Service Management 7th Edition by James Fitzsimmons, Mona Fitzsimmons

Exercise 38

Last National Bank is concerned about the level of service at its single drive-in window. A study of customer arrivals during the window's busy period revealed that, on average, 20 customers per hour arrive, with a Poisson distribution, and they are given FCFS service, requiring an average of 2 minutes, with service times having a negative exponential distribution.
a. What is the expected number of customers waiting in queue?
b. If Last National were using an automated teller machine with a constant service time of 2 minutes, what would be the expected number of drive-in customers in the system?
c. There is space in the drive for 3 cars (including the one being served). What is the probability of traffic on the street being blocked by cars waiting to turn into the bank driveway?
d. Last National is considering adding tellers at the current drive-in facility. It has decided on $5 per hour as the imputed cost of customer waiting time in the system. The hourly cost of a teller is $10. The average arrival rate of customers has reached 30 per hour. On the basis of the total hourly cost of tellers and customer waiting, how many tellers do you recommend? Assume that with use of pneumatic tubes, tellers can serve customers as though there were a single queue.