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The relation between burstiness and self-similarity of network traffic was identified in numerous papers in the past decade. These papers suggested that the widely used Poisson based models were not suitable for modeling bursty, local-area and wide-area network traffic. Poisson models were abandoned as unrealistic and simplistic characterizations of network traffic. Recent papers have challenged the accuracy of these results in today's networks. Authors of these papers believe that it is time to reexamine the Poisson traffic assumption. The explanation is that as the amount of Internet traffic grows dramatically, any irregularity of the network traffic, such as burstiness, might cancel out because of the huge number of different multiplexed flows. Some of these results are based on analyses of particular OC48 Internet backbone connections and other historical traffic traces. We analyzed the same traffic traces and applied new methods to characterize them in terms of packet interarrival times and packet lengths. The major contribution of the paper is the application of two new analytical methods. We apply the theory of smoothly truncated Levy flights and the linear fractal model in examining the variability of Internet traffic from self-similar to Poisson. The paper demonstrates that the series of interarrival times is still close to a self-similar process, but the burstiness of the packet lengths decreases significantly compared to earlier traces.