1. The problem statement, all variables and given/known data A barbershop has two barbers: an experienced owner and an apprentice. The owner cuts hair at the rate of 4 customers/hour, while the apprentice can only do 2 customers/hour. The owner and the apprentice work simultaneously, however any new customer will always go first to the owner, if the latter is available. The barbershop has waiting room for only 1 customer (in case both barbers are busy), any additional customers are turned away. Suppose customers walk by the barbershop at the rate of 6 customers/hour. 1. Construct a continuous-time Markov chain for this problem and explain your assumptions. 2. Write down the infinitesimal generator G of this chain. 3. Using your model nd the proportion of time the apprentice is busy cutting hair. 2. Relevant equations 3. The attempt at a solution 1. For the Markov chain, I don't know how to do it here but I guess is P(0,1)=1,P(1,2)=0.6,P(2,3)=0.5;P(1,0)=0.4,P(2,1)=0.5,P(3,2)=1 2. I attached a picture of my markov chain. 3. Then, for question 3, I calculated the corresponding equilibrium distribution and got: π0 =0.6, π1=0.6, π2=−0.6, π3=−0.6 which leads to the proportion to π2+ π3=0 So I guess there must be something wrong. I appreciate any hint!