Long Horizon End-to-End Delay Forecasts: A Multi-Step-Ahead Hybrid Approach

A long horizon end-to-end delay forecast, if possible, will be a breakthrough in traffic engineering. This paper introduces a hybrid approach to forecast end-to-end delays using wavelet transforms in combination with neural network and pattern recognition techniques. The discrete wavelet transform is implemented to decompose delay time series into a set of wavelet components, which is comprised of an approximate component and a number of detail components. Thus, it turns the problem of long horizon delay forecasting into a set of shorter horizon wavelet coefficient forecasting problems. A recurrent multi-layered perceptron neural network is applied to forecast coefficients of the wavelet approximate component, which represents the trend of the delay series. The k-nearest neighbors technique is used to forecast coefficients of the wavelet detail components, which reflect the burstiness of background traffic. The proposed approach has been verified in both simulation and over real heterogeneous networks showing promising results in terms of averaged normalized root mean square error. In addition, when compared to some existing and well known approaches it presents the superior performance.