Customers arrive at Mike's barber shop according to a Poisson process with rate λ customers per hour. Unfortunately Mike, the barber, has only five chairs in his shop for customers to wait when there is already a customer receiving a haircut. Customers who arrive when Mike is busy and all the chairs are occupied leave without waiting for a haircut. Mike is the only barber in the shop, and the time to complete a haircut is exponentially distributed with a mean of 1/μ hours.
a. Give the state-transition-rate diagram of the process.
b. What is the probability that there are three customers waiting in the shop?
c. What is the probability that an arriving customer leaves without receiving a haircut?
d. What is the probability that an arriving customer does not have to wait?