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 VBR 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