The recent years brought a phenomenal development of Internet. It is, therefore, important to find some ways to improve the performances. The first step in this direction is the characterization and modeling of the network traffic. It has been tested that the network traffic behaves like a self-similar process, while packets interarrivals time possess the long-range dependence property. In particular, we model them by using fractional Brownian motion and fractional Gaussian noise, respectively. Note that, the former is just the cumulative sum of the latter. By using these concepts, the traffic characterization reduces to the estimation of one value: the Hurst parameter. Numerous methods exist to evaluate this parameter. Nevertheless, a few studies take account of the inherent non-stationarity present in real data. For short samples, the stationarity hypothesis might hold. But for larger samples, this is hardly the case. As an example, for network traffic, the day cycle shows non-stationarity. By not considering the non-stationarity, an inaccurate or even inappropriate estimation may result. Our objective in this thesis is to test the robustness of several techniques such as aggregated variance method, rescaled range method, and wavelets method, in presence of a set of non-stationarity trends. We study the estimators on a known signal generated using Hosking, Davies and Harte method, or wavelets-based synthesis. We add various deterministic non-stationarity trends to the original signal. We considered polynomial, power-law, sinusoidal, and level-shift trends. Results help analyze the behavior of the estimators. All the simulations are carried out using Matlab. We show that, depending on the trend, the estimators react differently. We have also used real data to verify the effectiveness of estimators. Results confirm the observations that we have made with lab data. In particular, we show that the wavelets method provides several flaws. Especially, its results must be carefully analyzed when the data is non-stationary.