Estimating long-range dependence in impulsive traffic flows

Traffic flow in high-speed data network systems is often impulsive and long-range dependent. Impulsiveness implies a heavy-tailed marginal distribution, thus lack of finite second-order statistics. Hence, traditional methods for quantifying the long-range dependence of traffic based on its second-order statistics are not applicable. Long-range dependence and self-similarity play an important role in traffic engineering. We have recently shown that the generalized codifference can quantify the dependence structure of impulsive self-similar processes, such as high-speed network traffic. We propose an estimator for the generalized codifference and provide the conditions for it to be asymptotically consistent. We show that these conditions are satisfied for the EAFRP which is a process proposed for modeling high-speed network traffic. We provide simulation results to demonstrate the properties of the proposed estimator, and show how it can be a useful tool in maintaining fairness among users sharing limited network resources.