Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and long range dependence at very large time scales to highly non-Gaussian marginals and multifractal scaling on small scales. This behavior can be explained by forming two components of the traffic according to the speed of connections, one component absorbing most traffic and being mostly Gaussian, the other constituting virtually all the small scale bursts. Towards a better understanding of this phenomenon, we propose a novel tree-based model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.