A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime
We show that, contrary to the common wisdom, the cumulative input process in a fluid
queue with cluster Poisson arrivals can converge, in the slow growth regime, to a fractional
Brownian motion, and not to a Lévy stable motion. This emphasizes the lack of robustness
of Lévy stable motions as ”birds-eye” descriptions of the traffic in communication networks.