Estimation of the memory parameter of the infinite-source Poisson process. (English) Zbl 1127.62070

Summary: 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 referred to as the 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.
We present a wavelet-based estimator of the Hurst index of this process, when it is observed either continuously or discretely over an increasing time interval. Our estimator is shown to be consistent and robust to some form of non-stationarity. Its rate of convergence is investigated.


62M09 Non-Markovian processes: estimation
62G05 Nonparametric estimation
65T60 Numerical methods for wavelets
60K25 Queueing theory (aspects of probability theory)
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI arXiv


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