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

McNeese 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 M$/$M$/1($dedicated$)$ queues that each serve $\frac{}{2}$ arrivals

Scenario $2$: one M$/$M$/2($pooled$)$ queue that serves all $$ arrivals

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

The credit union is now considering staffing based on a service level of $95\%($that is$,$ a delay

probability of only five percent$).$ What is the optimal number of tellers to staff?

Considering the optimal staffing level $($derived above$),$ what is the average number of cus$-$

tomers in the system?

Considering the optimal staffing level, what is the average time $($minutes$)$ a customer spends

in the system?

$($a$)5$ minutes

$($b$)9$ minutes

$($c$)11$ minutes

$($d$)14$ minutes

Suppose the credit union is now considering staffing based on a service level of $99\%($largely

due to customer complaints$).$ What is the optimal number of tellers to staff now?

$($a$)3$ tellers

$($b$)4$ tellers

$($c$)5$ tellers

$($d$)6$ tellers