Prediction of long-range-dependent discrete-time fractional Brownian motion process

In this paper, we propose an approach to linear minimum-mean-square-error (MMSE) prediction of a discrete-time fractional Brownian motion (dt-fBm) traffic arrival process, a long range dependent traffic model that well represents the characteristics of observed Internet traces. Linear multi-step forecasts of the future values of the dt-fBm process and the Corresponding prediction errors are first derived. We then proposed sliding window finite-memory predictors suitable for the practical implementation. Simulations using real-life traffic traces are performed to compare the proposed finite-memory dt-fBm predictors with fractional auto-regressive integrated moving average predictors and an empirical predictor. We find that the multi-scale sliding window dt-fBm predictor achieves best performance on forecasting the future traffic level.