Artículos

Shot Noise Modeling of Heavy Tailed Activity Periods

Modelo de Ruido de Disparo para Periodos de Actividad con Distribución de Colas Pesadas

David Muñoz Rodríguez¹, Francisco Davila¹, Marlene Angulo Bernal^2,3, Deni L. Torres Román³, and John Fonseka⁴

1 ITESM; Center for Electronics and Telecommunications; Monterrey, N.L, 64849, MEXICO.
dmunoz@itesm.mx

2 UABC, Campus Mexicali, México
mangulo@uabc.mx

3 CINVESTAV, Campus Guadalajara, México
mangulo@gdl.cinvestav.mx, dtorres@gdl.cinvestav.mx

4 University of Texas at Dallas, Engineering and Computer Sc., Richardson, USA
kjp@utdallas.edu

Article received on January 27, 2005; accepted on January 13, 2006

Abstract

For web users, transmission activity is often described in terms of the number of file requests and file sizes that have a slowly decaying survivability function. In this article we model this line activity using a flexible shot–noise representation that enables us to analyze the infrared catastrophe effect introduced by the heavy–tailed characteristics. The proposed methodology is based on the α–stable characteristics of the traffic pattern. In addition, the effective bandwidth estimation of the proposed traffic model is presented. It provides a useful approach for the data network design and the admission control mechanism. Numerical results demonstrate the impact of the different statistical parameters on the spectral performance.

Keyword: Stochastic processes, Shot noise, Traffic models.

Resumen

La actividad en la transmisión de los usuarios Web es frecuentemente descrita en términos del número de solicitudes de archivos y de sus tamaños, donde la función de sobrevivencia del tamaño de los archivos tiene un decaimiento lento. En este artículo se modela la actividad de línea utilizando una representación flexible del ruido de disparo que permite analizar el efecto catástrofe infrarroja introducido por las características de las distribuciones de cola pesada. La metodología propuesta es basada en las características α–estables del patrón de tráfico, presentando además la estimación del ancho de banda efectivo del modelo propuesto, lo cual brinda un enfoque muy útil para el diseño de redes de datos y los mecanismos de control de admisión. Los resultados numéricos demuestran el impacto de los diversos parámetros estadísticos en el desempeño espectral.

Palabras clave: Procesos estocásticos, ruido de disparo, modelos de tráfico.

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