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.

Q1) Find the total number of people waiting in the queues under the new system.

Round your final answer to 4 decimal places.

Q2) Find the average wait time (in minutes) in the new system for the Type 1 clients.

Q3) Find the total time (in minutes) in the new system for the Type 2 clients.

Q4) Find the average service time (in minutes) in the existing system.