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Correlation matching method for the weak stationarity test of LRD traffic

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Abstract

The stationarity test of long-range dependent (LRD) traffic remains a challenge problem in the field of traffic engineering. Due to the importance of traffic theory in the Internet, to find a solution to that problem is greatly desired. This paper presents a method of the weak stationarity test of a single history LRD traffic series of finite length. How to apply this method to testing the stationarity of real traffic is demonstrated. The results in this paper suggest that there may be no general conclusion that traffic is either stationary or non-stationary since the stationarity of traffic is observation-scale dependent. Some of the investigated real-traffic traces that are stationary in an observation scale may be non-stationary in a larger observation scale.

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References

  1. Papoulis, A. (1984). Probability, random variables, and stochastic processes. New York: McGraw-Hill.

    Google Scholar 

  2. Priestley, M. B. (1965). Evolutionary spectra and non-stationary processes. Journal of the Royal Statistical Society: Series B, 27(2), 204–237.

    Google Scholar 

  3. Al-Shoshan, A. I. (1999). Time-varying modeling of a nonstationary signal. Telecommunication Systems, 12(4), 389–396.

    Article  Google Scholar 

  4. Bendat, J. S., & Piersol, A. G. (2000). Random data: analysis and measurement procedure (3rd ed.). New York: Wiley.

    Google Scholar 

  5. Von Sachs, R., & Neumann, M. H. (2000). A wavelet-based test for stationarity. Journal of Time Series Analysis, 21(5), 597–613.

    Article  Google Scholar 

  6. Ling, S. (2004). Estimation and testing stationarity for double-autoregressive models. Journal of the Royal Statistical Society: Series B, 66(1), 63–78.

    Article  Google Scholar 

  7. Psaradakis, Z. (2006). Blockwise bootstrap testing for stationarity. Statistics & Probability Letters, 76(6), 562–570.

    Article  Google Scholar 

  8. Rodrigues, P. M. M., & Rubia, A. (2008). A note on testing for nonstationarity in autoregressive processes with level dependent conditional heteroskedasticity. Statistical Papers, 49(3), 581–593.

    Article  Google Scholar 

  9. Borgnat, P., & Flandrin, P. (2009). Stationarization via surrogates. Journal of Statistical Mechanics: Theory and Experiment, 29, 1–14.

    Google Scholar 

  10. Tsybakov, B., & Georganas, N. D. (1998). Self-similar processes in communications networks. IEEE Transactions on Information Theory, 44(5), 1713–1725.

    Article  Google Scholar 

  11. Nogueira, A., Salvador, P., Valadas, R., & Pacheco, A. (2003). Modeling network traffic with multifractal behavior. Telecommunication Systems, 24(2–3), 339–362.

    Article  Google Scholar 

  12. Li, M. (2007). Modeling autocorrelation functions of long-range dependent teletraffic series based on optimal approximation in Hilbert space-a further study. Applied Mathematical Modelling, 31(3), 625–631.

    Article  Google Scholar 

  13. Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1994). On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 2(1), 1–15.

    Article  Google Scholar 

  14. Paxson, V., & Floyd, S. (1995). Wide area traffic: the failure of Poisson modeling. IEEE/ACM Transactions on Networking, 3(3), 226–244.

    Article  Google Scholar 

  15. Beran, J. (1994). Statistics for long-memory processes. London: Chapman & Hall.

    Google Scholar 

  16. Jin, X., & Min, G. (2008). Performance modelling of generalized processor sharing systems with multiple self-similar traffic flows. Telecommunication Systems, 38(3–4), 111–120.

    Article  Google Scholar 

  17. Mandelbrot, B. B. (1976). Note on the definition and the stationarity of fractional Gaussian noise. Journal of Hydrology, 30(4), 407–409.

    Article  Google Scholar 

  18. Vaton, S. (1998). A new test of stationarity and its application to teletraffic data. In ICASSP’98: Vol. 6. Proceedings of the 1998 IEEE international conference on acoustics, speech and signal processing (pp. 3449–3452). Seattle.

  19. Abry, P., & Veitch, D. (1998). Wavelet analysis of long-range dependent traffic. IEEE Transactions on Information Theory, 44(1), 2–15.

    Article  Google Scholar 

  20. Zhang, Y., Paxson, V., & Shenker, S. (2000). The stationarity of Internet path properties: routing, loss, and throughput (ACIRI Technical Report). May 2000.

  21. Li, M., Zhang, Y.-Y., & Zhao, W. (2007). A practical method for weak stationarity test of network traffic with long-range dependence. International Journal of Mathematics and Computers in Simulation, 1(4), 307–311.

    Google Scholar 

  22. Heyman, D. P., & Lakshman, T. V. (1999). On the relevance of long-range dependence in network traffic. IEEE/ACM Transactions on Networking, 7(5), 629–640.

    Article  Google Scholar 

  23. Liu, C., Wiel, S. V., & Yang, J. (2003). A nonstationary traffic train model for fine scale inference from coarse scale counts. IEEE Journal on Selected Areas in Communications, 21(6), 895–907.

    Article  Google Scholar 

  24. Rincón, D., & Sallent, S. (2005). In LNCS : Vol. 3375. On-line segmentation of non-stationary fractal network traffic with wavelet transforms and log-likelihood-based statistics (pp. 110–123). Berlin: Springer.

    Google Scholar 

  25. Mitra, S. K., & Kaiser, J. F. (Eds.) (1993). Handbook for digital signal processing. New York: Wiley.

    Google Scholar 

  26. Fu, K. S. (Ed.) (1976). Digital pattern recognition. Berlin: Springer.

    Google Scholar 

  27. Li, M. (2005). An iteration method to adjusting random loading for a laboratory fatigue test. International Journal of Fatigue, 27(7), 783–789.

    Article  Google Scholar 

  28. http://ita.ee.lbl.gov/html/contrib/BC.html.

  29. http://ita.ee.lbl.gov/html/contrib/DEC-PKT.html.

  30. http://ita.ee.lbl.gov/html/contrib/LBL-PKT.html.

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Correspondence to Ming Li.

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Li, M., Chen, WS. & Han, L. Correlation matching method for the weak stationarity test of LRD traffic. Telecommun Syst 43, 181–195 (2010). https://doi.org/10.1007/s11235-009-9206-5

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