Due: Friday, March 27, 1998, 5:00pm, in the dropbox, Rosebrugh Building, 2nd Floor.

Question #1: Customers go to use a banking machine at the rate of 60 persons per hour during 9am - 12 noon, and at the rate of 90 persons per hour during 12 noon - 2pm. Each customer spend 0.5 minute in using the banking machine on average. Assume Poisson distributions for arrivals and an exponential distribution for the service time.

(a) (1.5 marks) What is the mean waiting time of a customer at the customer-banking machine system at 10am?

(b) (1.5 marks) What is the mean time a customer has to wait in the queue at 1pm?

Question #2: Cars arrive at a toll plaza in a Poisson manner. Currently, there are 2 electronic booths in operation, and each is capable of servicing 30 cars per hour. We assume the service time has an exponential distribution. It costs $18 per hour to operate a toll booth and waiting cost per car is $0.25 per minute spent at the plaza. It is predicted that the car arrival rate will increase to 60 cars per hour at the toll plaza in the near future.

(a) (1 mark) Will 2 booths in operation be enough for service in the near future? Why?

(b) (2.5 marks) Using the aid of the -n chart, determine the total system cost per hour if the number of booths in operation increases to 3 and 4.

(c) (1 mark) What will be the optimal number of booths in operation in the near future? Why?