SciELO - Scientific Electronic Library Online

 
vol.13 issue3Run-Time Assertion Checking with ÉnfasisActive Vibration Control Using On-line Algebraic Identification and Sliding Modes author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Computación y Sistemas

On-line version ISSN 2007-9737Print version ISSN 1405-5546

Comp. y Sist. vol.13 n.3 Ciudad de México Jan./Mar. 2010

 

Artículos

 

Analysis of LRD Series with Time–Varying Hurst Parameter

 

Análisis de Series LRD con Parámetro de Hurst Variante en el Tiempo

 

Sergio Ledesma Orozco*, Gustavo Cerda Villafaña, Gabriel Aviña Cervantes, Donato Hernández Fusilier and Miguel Torres Cisneros

 

Department of Electrical and Computer Engineering, University of Guanajuato. *selo@salamanca.ugto.mx

 

Article received on September 05, 2008
Accepted on January 19, 2009

 

Abstract

It has been previously shown that actual network traffic exhibits long–range dependence. The Hurst parameter captures the degree of long–range dependence; however, because of the nature of computer network traffic, the Hurst parameter may not remain constant over a long period of time. An iterative method to compute the value of the Hurst parameter as a function of time is presented and analyzed. Experimental results show that the proposed method provides a good estimation of the Hurst parameter as a function of time. Additionally, this method allows the detection on changes of the Hurst parameter for long data series. The proposed method is compared with traditional methods for Hurst parameter estimation. Actual and synthetic traffic traces are used to validate our results. The proposed method allows detecting the changing points on the Hurst parameter, and better results can be obtained when modeling self–similar series using several values of the Hurst parameter instead of only one for the entire series. A new graphical tool to analyze long–range dependent series is proposed. Because of the nature of this plot, it is called the transition–variance plot. This tool may be helpful to distinguish between LAN and WAN traffic. Finally, the software LRD Lab* is deployed to analyze and synthesize long–range dependent series. The LRD Lab includes a simple interface to easily generate, analyze, visualize and save long–range dependent series.

Keywords: Estimation of Hurst parameter, self–similarity, long–range dependence, time–varying Hurst parameter.

 

Resumen

Ha sido previamente propuesto que el tráfico real de redes de computadoras exhibe dependencia de rango amplio. El parámetro de Hurst captura la cantidad de dependencia de rango amplio; sin embargo, debido a la naturaleza del tráfico en redes de computadoras, el parámetro de Hurst puede no permanecer constante durante un periodo largo de tiempo. Un método iterativo para calcular el valor del parámetro de Hurst como una función del tiempo es presentado y analizado. Los resultados experimentales demuestran que el método propuesto proporciona una buena estimación del parámetro de Hurst como una función del tiempo. Adicionalmente, este método permite la detección de cambios en el parámetro de Hurst para series largas. El método propuesto es comparado con métodos tradicionales para estimar el parámetro de Hurst. Series de datos reales y sintéticas son usadas para validar los resultados. El método propuesto permite detectar los puntos de cambio del parámetro de Hurst, y mejores resultados pueden ser obtenidos al modelar series similares a sí mismas usando varios valores del parámetro de Hurst en lugar de solamente uno para toda la serie. Una nueva herramienta gráfica para analizar series con dependencia de rango amplio es propuesta. Debido a la naturaleza de esta gráfica, ésta se llama gráfica de transición de varianza. Esta herramienta puede ser usada para distinguir entre tráfico LAN y WAN. Finalmente, el software LRD Lab* es desarrollado para analizar y sintetizar series con dependencia de rango amplio. El LRD Lab incluye una interfase sencilla para generar, analizar, visualizar y almacenar series con dependencia de rango amplio.

Palabras clave: Estimación del parámetro de Hurst, similar así mismo, dependencia de rango amplio, parámetro de Hurst variante en el tiempo.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

This work was sponsored by CONACYT, DINPO and PROMEP.

 

References

1. Beran, J. (1992). Statistical methods for data with long–range dependence. Statistical Science, 7(4), 404–427.        [ Links ]

2. Beran, J., Sherman, R., Taqqu, M. S. & Willinger, W. (1995). Long–range dependence in variable–bit–rate video traffic. IEEE Transactions on Communications, 43(234), 1566–1579.        [ Links ]

3. Beran, J. & Terrin, N. (1992). Estimation of the long–memory parameter, based on a multivariate central limit theorem. Journal of Time Series Analysis, 15(3), 269–278.        [ Links ]

4. Cappe, O., Moulines, E., Pesquet, J. C, Petropulu A. P. & Yang, X. (2002). Long–range dependence and heavy–tail modeling for teletraffic data. IEEE Signal Processing Magazine, 19(3), 14–27.        [ Links ]

5. Erramilli, A., Narayan, O. & Willinger, W. (1996). Experimental queueing analysis with long–range dependent packet traffic. IEEE/ACM Transactions on Networking, 4(29), 209–223.        [ Links ]

6. Fox, R. & Taqqu, M. S. (1985). Large–sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The Annals of Statistics, 4(2), 517–532.        [ Links ]

7. Garret, M. W. & Willinger, W. (1994). Analysis, modeling and generation of self–similar VBR video traffic. Computer Communications Review, 24(4), 269–280.        [ Links ]

8. Heyde, C. C. & Gay, R. (1993). Smoothed periodogram asymptotics and estimation for processes and fields with possible long–range dependence. Stochastic Processes and Their Applications, 45(1), 169–182.        [ Links ]

9. Karagiannis, T., Molle, M. & Faloutsos, M. (2004). Long–range dependence: ten years of Internet traffic modeling, IEEE Internet Computing, 8(5), 57–64.        [ Links ]

10. Krunz, M. & Matta, I. (2002). Analytical investigation of the bias effect in variance–type estimators for inference of long–range dependence. Computer Networks, 40(3), 445–458.        [ Links ]

11. Ledesma, S. & Liu, D. (2000). Synthesis of fractional Gaussian noise using linear approximation for generating self–similar network traffic. ACM Computer Communication Review, 30(2), 4–17.        [ Links ]

12. Ledesma, S., Liu, D. & Hernandez, D. (2007). Two approximation methods to synthesize the power spectrum of fractional Gaussian noise. Computational Statistics and Data Analysis, 52(2), 1047–1062.        [ Links ]

13. Leland, W. E. & Wilson, D. V. (1991). High time–resolution measurement and analysis of LAN traffic: Implications for LAN interconnection. IEEE Conference on Computer Communications INFOCOM, Florida, USA, 1360–1366.        [ Links ]

14. 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.        [ Links ]

15. Mandelbrot, B. B. & Wallis, J. R. (1969). Some long–run properties of geophysical records. Fractals in the earth sciences, New York: Plenum Press.        [ Links ]

16. Michiel, H. & Laevens, K. (1997). Teletraffic engineering in a broad–band era. Proceedings of the IEEE, 85(12), 2007–2033.        [ Links ]

17. Oppenheim, A. V. & Schafer, R. W. (1989). Discrete–time signal processing, Upper Saddle River, N.J., Prentice Hall.        [ Links ]

18. Paxson, V. (1997). Fast, approximate synthesis of fractional Gaussian noise for generating self–similar network traffic. ACM SIGCOMM Computer Communications Review, 27(5), 5–18.        [ Links ]

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

20. Purczynski, J. & Wlodarski, P. (2005). On fast generation of fractional Gaussian noise. Computational Statistics and Data Analysis, 50(10), 2537–2551.        [ Links ]

21. Ramirez, J. C. & Torres, R. D. (2006). Local and Cumulative Analysis of Self–similar Traffic Traces, IEEE Proceedings of the 16th International Conference on Electronics, Communications and Computers (CONIELECOMP'06), 37(1), 27–33.        [ Links ]

22. Roughan, M., Veitch, D. & Abry, P. (1998). On–line estimation of the parameters of long–range dependence. Proceedings of GLOBECOM'98, Sydney, Australia, 3716–3721.        [ Links ]

23. Stoev, S., Taqqu, M. S., Park, C, Michailidis, G. & Marrón, J. S. (2006). LASS: a tool for the local analysis of self–similarity. Computational Statistics & Data Analysis, 50(9), 2447–2471.        [ Links ]

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

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

26. Veitch, D. & Abry, P. (1999). A wavelet based joint estimator of the parameters of long–range dependence. IEEE Transactions on Information Theory, 45(3), 878–897.        [ Links ]

27. Zukerman, M., Neame T. D. & Addie, R. G. (2003). Internet traffic modeling and future technology implications. IEEE Conference on Computer Communications INFOCOM, California, USA, 587–596.        [ Links ]

 

Notas

* The LRD Lab can be downloaded at http://www.fimee.ugto.mx/profesores/sledesma/documentos/index.htm

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License