Today we continue our discussion on streaming proxy design. We were discussing the ideal case for the analytical model. We said that it corresponds to when the cache is always used to populate the most popular media objects. In this case, the delayed startup ratio was the ratio of the mean arrival rate of the t+1th to Nth media object over that of all of the media objects. Representing this in terms of the skew ratio,we notice that the upper bound is when skew factor is not equal to 1. We can now find the byte hit ratio in this case.  Again, we find the upper bound by using t = Beta .U / Alpha where U is the the total cache size divided by the average length of objects. t was the number of most popular objects sorted by popularity whose segments within the startup length would fill the reserved portion of the cache size. The max delay startup ratio occurs when skew factor is not equal to 1.  We can express this in the same ratio of arrival rates as the definition of the delay startup ratio.
Next to derive an upper bound on the byte hit ratio in the ideal case, let us consider the misses when the object is accessed for the first time.  The byte hit ratio in this case is expressed as 1 minus a ratio where the numerator is the startup length of the t+1th to the Nth objects times the average arrival rate  and that of the beyond-startup-length of the q+1 th to the Nth media objects times the average arrival rate and the denominator is the full length of all the N media objects times the average arrival rate.
The reason we subtract it from one is because we want the remaining that corresponds to the non-reserved cache space.
#codingexercise

GetOddNumberRangeSumCubeRootPowerEighteen) (Double [] A)

{

if (A == null) return 0;

Return A.OddNumberSumCubeRootPowerEighteen();

}