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We review evidence that Internet traffic is characterized by long-tailed distributions of interarrival times, transfer times, burst sizes, and burst lengths. We propose a new statistical technique for identifying long-tailed distributions, and apply it to a variety of datasets collected on the Internet. We find that there is little evidence that interarrival times and transfer times are long-tailed, but that there is some evidence for long-tailed burst sizes. We speculate on the causes of long-tailed bursts.