On convergence of superposition of on/of processes

Abstract

Cumulative broadband network traffic is known to be well approximated by stable Levy motion or by fractional Brownian motion depending on whether connection rates are modest or large relative to heavy tailed connection length distribution tails. These results were framed as limit theorems for a sequence of cumulative input processes. We discuss analogous limit theorems for superposition of ON/OFF processes with mutually dependent and heavy tailed consecutive ON and OFF durations.