In this work we propose an analytic framework for managing the optimal bandwidth required for a smooth playback of a stored video streaming service. First, we argue that the mean buffering delay in the node is minimized if the video packets are paced to a fixed interval at the beginning of the transfer. Second, we argue that an appropriate level of bandwidth has to be maintained so that neither buffer-underflow nor buffer-overflow occurs, via which a smooth playback of video stream can be maintained. From the numerical evaluation, we found that the paced packet stream experiences smaller delay than the original random packet stream. Next, we computed a range of bandwidth for a video stream so that neither buffer-underflow nor buffer-overflow occurs, and we showed that paced packet stream requires smaller bandwidth than the original random packet stream.