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.