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Long Range Dependent (LRD) network traffic does not behave like the traffic generated by the Poisson model or other Markovian models. From the network performance point of view, the main difference is that LRD traffic increases queueing delays due to its burstiness over many time scales. LRD behavior has been observed in different types and sizes of networks, for different applications (e.g., WWW) and different traffic aggregations. Since LRD behaviour is not rare nor isolated, accurate characterization of LRD traffic is very important in order to predict performance and to allocate network resources. The Hurst parameter is commonly used to quantify the degree of LRD and the burstiness of the traffic. In this paper we investigate the validity and effectiveness of the Hurst parameter. To this end, we analyze the UCLA Computer Science Department network traffic traces and compute their Hurst parameters. Queueing simulation is used to study the impact of LRD and to determine if the Hurst parameter accurately describes such LRD. Our results show that the Hurst parameter is not by itself an accurate predictor of the queueing performance for a given LRD traffic trace.