Internet traffic modeling and forecasting using non-linear time series model GARCH

Abstract

Forecasting of network traffic plays a very important role in many domains such as congestion control, adaptive applications, network management and traffic engineering. Characterizing the traffic and modeling are necessary for efficient functioning of the network. A good traffic model should have the ability to capture prominent traffic characteristics, such as long-range dependence (LRD), self-similarity, and heavy-tailed distribution. Because of the persistent dependence, modeling LRD time series is a challenging task. In this thesis, we propose a non-linear time series model, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) of order p and q, with innovation process generalized to the class of heavy-tailed distributions. The GARCH model is an extension of the AutoRegressive Conditional Heteroskedasticity (ARCH) model, has been used in many financial data analysis. Our model is fitted on a real data from the Abilene Network which is a high-performance Internet-2 backbone network connecting research institutions with 10Gbps bandwidth links. The analysis is done on 24 hours data of three different links aggregated every 5 minutes. The orders are selected based on the minimum modified Akaike Information Criterion (AICC) using Introduction to Time Series Modeling (ITSM) tool. For our model the best minimum order was found to be (1,1). The goodness of fit is evaluated based on the Q-Q (t-distributed) plot and the ACF plot of the residuals and our results confirm the goodness of fit of our model. The forecast analysis is done using a simple one-step prediction. The first 24 hrs of the data set are used as the training part to model the traffic; the next 24 hrs are used for performing the forecast and the comparison. The actual traffic data and the predicted traffic data is compared to evaluate the performance of the model. Based on the prediction error the performance metrics are evaluated. A comparative study of GARCH model with other existing models is performed and our results confirms the simplicity and the better performance of our model. The complexity of the model is measured based on the number of parameters to be estimated. From this study, the GARCH model is found to have the ability to forecast aggregated traffic but further investigation need to be conducted on a less aggregated traffic. Based on the forecast model developed from the GARCH model, we also intend to develop a dynamic bandwidth allocation algorithm as a future work.