can someone please show me step by step how to solve this continuous time markov chain problem?

thanks

A video system consists of a server and a cache, and the most popular videos are stored in the cache. New videos are added to the server according to a Poisson process with rate its. Each video spends an exponential amount of time T, ~ exp(p._,) in the server. After this time, a video is moved to the cache with probability o. (we assume that or percent of the videos are popular and thus moved to the cache), it is removed from the system entirely with probability [3 (we assume that [3 percent of the videos are unpopular), or, it stays on the server. Once a video is in the cache, it remains there for an exponential amount of time Tc ~ exp(pc). After this time, a video is moved back to the server with probability y (y is percent of the cached videos turned out not to be that popular), or, it stays in the cache. The cache has limited storage capacity and can only store N videos. If a video is eligible to go into the cache when it is full, it stays in the server for an additional exponential amount of time T, ~ exp(p._,) and so on as above. 1) Model the system as a CTMC and draw the state diagram. Him: The state of this CTMC is a vector of two variables. 2) What fraction of videos must wait in order to get a spot in the cache, expressed in terms of the stationary distribution? Note; There is no need to nd the stationary distribution in closed form. 3) What is the stability condition for this system