# On average, 100 customers arrive per hour at Gotham City Bank

August 31, 2017

Question
On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of 2 minutes to serve a customer. Interarrival and service times are exponentially distributed. The bank currently has 4 tellers working. The bank manager wants to compare the following two systems with regard to the average number of customers present in the bank and the probability that a customer will spend more than 8 minutes in line.
• System 1: Each teller has his or her own line (and no moving between lines is permitted). Arriving customers are equally likely to choose any teller.
• System 2: All customers wait in a single line for the first available teller.

If you were the bank manager, which system would you prefer?

Use the attached Excel templates that are appropriate for this problem showing the formation of the model and solution to the problem.

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