Suppose customers arrive one at a time, completely at random, at an ATM at the rate of 5 per hour. Customers take an average of 8 minutes to complete their transactions. That is, the service rate is 7.5 per hour.

Historical data have shown that both the inter-arrival and service times closely follow some exponential distribution. Customers queue up on a first-come, first-served basis. Assume that there is only one ATM.

(a) What is the average waiting time in this M/M/1 queue? 

(b) What is the average queue length? 

(c) Based on the average waiting time and the average queue length, is it necessary for the bank to add another ATM machine? Why?