Due to the variety of services and applications available on today's Internet, many properties of the traffic stray from the classical characteristics (Gaussianity and short memory) of standard models. The goal of the present contribution is to propose a statistical model able to account both for the non Gaussian and long memory properties of aggre- gated count processes. First, we introduce the model and a procedure to estimate the corresponding parameters. Second, using a large set of data taken from public reference repositories (Bellcore, LBL, Auckland, UNC, CAIDA) and collected by ourselves, we show that this stochastic process is relevant for Internet traffic modeling for a wide range of aggregation levels. In conclusion we indicate how this modeling could be used in IDS design.