14&15

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 u = 6 per hour) 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 X/2 arrivals Scenario 2: one M/M/2 (pooled) queue that serves all X arrivals A queuing analysis was conducted on each scenario, and the results are as follows: Scenario 1 Scenario 2 Utilization factor p=0.50 p=0.50 Mean number in the queue E[L] = 0.50 customers E(L) = 0.37 customers What is the probability that there is more than one customer in the system (waiting phuis service), in the form P(Z > 1), for Scenario 12 a. 0.25 OD 0.75 c: 0.5 od 0.1 Calculate the average time in line minutes) for Scenario 2 (Hitz remember to use the correct arrival rate detailed in the second bullet polut above) a 37 minutes Ob 10 minutes Oc 74 minutes o 5 minutes