Heavy tails versus long-range dependence in self-similar network traffic

Empirical studies of the traffic in computer networks suggest that network traffic exhibits self-similarity and long-range dependence. The ON/OFF model considered in this paper gives a simple 'physical explanation' for these observed phenomena. The superposition of a large number of ON/OFF sources, such as workstations in a computer lab, with strictly alternating and heavy-tailed ON- and OFF-periods, can produce a cumulative workload which converges, in a certain sense, to fractional Brownian motion. Fractional Brownian motion exhibits both self-similarity and long-range dependence. However, there are two sequential limits involved in this limiting procedure, and if they are reversed, the limiting process is stable Levy motion, which is self-similar but exhibits no long-range dependence. We study simulations limit regimes and provide conditions under which either fractional Brownian motion or stable Levy motion appears as limiting process.