A single repairperson looks after both machines 1 and 2. Each time it is repaired, machine i stays up for an exponential time with rate λi, i = 1, 2. When machine i fails, it requires an exponentially distributed amount of work with rate μi to complete its repair. The repairperson will always service machine 1 when it is down. For instance, if machine 1 fails while 2 is being repaired, then the repairperson will immediately stop work on machine 2 and start on 1.

What proportion of time is machine 2 down?