Question: A help desk center is currently running with one operator who answers customer questions through telephone. If the line is busy customers have to wait until the operator can serve them. The customer calls follow a Poisson probability distribution with a mean arrival rate of 17 calls per hour. Service time follows an exponential probability distribution and on average it takes 3 minutes to assist a customer over the phone.

a. What is the mean service rate in terms of customer per hour?

b. What is the probability that the system is idle?

c. What is the average number of customers waiting to be served?

d. What is the average time a customer has to wait?

e. What is the probability that a customer will have to wait for a consultant?

f. The manager believes that customers are waiting too long. The recommendation is that change the system so that the average waiting time must be less than 30 seconds. Do you believe the company is already meeting these goals? If not, what is your recommendation?