IP traffic modeling: most relevant time-scale and local Poisson property

We consider IP traffic modeling to evaluate the packet loss probability. It is well-known that IP traffic shows long-range dependence or self-similarity in a long time-scale, whereas it looks random in a short time-scale. Thus we consider the branching Poisson process that has such a multiple time-scale feature. We focus on a queue fed by branching Poisson input and briefly discuss the local Poisson property in a short time-scale. Further we construct an equivalent MMPP input in such a sense that the packet loss probability can be predicted by evaluating the queue fed by the MMPP input.