This paper studies and analyses the behavior of the Long-Range Dependence in network traffic after classifying traffic flows in aggregated time series. Following Differentiated Services architecture principles, the generic Quality of Service applications that requirements and use the transport control protocol, a basic classification criterion of time series is established. Using the fractal theory, the resulting time series are analyzed. The Hurst exponent is estimated and used as a measure of traffic burstiness and Long-Range Dependency in each traffic class. The traffic volume per class is also measured. The study uses traffic traces collected at the core switch at the Electric Engineering Department at Universidad de Santiago de Chile in different periods of network activity.