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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 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 ^ 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 [Lg] = 0.50 customers E [Lg = 0.37 customers

1:- For Scenario 1, what is the average time in line (minutes) for a customer?

2:- Derive the average time (minutes) spent in the system for Scenario 1.

3;-Now calculate the average time in line (minutes) for Scenario 2, Comparing to question one, what did you find?

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

1. 5 minutes
2. 9 minutes
3. 11 minutes
4. 14 minutes

5. 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?

6:-Considering the optimal staffing level, what is the average number of customers in the system?

7. Considering the optimal staffing level, what is the average time (minutes) spent in the system?

1. 5 minutes
2. 9 minutes
3. 11 minutes
4. 14 minutes

1 Statling with the M/M/ / Queue 2. Derive the average time (minctis) vorot in the pyotem for Scenario. 1 ete, what itel you finul? (a) S minutere (1) 9 misante (c) 11 minitrs (it) 14 timentes 1 (a) 5 minute (b) 9 tinuten (c) 11 minatew (d) It tuinution 1 Staffing with the M/M/s Queue MeNeese 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 seracster is their bukiest time, with incoming freshinen and transfer students opening accounts. On average, it takes a teller E[T]=10 minutes to saccessiully open an accotmt and the average arrival rate bas 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 MeNecse's upper-administration, the manager of the credit union is considering two passible scenarios for the service layout: - Scenario 1: two M/M/1 (dedicated) quetaes that each serve /2 arrivals - Scenario 2: one M/M/2 (pooled) queve that serves all d arrivals A queuing analysis was conducted on each soenario, and the results are as follows: 1. Fot Scenario 1, what is the average time in line (minates) for a catatotaer? 2. Derive the average time (minutes) spent in the system for Scenario 1. 3. Now calculate the average time in line (minutes) for Scenario 2. Comparing to question one, what did you find? 4. 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 5. 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? 6. Considering the optimal staffing level, what is the average number of customers in the system? 7. Considering the optimal staffing level, what is the average time (minutes) spent in the system? (a) 5 minutes (b) 9 minutes (c) 11 minutes (d) 14 minutes 1 Statling with the M/M/ / Queue 2. Derive the average time (minctis) vorot in the pyotem for Scenario. 1 ete, what itel you finul? (a) S minutere (1) 9 misante (c) 11 minitrs (it) 14 timentes 1 (a) 5 minute (b) 9 tinuten (c) 11 minatew (d) It tuinution 1 Staffing with the M/M/s Queue MeNeese 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 seracster is their bukiest time, with incoming freshinen and transfer students opening accounts. On average, it takes a teller E[T]=10 minutes to saccessiully open an accotmt and the average arrival rate bas 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 MeNecse's upper-administration, the manager of the credit union is considering two passible scenarios for the service layout: - Scenario 1: two M/M/1 (dedicated) quetaes that each serve /2 arrivals - Scenario 2: one M/M/2 (pooled) queve that serves all d arrivals A queuing analysis was conducted on each soenario, and the results are as follows: 1. Fot Scenario 1, what is the average time in line (minates) for a catatotaer? 2. Derive the average time (minutes) spent in the system for Scenario 1. 3. Now calculate the average time in line (minutes) for Scenario 2. Comparing to question one, what did you find? 4. 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 5. 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? 6. Considering the optimal staffing level, what is the average number of customers in the system? 7. Considering the optimal staffing level, what is the average time (minutes) spent in the system? (a) 5 minutes (b) 9 minutes (c) 11 minutes (d) 14 minutes