Internet Traffic Modeling with Lévy Flights

Measurements of local and wide-area network traffic in the 90's established the relation between burstiness and self-similarity of network traffic. Several papers demonstrated that the widely used Poisson based models could not be applied for the past decade's network traffic. If the traffic had been a Poisson process, the traffic's burst lengths would have been smoothed by averaging over a long time scale contradicting with the observations of the past decade's traffic characteristics. Poisson models were abandoned as unsuitable characterizations of network traffic. Recent papers have questioned the direct applicability of these results in networks of the new century. Some authors of these papers demand the revision of previous assumptions on the Poisson traffic models. They argue that as newer and newer network technologies are implemented and the amount of Internet traffic grows exponentially, the burstiness of network traffic might cancel out due to the huge number of aggregated traffic flows. Some results are based on analyses of high-speed Internet backbone links and other traffic traces. We analyzed the same traffic traces and applied novel methods to characterize them in terms of packet interarrival time. We demonstrate that the series of interarrival times is still close to a self-similar process.