Long range dependence in Internet backbone traffic

We report the first statistical analysis of Internet backbone traffic, based on traces with levels of aggregation 10 times larger and timestamp accuracy 1000 times better than in previous studies. We analyze the first three moments, marginal distributions and correlation structures of packet size, packet inter-arrival time, byte count and packet count, and find that the highly aggregated Internet backbone traffic is still long-range dependent and self-similar. In fact, all time series examined (packet size, inter-arrival time, byte count, packet count) exhibit long-range dependency and self-similarity. In addition to the now-classical analysis at large time-scales (> 100 ms), we report the first statistically relevant results on the short-term correlation ([50 μs, 10 ms]) of byte and packet count processes. We also study fitness of various analytical models to the traffic traces. The empirical queuing analysis confirms the long-range dependence detected through direct analysis by showing that the queue behavior at high level of aggregation still diverges greatly from that predicted by Poisson model. As expected, statistical multiplexing gains improve the queuing performance, leading to economy of scale.