A small company has two identical servers that are running at the same time. The time until either server fails is exponentially distributed with a mean of 1/λ. When a server fails, a technician starts repairing it immediately. The two servers fail independently of each other. The time to repair a failed server is exponentially distributed with a mean of 1/μ. As soon as the repair is completed the server is brought back on line and is assumed to be as good as new.
a. Give the state-transition-rate diagram of the process.
b. What is the fraction of time that both servers are down?