A small barber shop, operated by a single barber, has two chairs. One of the chairs is for the haircut, and the other one is for the waiting customers. Duration of haircuts are independent Exponential random variables with mean 20 minutes. Inter-arrival times of customers are also Exponential but their rates are state-dependent: When the shop is empty the rate of customers entering to the shop is 3 per hour. The entering rate decreases to 2 per hour if only the service chair is occupied. Otherwise, when both chairs are occupied, the input rate is zero.

Find the steady-state distribution of your state variable.