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Measurements of high-speed network traffic have shown that traffic data exhibits a high degree of self-similarity. Traditional traffic models such as AR and ARMA are not able to capture this long-range-dependence making them ineffective for the traffic prediction task. In this paper, we apply the fractional ARIMA (F-ARIMA) model to predict one-step-ahead traffic value at different timescales. F-ARIMA has the ability to capture both the short- and long-range dependent characteristics of the underlying data. We present a simplified adaptive prediction scheme to reduce the F-ARIMA computational complexity. The performance of the proposed F-ARIMA prediction model is tested on four different types of traffic data: MPEG and JPEG video, Ethernet and Internet. We also apply the F-ARIMA prediction model to a dynamic bandwidth allocation scheme. The results show that the performance of F-ARIMA outperforms the AR model. They also show that the prediction performance depends on the traffic nature and the timescale.