Problem $10-23($Algo$)$

You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows for the three different classes of service. Each class of service would be separate, with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. People for one class of service arrive every $3$ minutes and arrival times are exponentially distributed $($the standard deviation is equal to the mean$).$ It takes $15$ minutes to service each customer, and the standard deviation of the service times is $8$ minutes. You assign $6$ cashiers to each type of service.

a$.$ On average, how long will each line be at each of the cashier windows?

Note: Round your intermediate calculations to $4$ decimal places and final answer to $3$ decimal places.

Average number of customers in line

b$.$ On average, how long will a customer spend in the bank $($assume they enter, go directly to one line, and leave as soon as service is complete$)?$

Note: Round your intermediate calculations to $4$ decimal places and final answer to $3$ decimal places.

Time spent by a customer

minutes