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Minimize the total cost of waiting line system

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An average of 40 customers per hour arrives at a bank branch office (Poisson arrival) and wait in a single line to be served by the first available teller. The average time for each teller to service a customer is 4 minutes (exponentially distributed). Each teller earns $160/day and the bank branch office assesses a waiting cost of $50/day that a customer waits in the system.

a. How many tellers should be on duty in this bank branch office to minimize the total cost of this waiting line system?

b. If the bank branch office is operating at its optimal configuration, determine the probability that at least one teller is busy.

c. If the bank branch office is operating at its optimal configuration, determine the average time spent in the system per customer.

d. If the bank branch office is operating at its optimal configuration, determine the average time spent in the waiting line per customer.

e. If the bank branch office is operating at its optimal configuration, determine the average number of customers in the service process.

Reference no: EM133030663

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