Today we continue on our discussion of the streaming proxy design. We were finding the upper bound on the byte hit ratio and the startup ratio in the ideal case. Let us look into some analytical results to give us an understanding of these ratios in the ideal case. Given a total of 10000 original media objects where we use a cache with a size of 20% of the total object size, we initialize the number of objects possible with the average length of objects to be 2000. Skew ratio is set at 0.47 and the startup length percentage is set at 5%. It is observed that the decrease in the byte hit ratio is much slower than the decrease of the delayed startup ratio when B increases.  This implies that if we reduce the byte hit ratio by a small measure, we can trade for a significant large reduction in the delayed startup ratio.  This has been an objective of the proxy design principles. To find this tradeoff, the partial derivative of the upper bound on the delay startup ratio with respect to the reserved cache space percentage is calculated.  This yields the change in the delayed startup ratio. Similarly the partial derivative of the upper bound on the byte hit ratio with respect to the reserved cache space percentage yields the change in the byte hit ratio. From a relation with the change in delayed startup ratio  over the change in byte hit ratio, it can be shown that the delta delay over the delta hit  is always greater than 1 when alpha and Beta are less than 50%.
#codingexercise

GetOddNumberRangeSumCubeRootSumEighteen (Double [] A)

{

if (A == null) return 0;

Return A.OddNumberSumCubeRootSumEighteen();

}