 https://doi.org/10.1214/ss/1177011122
  2. J. Beran, 'Statistics for Long-Memory Processes,' Chapman and Hall, New York, 1994
  3. M. C. Cario and B. L. Nelson, 'Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Precesses,' INFORMS Journal on Computing, Vol.10(1), pp.72-81, 1998 https://doi.org/10.1287/ijoc.10.1.72
  4. D. R. Cox, 'Long-Range Dependence: a Review,' Statistics: An Appraisa, Iowa State Statistirol Library, The Iowa State University Press, H.A. David and H.T. David (eds.), pp.55-74, 1984
  5. A. J. Crilly, R.A. Earnshaw and H. Jones, 'Fractals and Chaos,' Springer-Verlag, New York, 1991
  6. M. W. Garrett and W. Willinger, 'Analysis, Modeling and Generation of Self-Similar VBR Video Traffic,' Computer Communication Review, Proceedings of ACM SIGCOMM'94, London, UK, Vol.24(4), pp.269-280, 1994 https://doi.org/10.1145/190809.190339
  7. J. D. Gibbons and S. Chakraborti, 'Nonparametric Statistical Inference,' Marcel Dekker, Inc., New York, 1992
  8. C. W. J. Granger, 'Long Memory Relationships and the Aggregation of Dynamic Models,' Journal of Econometrics, Vol.14, North-Holland Publishing Company, pp.227-238, 1980 https://doi.org/10.1016/0304-4076(80)90092-5
  9. J. R. M. Hosking, 'Modeling Persistence in Hydrological Time Series Using Fractional Differencing,' Water Resources Research, Vol.20(12), pp.1898-1908, 1984 https://doi.org/10.1029/WR020i012p01898
  10. M. Krunz and A. Makowski, 'A Source Model for VBR Video Traffic Based on M/G/${\infty}$ Input Processes,' Proceedings of IEEE INFOCOM'98, San Francisco, CA, USA, pp.1441-1448, 1998
  11. W-C. Lau, A. Erramilli, J. L. Wang and W. Willinger, 'Self-Similar Traffic Generation: the Random Midpoint Displacement Algorithm and its Properties,' Proceedings of IEEE International Conference on Cmmunications (ICC'95), Seattle, WA, pp.466-472, 1995 https://doi.org/10.1109/ICC.1995.525213
  12. W. E. Leland, M. S. Taqqu, W. WIllinger and D. V. Wilson, 'On the Self-Similar Nature of Ethernet Traffic (Extended Version),' IEEE ACM Transactions en Networking, Vol.2(1), pp.1-15, 1994 https://doi.org/10.1109/90.282603
  13. N. Likhanov, B. Tsybakov and N.D. Georganas, 'Analysis of an ATM Buffer with Self-Similar ('Fractal') Input Traffic,' Proceedings of IEEE INFOCOM'95, Boston, Massachusetts, pp.985-992, 1995 https://doi.org/10.1109/INFCOM.1995.515974
  14. B. B. Mandelbrot, 'A Fast Fractional Gaussian Noise Generator,' Water Resources Research, Vol.7, pp.543-553, 1971 https://doi.org/10.1029/WR007i003p00543
  15. B .B. Mandelbrot and J. R. Wallis, 'Computer Experiments with Fractional Gaussian Noises,' Water Resources Research, Vol.5(1) , pp.228-267, 1969 https://doi.org/10.1029/WR005i001p00228
  16. A. L. Neidhardt and J. L. Wang, 'The Concept of Relevant Time Scales and its Application to Queueing Analysis of Self-Similar Traffic (or Is Hurst Naughty or Nice?),' Perforrmnce Evaluation Review, Proceedings of ACM SIGMETRICS'98, Madison, Wisconsin, USA, pp.222-232, 1998 https://doi.org/10.1145/277858.277923
  17. I. Norros, 'A Storage Model with Self-Similar Input,' Queueing Systems, Vol.16, pp.387-396, 1994 https://doi.org/10.1007/BF01158964
  18. V. Paxson, 'Fast Approximation of Self-Similar Network Traffic,' Lawrence Berkeley Laboratory and EECS Division, University of California, Berkeley (No.LBL-36750), 1995
  19. V. Paxson and S. Floyd, 'Wide-Area Traffic: the Failure of Poisson Modeling,' Computer Communication Review, Proceedings of ACM SIGCOMM'94, London, UK, pp.257-268, 1994 https://doi.org/10.1145/190314.190338
  20. H.-O. Peitgen and D. Saupe, 'The Science of Practal Images,' Springer-Verlag, New York, 1988
  21. O. Rose, 'Traffic Modeling of Variable Bit Rate MPEG Video and Its Impacts on ATM Networks,' PhD thesis, Bayerische Julius-Maximilians-Universitat Wurzburg, 1997
  22. B. K. Ryu, 'Fractal Network Traffic: from Understanding to Implications,' PhD thesis, Graduate School of Arts and Sciences, Columbia University, 1996
  23. T. Taralp, M. Devetsikiotis, I. Lambadaris and A. Bose, 'Efficient Fractional Gaussian Noise Generation Using the Spatial Renewal Process,' Proceedings cf IEEE International Conference on Communications (ICC'98), Atlanta, GA, USA, pp.7-11, 1998 https://doi.org/10.1109/ICC.1998.683067