1 Staffing with the M/M/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 (equivalent to a vi = 6 per hour) and the average arrival rate has been 1 = 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 X/2 arrivals Scenario 2: one M/M/2 (pooled) queue that serves all X arrivals A queuing analysis was conducted on cach scenario, and the results are as follows: Scenario 1 Scenario 2 Utilization factor p=0.50 p=0.50 Mean number in the queue ELI=0,50 customers EL1 = 0.37 customers For Scenario 1, what is the average time in line minutes) for a customer, EW.)? (Hint: remember to use the correct arrival rate detailed in the first bullet point above.) O a. 10 minutes b. 5 minutes C. 8.7 minutes d. 20 minutes Clear my choice The credit union is now considering adding a third teller (in the form of an M/M/3) with the goal of solving the following argument: arg min $15s + S11E (L) *E(23) Recall the term "arg min" or "argument of the minima" gives the solution s such that the function (s) = $158 + $11E|L,) attains its minimum value. Before solving this problem, what is the utilization p for 8 = 3? (Hint: remember that and u were given in the opening scenario.) a. 0.33 b. 0.4 C. 0.67 d. 0.5 Using your answer to the above question, what is the average number in the queue E [L] for $ = 3? a. 0.85 customers b. 2.03 customers c. 0.07 customers d. 1.02 customers Using your answer to the above question, determine the total cost $ (8) = $158 + $11E (L) for 8 = 3. a. $54.35 b. $45.77 c. $56.22 d. $67.33