For questions $4$ to $12$: Imagine that you are an investor who has to decide between two types of businesses $($e$.$g$.,$ restaurants$)$ to make your investment. Both businesses have the same average arrival time and the same average service time, but their distributions are different:

Business $1$: Customers arrive at a rate of $1$ per minute and it takes an average of $0\mathrm{.}5$ minutes to provide the service to the customer. There is only one server. Interarrival times and service times are exponential.

Business $2$: Customers arrive at a rate of $1$ per minute and it takes an average of $0\mathrm{.}5$ minutes to provide the service to the customer. There is only one server. Interarrival time and service time are neither exponentially nor deterministic. The interarrival time has a standard deviation of $0\mathrm{.}5$ minutes and the service time a standard deviation of $0\mathrm{.}5$ minutes as well.

Flag question: Question $4$

Question $41$ pts

What type of queueing model should be used for Business $1?$

Group of answer choices

MM$1$

MD$1$

GG$1$

MM$2$

None of the other answers

Flag question: Question $5$

Question $51$ pts

What type of queueing model should be used for Business $2?$

Group of answer choices

MM$1$

MD$1$

GG$1$

MM$2$

None of the other answers

Flag question: Question $6$

Question $61$ pts

What is the service rate for Business $2?$

Group of answer choices

$0\mathrm{.}5$ customers$/$minute

$1$ customers$/$minute

$1\mathrm{.}5$ customers$/$minute

$2$ customers$/$minute

None of the other answers

Flag question: Question $7$

Question $71$ pts

How many customers $($on average$)$ are waiting in line to be served in Business $1?$

Group of answer choices

$0\mathrm{.}3125$

$0\mathrm{.}5$

$0\mathrm{.}75$

$1$

None of the other answers

Flag question: Question $8$

Question $81$ pts

How many customers $($on average$)$ are waiting in line to be served in Business $2?$

Group of answer choices

$0\mathrm{.}25$

$0\mathrm{.}3125$

$0\mathrm{.}50$

$0\mathrm{.}8125$

None of the other answers

Flag question: Question $9$

Question $91$ pts

What is the average waiting time $($in min$)$ in line of customers in Business $1?$

Group of answer choices

$0\mathrm{.}25$

$0\mathrm{.}31$

$0\mathrm{.}5$

$1$

None of the other answers

Flag question: Question $10$

Question $101$ pts

What is the average waiting time $($in min$)$ in line of customers in Business $2?$

Group of answer choices

$0\mathrm{.}25$

$0\mathrm{.}31$

$0\mathrm{.}5$

$1$

None of the other answers

Flag question: Question $11$

Question $111$ pts

What is the average waiting time $($in min$)$ in the system of customers in Business $1?$

Group of answer choices

$0\mathrm{.}5$

$0\mathrm{.}75$

$0\mathrm{.}81$

$1\mathrm{.}0$

None of the other answers

Flag question: Question $12$

Question $122$ pts

$(2$ points$)$ You want to compare the utilization of both servers. Which of the following statements is true?

Group of answer choices

The utilization of the server in Business $1$ is higher than that of server in Business $2.$

The utilization of the server in Business $2$ is higher than that of server in Business $1.$

Both servers have the same utilization.

We cannot conclude based on the information available.