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.

Waiting Line Problem$\_$Final.jpg

Flag question: Question $27$

Question $271$ pts

What is the arrival rate value to the system in customers per hour?

Group of answer choices

$0\mathrm{.}2$

$0\mathrm{.}083$

$12$

$3$

$5$

Flag question: Question $28$

Question $281$ pts

What is the service rate value of a server in customers per hour?

Group of answer choices

$0\mathrm{.}083$

$5$

$0\mathrm{.}2$

$12$

$1\mathrm{.}667$

Flag question: Question $29$

Question $291$ pts

What is the arrival rate value to a queue in customers per hour under Policy $1?$

Group of answer choices

$4$

$0\mathrm{.}028$

$1\mathrm{.}667$

$0\mathrm{.}067$

$1$

Flag question: Question $30$

Question $301$ pts

What is the utilization of a server under Policy $1?$

Group of answer choices

$0\mathrm{.}139$

$0\mathrm{.}6$

$0\mathrm{.}333$

$0\mathrm{.}417$

$0\mathrm{.}8$

Flag question: Question $31$

Question $311$ pts

What is the average time a customer spends in a queue in minutes under Policy $1?$

Group of answer choices

$18$

$48$

$8\mathrm{.}571$

$6$

$1\mathrm{.}935$

Flag question: Question $32$

Question $321$ pts

What is the average number of customers in a queue under Policy $1?$

Group of answer choices

$0\mathrm{.}4$

$0\mathrm{.}054$

$18$

$0\mathrm{.}238$

$3\mathrm{.}2$

Flag question: Question $33$

Question $331$ pts

What is the average time a customer spends in the system in minutes under Policy $1?$

Group of answer choices

$30$

$60$

$20\mathrm{.}571$

$18$

$13\mathrm{.}935$

Flag question: Question $34$

Question $341$ pts

What is the average number of customers in the system under Policy $1?$

Group of answer choices

$4$

$0\mathrm{.}06$

$3$

$1\mathrm{.}5$

$12$

Flag question: Question $35$

Question $351$ pts

What is the utilization under Policy $2?$

Group of answer choices

$0\mathrm{.}8$

$0\mathrm{.}139$

$0\mathrm{.}333$

$0\mathrm{.}417$

$0\mathrm{.}6$

Flag question: Question $36$

Question $361\mathrm{.}5$ pts

What is the average time a customer spends in the queue in minutes under Policy $2?$

Group of answer choices

$4\mathrm{.}771$

$3\mathrm{.}806$

$13\mathrm{.}3$

$2\mathrm{.}051$

$8\mathrm{.}093$

Flag question: Question $37$

Question $371$ pts

What is the average number of customers in the queue under Policy $2?$

Group of answer choices

$23\mathrm{.}857$

$2\mathrm{.}660$

$0\mathrm{.}171$

$0\mathrm{.}761$

$0\mathrm{.}405$

Flag question: Question $38$

Question $381$ pts

What is the average time a customer spends in the system in minutes under Policy $2?$

Group of answer choices

$25\mathrm{.}300$

$14\mathrm{.}051$

$20\mathrm{.}093$

$16\mathrm{.}771$

$15\mathrm{.}806$

Flag question: Question $39$

Question $391$ pts

What is the average number of customers in the system under Policy $2?$

Group of answer choices

$1\mathrm{.}398$

$0\mathrm{.}053$

$1\mathrm{.}005$

$5\mathrm{.}060$

$0\mathrm{.}020$

Flag question: Question $40$

Question $401$ pts

The average customer waiting time in the queue under Policy $1$ is $\_\_\_\_\_\_\_\_$ Policy $2.$

Group of answer choices

greater than or equal to

less than

less than or equal to

greater than

equal to

Flag question: Question $41$

Question $411$ pts

Which components of the average waiting time in the queue formula are affected when transitioned from Policy $1$ to Policy $2?$

Group of answer choices

Service Time effect, Utilization effect

Variability effect

Utilization effect, Variability effect

Service Time effect, Utilization effect and Variability effect

Service Time effect, Variability effect

Flag question: Question $42$

Question $421$ pts

Which policy would you recommend to TSA?

Group of answer choices

Neither Policy $1$ nor Policy $2$

Policy $1$

Policy $2$

Both Policy $1$ and Policy $2$