Today  we continue our discussion on streaming proxy design. We were saying that the reality is that cache size may be bounded. We may not be able to cache the number of segments required for continuous delivery of a media object if there are lots of media objects. One way to overcome this was to determine the priority of media objects. Given a higher priority in reducing proxy jitter,  the proxy can choose to evict segments of the object whose cached data length is less than its prefetching length. This will allow the prefetching of the cached segment to be always in time.  Even if the segments of popular objects are evicted, the overall proxy jitter reduces at the cost of a little byte hit ratio. Thus we have seen that the byte hit ratio can be traded for less proxy jitter.
This conflict between improving the byte hit ratio and reducing the proxy jitter helped the authors to revise the principle of designing a better proxy based on proxy jitter. They noted that segment based proxy caching strategies always perform well in the byte hit ratio but not so well in the delayed startup ratio. This is further explained when evaluating the adaptive lazy segmentation based scheme.
We also look at the tradeoff between Byte hit ratio and delayed startup ratio. We could see some conflicting interests in this tradeoff from the previous discussion but we build an analytical model now.  This analytical model is based on the following assumptions:
1) The popularity of the objects follow a Zipf like distribution
2) The request arrival interval process follows a Poisson distribution with a mean arrival rate lambda.
3) The clients view the requested objects completely. This is to simplify the analysis and does not affect the conclusion.
After we build the model, we will evaluate it with analytical results.
Then we review the author's improved Adaptive-Lazy Segmentation Strategy.
The assumption 1) describes the probability set pi in terms of the fraction of fi to the total fi. fi is the inverse of i raised to the power theta and i can vary from 1 to N the total number of objects. Theta is the skew factor and is positive.
The assumption 2) describes the sampling process as independent and sampled from the aggregate arrival interval process based on probability set pi where the sum of pi equals 1.
The assumption 3) lets us calculate the mean arrival rate as lambda times pi.
In addition to these assumptions, the following definitions make it easier to calculate the delayed startup ratio.
The startup length is the length of the beginning part of an object.  If this part is cached, then there is no startup delay. Let alpha be this percentage of the full object length. Let Beta be the percentage of the total cache space reserved for caching the startup lengths of objects.