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 X = 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 /2 arrivals • Scenario 2: one M/M/2 (pooled) queue that serves all A 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 customersEL] = 0.37 customers Considering s*, what is the average number of customers in the system, E [L]? a. 1.07 customers b. 2.51 customers C. 1.37 customers d. 3.01 customers
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 X = 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 /2 arrivals • Scenario 2: one M/M/2 (pooled) queue that serves all A 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 customersEL] = 0.37 customers Considering s*, what is the average number of customers in the system, E [L]? a. 1.07 customers b. 2.51 customers C. 1.37 customers d. 3.01 customers
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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 (equivalent to a µ = 6 per hour) and the average arrival
rate has been A = 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 /2 arrivals
• Scenario 2: one M/M/2 (pooled) queue that serves all A 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
Considering s*, what is the average number of customers in the system, E [L]?
O a.
1.07 customers
O b. 2.51 customers
O c.
1.37 customers
O d. 3.01 customers](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff348f17e-e34d-4178-ab5f-f91eb7326134%2Fc3a32523-0f32-499e-b2db-24192496ba14%2Fk295uq_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 µ = 6 per hour) and the average arrival
rate has been A = 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 /2 arrivals
• Scenario 2: one M/M/2 (pooled) queue that serves all A 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
Considering s*, what is the average number of customers in the system, E [L]?
O a.
1.07 customers
O b. 2.51 customers
O c.
1.37 customers
O d. 3.01 customers
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