# Pre-scheduled random arrivals and Fermi statistics

ARGOMENTI: Seminari

SEMINARI DI CALCOLO DELLE PROBABILITA'
Il Prof. Benedetto Scoppola, dell'Universita' di Roma - Tor Vergata, terra' mercoledi 22 aprile alle ore 15:00 in aula 2AB/40 un seminario dal titolo "Pre-scheduled random arrivals and Fermi statistics".

-Abstract
We consider a point process adding to each integer i a random delay xi_i, where the xi_i's are i.i.d. random variables with finite variance sigma2. This process, with a suitable rescaling of the distribution of xi_i's, converges to the Poisson process in total variation for large sigma. We then study a simple queueing system with our process as arrival process, and we provide a complete analytical description of the system. Although the arrival process is very similar to the Poisson process, due to negative autocorrelation the resulting queue is very different from the Poisson case. We found interesting connections of this model with the statistical mechanics of Fermi particles. This model is motivated by air traffic systems.

Rif. int. P. Dai Pra