The TSA $($Transportation Security Administration$)$ at a major airport is evaluating a new policy for screening its customers.

Current Policy $($Policy $1)$:

The TSA manages three independent queues, with one sever responsible for each. The customers arrive at the system and are immediately divided equally, likely to each separate queue.

$($Hint: For a system with $"$n$"$ independent queues and arrival rate to the system is

$,$ the arrival rate to each queue is

$)$

New Policy $($Policy $2)$:

The new policy that TSA is preparing is to pool all three servers and manage customers' waiting with a single queue. This is equivalent to a multi$-$server waiting system with three servers $($m $=3).$

You are hired as an Operations analyst to evaluate both policies. The TSA has provided you with the following data. The inter$-$arrival time between customers arriving at the system and service time for each customer by a server follows an exponential distribution with a mean of $5$ and $12$ minutes, respectively.