Video caching provides an effective solution to the problem of increasing power consumption due to Internet infrastructure. The present work is the extension of [1] where we provided an approximate solution for optimal caching size. In this paper, we classify videos in N sets based on estimated arrival rate and analyze the power consumption of the video service. We analytically obtain the value of threshold for arrival rate to decide which videos to cache. We derive lower and upper bounds for caching size and show that the optimal caching size lies between these bounds. Further, we obtain a condition for the existence of lower and upper bounds. We perform simulations to analyze the performance of these bounds with optimal caching size. © 2014 IEEE.