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Network traffic measurement studies have shown the presence of self similar behavior in both local area and wide area traffic traces. In this study we investigated the magnitude of the self similarity behavior of network traffic and its Hurst measurement, H. Our study has revealed several characteristics of H based on the network traffic changes. From the finding, H can be used as traffic load indicated only if the sampling size is large. On the other hand for a smaller sampling size, H can be used to indicate the change in traffic pattern. However network traffic does not always exhibit self similarity property. Activities such as peer-to-peer can steer the traffic to lose this property.