A major banking institution, Best Bank, plans to open a new branch office in Little-town. Preliminary estimates suggest that two tellers (and teller windows) should be provided, but this decision now awaits further analysis.
Marketing surveys indicate that the new Little-town bank will attract enough business that customers requiring teller service will enter the bank at the rate of about one per minute on the average. Thus, the average time between consecutive customer arrivals is estimated to be one minute.
No parking is available near the bank, so a special parking lot for bank customers only will be provided. A parking lot attendant will be on duty to validate each customer's parking before he or she leaves the car to enter the bank. This validation process takes at least 0.5 minutes, so the minimum time between consecutive arrivals of customers into the bank is 0.5 minutes. The amount by which the interarrival time exceeds 0.5 minutes is estimated to have an exponential distribution with a mean of 0.5 minutes.
Therefore, the total interarrival time has a translated exponential distribution with a mean of (0.5 + 0.5) = 1.0 minute. (A translated exponential distribution is just an exponential distribution with a constant added.) Based on past experience in other branch offices, it is known that the time required by a teller to serve a customer will vary widely from customer to customer, but the average time is about 1.5 minutes. This experience also indicates that service time has approximately an Erlang distribution with a mean of 1.5 minutes and a shape parameter of k = 4, which provides a standard deviation of 0.75 minute (half that for an exponential distribution with the same mean).
These data suggest that two tellers should be able to keep up with the customers quite well. However, management wants to be sure that customers will not frequently encounter a long waiting line and an excessive wait before receiving service. Therefore, computer simulation will be used to study these measures of performance.
a. Use the Queueing Simulator with 5,000 customer arrivals to estimate the usual measures of performance for this queueing system if two tellers are provided.
b. Repeat part a if three tellers are provided.
c. Now perform some sensitivity analysis by checking the effect if the level of business turns out to be even higher than projected. In particular, assume that the average time between customer arrivals turns out to be only 0.9 minutes (0.5 minutes plus a mean of only 0.4 minutes). Evaluate the alternatives of two tellers and three tellers under this assumption.
d. Suppose you were the manager of this bank. Use your computer simulation results as the basis for a managerial decision on how many tellers to provide? Justify your answer.