Pré-Publication, Document De Travail Année : 2007

Estimation of the Memory Parameter of the Infinite Source Poisson Process

Résumé

Long range dependence induced by heavy tails is a widely reported feature of internet traffic. Long range dependence can be defined as the regular variation of the variance of the integrated process, and half the index of regular variation is then refered to as the {\em Hurst index}. The infinite source Poisson process (a particular case of which is the $M/G/\infty$ queue) is a simple and popular model with this property, when the tail of the service time distribution is regularly varying. The Hurst index of the infinite source Poisson process is then related to the index of regular variation of the service times. In this paper, we present a wavelet based estimator of the Hurst index of this process, when it is observed either continously or discretely over an increasing time interval. Our estimator is shown to be consistent and robust to some form of nonstationarity. Its rate of convergence is investigated.

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Dates et versions

hal-00008797 , version 1 (16-09-2005)
hal-00008797 , version 2 (16-09-2005)
hal-00008797 , version 3 (21-03-2007)
hal-00008797 , version 4 (03-09-2007)

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Gilles Fay, François Roueff, Philippe Soulier. Estimation of the Memory Parameter of the Infinite Source Poisson Process. 2007. ⟨hal-00008797v3⟩
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