Two machines, equal rates
Normalise the two-machine repair model when \lambda=\mu, and find the stationary probability that both machines are operating.
Worked answer (click to show)
When \lambda=\mu the unnormalised weights are (1,2,2), which sum to 5. The stationary distribution is (1/5,2/5,2/5). Both machines are operating in state 0, which has probability 1/5.