Estimating heavy-tails in long-range dependent wireless traffic

Wireless traffic and packet-based traffic in general possess heavy-tail marginal distributions and long-range dependence (LRD). The tail parameter α of a heavy-tail distribution controls the variability of its realizations. Several traffic models, statistical test and resource management algorithms rely on the accurate estimation of the tail parameter. Conventional estimators for the tail parameter only work well when the data is short range dependent. In this paper we propose a new method to estimate the tail parameter from LRD data. This is achieved by utilizing the wavelet transform and extreme value theory. The algorithm is then applied to two stochastic processes that possess both heavy-tail marginal distributions and LRD. Results from our simulation show that the proposed method gives good estimates of α. We then estimate the tail parameter from a recently collected IEEE 802.11b traffic trace.