A service facility can hold up to six customers who arrive according to a Poisson process with a rate of λ customers per hour. Customers who arrive when the facility is full are lost and never make an attempt to return to the facility. Whenever there are two or fewer customers in the facility, there is only one attendant serving them. The time to service each customer is exponentially distributed with a mean of 1/μ hours. Whenever there are three or more customers, the attendant is joined by a colleague, and the service time is still the same for each customer. When the number of customers in the facility goes down to 2, the last attendant to complete service will stop serving. Thus, whenever there are 2 or less customers in the facility, only one attendant can serve.
a. Give the state-transition-rate diagram of the process.
b. What is the probability that both attendants are busy attending to customers?
c. What is the probability that neither attendant is busy?