In this paper we investigate practical problems of fractal characterization of network tra c focusing on the estimation and interpretation of the Hurst parameter. The analysis is based on our measurement study of ATM WAN tra c. We point out that in order to use the fractal characterization framework in practice we are faced with various misleading e ects that can deceive our self-similarity tes...

As an important parameter to describe the sudden nature of network traffic, Hurst index typically conducts behaviors of both self-similarity and long-range dependence. With the evolution of network traffic over time, more and more data are generated. Hurst index estimation value changes with it, which is strictly consistent with the asymptotic property of long-range dependence. This paper prese...

The Hurst effect plays an important role in many areas such as physics, climate and finance. It describes the anomalous growth of range and constrains the behavior and predictability of these systems. The Hurst effect is frequently taken to be synonymous with Long-Range Dependence (LRD) and is typically assumed to be produced by a stationary stochastic process which has infinite memory. However...

Distributed denial-of-service DDoS flood attacks remain great threats to the Internet. To ensure network usability and reliability, accurate detection of these attacks is critical. Based on Li’s work on DDoS flood attack detection, we propose a DDoS detection method by monitoring the Hurst variation of long-range dependant traffic. Specifically, we use an autoregressive system to estimate the H...

The article is devoted to analysis of currency quotes behavior on the currency market by defining dynamic changes over time. The main tool of fractal analysis is the Hurst under the hypothesis of fractal market. For 17 major currency pairs on closing prices and the prices maximum-minimum the Hurst index is calculated by formula for the adjusted R/S analysis. Values at the currency markets of di...

Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Bro...

Time scale dependence on the working nature of wavelet analysis makes it a valuable tool for Hurst parameter estimation. Similar to other wavelet-based signal processing applications, the selection of a particular wavelet type and vanishing moment in wavelet based Hurst estimation is a challenging problem. In this paper, we investigate the best Daubechies wavelet in wavelet based Hurst estimati...

The intensity of long-range dependence (LRD) of the communications network traffic can be measured using the Hurst parameter. There are various estimators of Hurst parameter which differ in reliability of their results. Getting reliable estimator can help to improve traffic characterization, performance modelling, planning and engineering of the real networks. This paper deals with the comparis...

In this study we propose a bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Ro...

Optimal linear predictors can be utilised in ABR control algorithms for the management of self-similar network traffic. However, estimates of the Hurst parameter are required to generate these predictors, and uncertainity in these estimates results in a potential mismatch of the predictors to the traffic. When mismatched congestion control algorithms are used within the network, the impact on t...