An airline reservation system has two computers, only one of which is in operation at any given time. A computer may break down on any given day with probability p ∈ (0,1). There is a single repair facility which takes two days to restore a computer to normal. The facilities are such that only one computer at a time can be dealt with. Form a Markov chain that models the situation (make sure to keep track of the number of machines in operation as well as the status of the machine - if there is one - at the repair facility).
Find the stationary distribution.
What percentage of time (on average) are no machines operable?
What percentage of time (on average) is exactly one machine operable?