Optimally scheduling video-on-demand to minimize delay when sender and receiver bandwidth may differ

We establish tight bounds on the intrinsic cost (either minimizing delay d for fixed sender and receiver bandwidths, or minimizing sender bandwidth for fixed delay and receiver bandwidth) of broadcasting a video of length m over a channel of bandwidth S in such a way that a receiver (with bandwidth R), starting at an arbitrary time s, can download the video so that it can begin playback at time s + d.Our bounds are realized by a simple just-in-time protocol that partitions the video into a fixed number of segments, partitions the sender bandwidth into an equivalent number of equal bandwidth subchannels, and broadcasts each segment repeatedly on its own subchannel. The protocol is suitable for the broadcast of compressed video and it can be implemented so that video information is packaged into discrete fixed length packets incurring only a modest overhead (measured in terms of increased delay).Our primary contribution is a lower bound on the required delay that applies to all protocols. This lower bound matches the behavior of our just-in-time protocol in the limit as the number of segments approaches infinity, provided the video compression satisfies some uniform upper bound. For a fixed number of segments, our protocol is optimal within a broad class of protocols, even if the video is compressed arbitrarily.