Today  we continue our discussion on streaming proxy design. We were reviewing the assumptions for building an analytical model. The first assumption is that the popularity of media objects follows a zipf distribution. The second assumption was that the request arrival interval  process occurs at a known average rate and independent of time. The third assumption  was that the clients view the media objects completely. The first assumption gives us a probability set  pi. The second assumption gives us a sampling process where the sum of pi equals 1. The third assumption gives us a mean arrival rate as lambda times pi. We also reviewed the added definition of startup length. This is the percentage alpha of the full length of the media object. And Beta is the percentage of the total cache space reserved for all the startup lengths.
This help us determine the startup ratio. To build the model, we consider the ideal case that the cache space is allocated to cache the most popular objects, then the startup lengths of the first t most popular objects can remain in the reserved portion of the cache. This can be extended to imply that the rest of the cache is used for the q most popular objects beyond their startup length. Therefore the delayed startup ratio can be expressed as the sum of the mean arrival rate of the t+1th to the Nth media object over that of all the N media objects.

#codingexercise
GetOddNumberRangeSumCubeRootPowerSixteen) (Double [] A)
{
if (A == null) return 0;
Return A.OddNumberSumCubeRootPowerSixteen();
}