A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive up teller service. The drive up service will have three tellers and a single waiting line. At another branch of the bank in a similar setting, the average service time for drive up tellers is 4 minutes per customer and average arrival rate is 36 customers per hour. It is expected that the new bank will have similar characteristics. What is the average time that a customer would have to wait in line before being served?
Question 9 options:
4.3 

8.3 

2.7 

6.7 

None, each customer would be served immediately. 
From the problem descriptions, we can extract the following information.
Service time = 4 minutes per customer
Service rate µ = 1/service time = ¼ = 0.25 customers per minute. The arrival rate is given in hour, so we need to convert the service rate in customers per hour. Service rate µ = 0.25*60 = 15 customers per hour
Arrival rate λ = 36 customers per hour
The average waiting time in the queue Wq= Lq/λ, where Lq= number of customers in the queue
Lq can be obtained using the formula as well as the table. To obtain the value of Lq through the table, we need the utilization factor.
Utilization factor = λ/µ = 36/15 = 2.4
For utilization factor 2.4 and number of servers 3, value of Lq = 2.589
Wq = 2.589/36 = 0.071916667 hour = 4.315 minutes
Correct answer: 4.3
Table for your reference:
Hope the answer will help you. Thank you.
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