Community Bank is planning to expand its drive-in facility. Observations of the existing single-teller window reveal that customers arrive at an average rate of 10 per hour, with a Poisson distribution, and that they are given FCFS service, with an average transaction time of 5 minutes. Transaction times have a negative exponential distribution. Community Bank has decided to add another teller and to install four remote stations with pneumatic tubes running from the stations to the tellers, who are located in a glassed-in building. The cost of keeping a customer waiting in the system is represented as a $5-per-hour loss of goodwill. The hourly cost of a teller is $10.
a. Assume that each teller is assigned two stations exclusively, that demand is divided equally among the stations, and that no customer jockeying is permitted. What is the average number of customers waiting in the entire system?
b. If, instead, both tellers work all the stations and the customer waiting the longest is served by the next available teller, what is the average number of customers in the system?
c. What hourly savings are achieved by pooling the tellers?