(a) Carlton Savings and Loan has one drive-in service window. The arrival of cars
occurs at a mean rate of 10 cars per hour. The mean service rate is 12 cars per
hour.
Use this information to answer the problems that follow. Work to 2 decimal
places.
(i) What is the probability that the service facility is idle? [2]
(ii) What is the average number of cars in the system? [2]
(iii) What is the probability that there are at least two cars in the system? [2]
(iv) How long, on average, would a customer have to wait before being
attended to? Give your answer in minutes. [2]

(b) Discuss the tradeoff between the cost of increasing service capacity and the cost of keeping customers waiting. [3]

(c) If the arrival rate of a single-channel queuing system is halved, will the average
time a unit spends waiting for service halve? Justify your answer. [4]