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.

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Acknowledgments

This work was sponsored by CONACYT, DINPO and PROMEP.

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Notas

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