We discuss active prefetching from the paper "designs of high quality streaming proxy systems" by Chen, Wee and Zhang. The objective of active prefetching is to determine when to fetch which uncached segment  so that proxy jitter is minimized.  The paper assumes the media objects are segmented, the bandwidth is sufficient to stream the object smoothly and that each segment can be fetched in a unicast channel. Each media object has its inherent encoding rate - this is the playback rate and is denoted with an average value. Prior session data transmission rates are noted.
For a requested media object, if there are n segments cached in the proxy, then the objective is to schedule the prefetching of the n+1 th segment so that proxy jitter is avoided. At position x, the length  of the to be delivered data is L-x and the  Assuming Bs as the average playback rate and Bt as the average data transfer rate,  we avoid proxy jitter when the time to transfer  sum of all such remaining lengths L-x for each of the n segments and the n+1 segment over Bs is greater than the time for the the n+1 th segment over the average data transfer rate.
This is a way of saying that the prefetch time must not exceed the delivery time. From the equation above, the position can be varied such that the latest prefetch scheduling point is one where the arrival is just sufficient to meet demand. The buffer size would then reach minimum.
Determining the prefetching scheduling point should then be followed by a prefetching scheme and resource requirements.
If the media object is uniformly segmented, then we can determine the minimum buffer size required to avoid proxy jitter. There are three ranges which we are interested in. The first segment, the second segment and the segment upto the ratio Bs/Bt and the segments thereafter will have same minimum buffer size but they may or may not be able to avoid proxy jitter. The threshold for the number of segments we need to prefetch is Bs/Bt.