Predicting bursts and serious deteriorations in Internet traffic is important. It enables service providers and users to define robust quality of service metrics to be negotiated in service level agreements (SLA). Traffic exhibits the heavy tail property for which extreme value theory is the perfect setting for the analysis and modeling. Traditionally, methods from EVT, such as block maxima and peaks over threshold were applied, each treating a different aspect of the prediction problem. In this work, the r-largest order statistics method is applied to the problem. This method is an improvement over the block maxima method and makes more efficient use of the available data by selecting the r largest values from each block to model. As expected, the quality of estimation increased with the use of this method; however, the fit diagnostics cast some doubt about the applicability of the model, possibly due to the dependence structure in the data. © 2011 IEEE.