There are four possible states in total: no machine is down, only machine 1 is down, only machine 2 is down, and both machines are down. Formulate and solve the balance equations based these four state
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 i 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? Then compute the probability that machine 2 is down.)
There are four possible states in total: no machine is down, only machine 1 is down, only machine 2 is down, and both machines are down. Formulate and solve the balance equations based these four states.
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