  This paper presents an exhaustive study on the arrivals process at eight
important European airports. Using inbound traffic data, we define, compare,
and contrast a data-driven Poisson and PSRA point process. Although, there is
sufficient evidence that the interarrivals might follow an exponential
distribution, this finding does not directly translate to evidence that the
arrivals stream is Poisson. The main reason is that finite-capacity constraints
impose a correlation structure to the arrivals stream, which a Poisson model
cannot capture. We show the weaknesses and somehow the difficulties of using a
Poisson process to model with good approximation the arrivals stream. On the
other hand, our innovative non-parametric, data-driven PSRA model, predicts
quite well and captures important properties of the typical arrivals stream.
