Bernardo D'Auria and Sidney Resnick

We consider an infinite-source Poisson process to model end user inputs to a data network. We assume that the sources initiate transmissions according to a Poisson process and that transmission rates and durations are independent random variables. We analyze the traffic process that is obtained by discretizing time in slots of length $\delta$ and considering the quantity of transmitted data in adjacent time intervals. We study this discrete time process as the slot length $\delta$ goes to $0$. This analysis extends and complements work in D'Auria and Resnick, 2006 where an analogous model was studied which assumed independence of the transmission rates and the file sizes. It is striking that the two cases show rather different behaviour. While the cumulative input per slot in D'Auria and Resnick, 2006 converges marginally to a normal distribution, in the model considered here we have an approximating distribution which is stable with infinite second moment. We also study dependence across time slots, characterize its slow rate of decay, and provide a detailed comparison of the two models.