High variability versus long-range dependence for network performance

We investigate a stochastic model for high-speed network traffic, apparently exhibiting ''long range dependence''. Indeed, by defining long range dependence as a second-order property, we show that the model looks like a fractional Brownian motion, when time and space are scaled appropriately. However, when distributional limits are taken, for an appropriately normalized version of the model, long range dependence vanishes in the limit, being replaced by ''high variability''. We quantify the limit precisely and show that it is a Levy motion with stationary independent increments and marginals having a stable distribution which matches well actual VER Video traces. Using the Levy process in a queueing system we find that the probability of buffer overflow matches the one computed by using the pre-limit model.