Data stream mining algorithm, such as the popular classifier implemented by Hoeffding tree algorithm (HTA) is acclaimed to be able to handle high speed data streams that potentially amounts to infinity. It emerges as a hot research area recently on applying HTA in different applications that require real-time responses and fast decision making. In particular, we discovered the effect of Internet traffic on Hoeffding bound (HB) which is one of the key performance indicators in HTA stream mining is related to fluctuation. The error of HB oscillates with the fluctuation of data rate in realtime data stream which causes frequent HTA tree reconstruction, and in turn that has an adverse effect on the overall prediction accuracy. From the experiment in this paper, we observe that the HB is related to HTA's accuracy. And data streams extracted from Internet traffic exhibit fluctuations of highly variable data rates, they influence significantly on HB value. A simple and effective mechanism without the need of arbitrating or intervening with the traffic data rates is proposed in this paper for smoothing the HB fluctuation. From our simulation, the results show that the HB fluctuation is smoothed, and the accuracy in HTA is stabilized. It is believed that the proposed technique can subside the problem of stream mining in network environment where traffic is fluctuating.