A single server queuing system has a finite capacity K$.$ The customers arrive according to a PP$(\backslash$lambda $)$ and demand iid Exp$(\backslash$mu $)$ service times. The server is subject to failures and repairs as follows: the server serves for an Exp$(\backslash$theta $)$ amount of time and then fails. Once it fails all the customers in the system go away instantaneously. The server takes an Exp$(\backslash$alpha $)$ time to get repaired. While the server is down, no new customers are allowed to enter the system. If the system is full, the arriving customers depart immediately without getting served.