Real-world IP network traffic is susceptible to external and internal factors such as new internet service integration, traffic migration, internet application, etc. Due to these factors, the actual internet traffic is non-linear and challenging to analyze using a statistical model for future prediction. In this paper, we investigated and evaluated the performance of different statistical prediction models for real IP network traffic; and showed a significant improvement in prediction using the rolling prediction technique. Initially, a set of best hyper-parameters for the corresponding prediction model is identified by analyzing the traffic characteristics and implementing a grid search algorithm based on the minimum Akaike Information Criterion (AIC). Then, we performed a comparative performance analysis among AutoRegressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA), SARIMA with eXogenous factors (SARIMAX), and Holt-Winter for single-step prediction. The seasonality of our traffic has been explicitly modeled using SARIMA, which reduces the rolling prediction Mean Average Percentage Error (MAPE) by more than 4% compared to ARIMA (incapable of handling the seasonality). We further improved traffic prediction using SARIMAX to learn different exogenous factors extracted from the original traffic, which yielded the best rolling prediction results with a MAPE of 6.83%. Finally, we applied the exponential smoothing technique to handle the variability in traffic following the Holt-Winter model, which exhibited a better prediction than ARIMA (around 1.5% less MAPE). The rolling prediction technique reduced prediction error using real Internet Service Provider (ISP) traffic data by more than 50\% compared to the standard prediction method.

本文研究实际IP网络流量的统计模型预测，使用滚动预测方法得到显著的预测性能改进。通过评估自回归移动平均模型、带时序因子的自回归移动平均模型、带外生因子的自回归移动平均模型、Holt-Winter模型等方法，以及结合SARIMAX方法使用SARIMA模型等手段，分析其表现差异与影响因素，并得出SARIMAX方法下滚动预测均方误差为6.83％的最佳预测结果。

基于统计轮廓模型的互联网流量预测实证研究