Two copier machines in the ISE department are maintained by a single repairman, Justin. Machine i functions for an exponentially distributed amount of time with rate i before it breaks down. The repair times for copier i are exponential with rate i. The repairman can only work on one machine at a time. Because machine 1 is more important than machine 2, so that the repairman will always work on machine 1 if it is down, regardless of the state of machine 2. (In case machine 2 is currently being repaired by the repairman when machine 1 fails, the repairman will instantaneously switch to machine 1. The repair of machine 2 will resume later.) Required:
a. Formulate a Markov chain model for this situation with state space {0, 1, 2, 12, 21).
b. Suppose that λ 1-1, μ1-2, A2-3, μ2-4. Find the stationary distribution.