# On average, 100 customers arrive per hour at Gotham City Bank - 94982

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## shri21

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On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two minutes to serve a customer. Inter-arrival and service times are exponentially distributed. The bank currently has four 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 eight 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? System 1 M/M/4 (Four servers and Four queues) Data Arrival rate (l) 25 Service rate (m) 30 Number of servers(s) 4 System 2 M/M/4 (Four servers and One queue) Data Arrival rate (l) 100 Service rate (m) 30 Number of servers(s) 4
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