On Long-range-dependence Synthetic Data Generation through Heavy-tailed Distributions

Comprehensive analysis of the Internet traffic conducted over the last decade revealed the concept of longrange dependence (LRD) in the collected data traces. Some of this analysis work proved that this property is a result of the heavy tailed distribution of the packet inter-arrival time, which is a result of the heavy tailed distribution of packet size of the traffic sources. In this paper, we use this fact to build a traffic generator model that is based on multiplexing sources of heavy-tailed inter-arrival times and then counting the number of arrivals in the successive periods of length T. To come up with a parameterized model, we also study the effect of the heavy tailed distribution parameters (i.e. the Pareto distribution), and the time scale along with the number of multiplexed sources on the LRD of the generated traffic. Our model is different from the on/off models proposed in the literature that need to multiplex a very large number of sources, while we need only a few sources. Our findings are; 1. The LRD level is higher for sources with heavier tails; 2. There is a need to multiplex only a few sources; 3. The LRD level is higher for larger time scales; 4. Fixing the time scale and tuning the tail of the distribution helps us to come up with a parameterized linear model that only has one parameter, which is the Hurst parameter.