
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 $\displaystyle mean$ $\displaystyle \mu = 3.$ And then off the phone an exponential amount of time with $\displaystyle rate$ $\displaystyle \lambda = 1.$
Formulate a Markov chain model $\displaystyle \{0,1,2,12\}$ where the states indicate who is on the phone.
$\displaystyle (a)$Find the stationary probabilities.
$\displaystyle (b)$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.