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...

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.

. 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?