Suppose we broadcast a video using bandwidth S. A person may tune their television, which can receive any R/S fraction of the bandwidth, to this channel at any time in order to watch the video. We would like to minimize the delay between when they tune to the

channel and when they can start watching the video. Let m be the length of the video (in minutes). We can certainly guarantee a delay of at most m minutes simply by repeatedly broadcasting the video back-to-back; no matter when a person tunes in, they know the video will start within m minutes.

If the television has memory and can record from the channel into the memory while simultaneously displaying from the memory, we can do better. Of course, if we knew what video a person would request, we could store the entire video in the television memory and there would be no delay in showing the video. Assume that this is not possible and, in fact, that the television memory is empty when the person selects a video (i.e. tunes to a channel).

How small of a delay could we hope to achieve?