Estimation Peer-to-Peer Network’s Bursty-Traffic Parameters

Abstract

Abstract: Data traffic traces are known to be bursty with long range dependence, due to large and wildly fluctuating file sizes of data transfers. This is especially true in Peer-to-peer network data traffic. The exact self-similarity model of long range dependence can pose analytical and practical problems at very small and very large time lags. In our model, the time series of the traffic trace (referred to as the signal) is assumed to possess an autocovariance profile corresponding to exact self-similarity over a range of lags, {k}, satisfying M < k < L. At lower lags, exact self-similarity may breakdown, or additive moving average type noise (inaccuracies) may corrupt the autocovariances. At very high lags, far beyond the number of observed samples, the autocovariance structure is irrelevant and may be assumed to be infinite summable. Therefore, L can be as large as desired. Applications of such a model are discussed. The mean, variance, and the Hurst parameter of the signal, as well as the autocovariances of any independent zero mean moving average type additive noise are assumed to be unknown. A class of linear combinations of sample average second order statistics of noisy observations is constructed. They are unbiased estimates of their corresponding expectations. These expectations are shown to be devoid of the noise statistics. The ratio of two such expectations eliminates the signal variance. The ratio is a well behaved monotonic function of the only remaining unknown, the Hurst parameter. Equating the ratio of these expectations to the ratio of the corresponding sample averages from the noisy observations leads to a very easily solvable nonlinear equation with a unique root. The other parameters of bursty traffic are easily estimated with the help of the estimated Hurst parameter. The result and related issues are discussed. Key-Words: Peer-to-peer network traffic, Traffic modeling and analysis, Self-similarity, Hurst parameter, and Parameter estimation