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abstract:
We consider a cluster Poisson model with heavy-tailed interarrival
times and cluster sizes as a generalization of an infinite source
Poisson model, where the file sizes have a regularly varying tail
distribution function or a finite second moment. One result is that
this model reflects long range dependence of teletraffic data. We
show that depending on the heaviness of the file sizes, the
interarrival times and the cluster sizes we have to distinguish
different growths rates for the time scale of the cumulative traffic. The mean corrected cumulative input process converges to a
fractional Brownian motion in the fast growth case. However, in the
intermediate and the slow growth case we can have convergence to a
stable Lévy motion or a fractional Brownian motion as well depending
on the heaviness of the underlying distributions. These results are
contrary to the idea that cumulative broadband network traffic
converge in the slow growth case to a stable process. Furthermore,
we derive the asymptotic behavior of the cluster Poisson point
process which models the arrival times of data packets and the
individual input process itself. |
