A small barbershop, operated by a single barber, has room for at most two cus- tomers. Potential customers arrive at a Poisson rate of three per hour, and the successive service times are independent exponential random variables with mean
4 hour.
(a) What is the average number of customers in the shop?
(b) What is the proportion of potential customers that enter the shop?
(c) If the barber could work twice as fast, how much more business would he do?