Question: Company S currently has three counters, each staffed by a single employee, and a single first-come- first-serve queue for all customers to join. You

Company S currently has three counters, each staffed by a single employee, and a single first-come- first-serve queue for all customers to join. You think that the current system is wrong. You would like to redesign the queues so that there is a dedicated queue and a dedicated server for each customer type (type 1, type 2, and type 3). No customers cross between servers. Type 1 clients arrive at a rate of 19 per hour. Type 2 clients arrive at a rate of 15 per hour. Type 3 clients arrive at a rate of 6 per hour. Each of the three serving employees takes an average of 3 minutes to complete a transaction. Assume inter-arrival and service times follow an exponential distribution. Find the total time in the existing system (waiting and service time). Round your answer to 4 decimal places.

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