Traffic with an fBm limit: Convergence of the stationary workload process

Highly-aggregated traffic in communication networks is often modeled as fractional Brownian motion (fBm). This is justified by the theoretical result that the sum of a large number of on-off inputs, with either on-times or off-times having a heavy-tailed distribution with infinite variance, converges to fBm, after rescaling time appropriately. For performance analysis purposes, the key question is whether this convergence carries over to the stationary buffer content process. In this paper it is shown that, in a heavy-traffic queueing environment, this property indeed holds.