$1$ Staffing with the $\frac{M}{M}\frac{?}{s}$ Queue

MoNeese is determining the staffing level for their credit union located within the university, and

has recently hired two tellers $($servers$).$ The beginning of the fall semester is their busiest time, with

incoming freshmen and transfer students opening accounts. On average, it takes a teller $E[T]=10$

minutes to successfully open an account and the average arrival rate has been $=6$ per hour. As

always, we use the exponential distribution as a reasonable approximation for both the interarrival

and service times. After meeting with McNeese's upper$-$administration, the manager of the credit

union is considering two possible scenarios for the service layout:

Scenario $1$: two $\frac{M}{M}\frac{?}{1}($dedicated$)$ queues that each serve $\frac{}{2}$ arrivals

Scenario $2$: one $\frac{M}{M}\frac{?}{2}($pooled$)$ queue that serves all $$ arrivals

A queuing analysis was conducted on each scenario, and the results are as follows:

Derive the average time $($minutes$)$ spent in the system for Scenario $1.$

Now calculate the average time in line $($minutes$)$ for Scenario $2.$ Comparing to question

one, what did you find?

Considering Scenario $2,$ what is the average time $($minutes$)$ spent in the system?

$($a$)5$ minutes

$($b$)9$ minutes

$($c$)11$ minutes

$($d$)14$ minutes