The long-memory infinite source Poisson model: scaling limit and its representation

It is known for standard communication models with long-range dependence that under two different scalings in time and space either fractional Brownian motion or stable Lévy processes arises in the asymptotic limit. In a third, intermediate, scaling regime a limit process appears, which is neither Gaussian nor stable, and not self-similar. In this paper such a limit theorem is established for the infinite source Poisson arrival flow model. The main result is that the new limit process is identified as the time integral of a centered Poisson measure.