## Markov chain

Two salesmen in an office are either on the phone or not.

Either salesmen is on the phone an exponential amount of time with $mean$ $\mu = 3.$ And then off the phone an exponential amount of time with $rate$ $\lambda = 1.$

Formulate a Markov chain model $\{0,1,2,12\}$ where the states indicate who is on the phone.

$(a)$Find the stationary probabilities.
$(b)$Suppose they upgrade their phone system so that a call to a busy line is forwarded to the other line and lost if the second line is busy. Find the new stationary probabilities.