Customers arrive at a carnival ride at rate . The ride takes an exponential amount of time with rate , but when it is in use, the ride is subject to breakdowns at rate ˛. When a breakdown occurs all of the people leave since they know that the time to fix a breakdown is exponentially distributed with rate ˇ. (i) Formulate a Markov chain model with state space f1; 0; 1; 2; : : :g where 1 is broken and the states 0; 1; 2; : : : indicate the number of people waiting or in service. (ii) Show that the chain has a stationary distribution of the form .1/ D a; .n/ D b n for n  0.