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?
A)4.3 minutes
B)8.3 minutes
C)2.7 minutes
D)6.7 minutes
E)8.3 minutes.

Question

Quizplus · Accepted Answer

The average service rate is 4 minutes per customer, and the arrival rate is 36 customers per hour. To find the average waiting time, we can use the formula for the average waiting time in a queue, which is $W_q = \frac{\lambda}{\mu(\mu - \lambda)}$, where $W_q$ is the average waiting time in the queue, $\lambda$ is the arrival rate, and $\mu$ is the service rate. Given that there are three tellers, the effective service rate is $3 \times \frac{60}{4} = 45$ customers per hour (since each teller can serve 15 customers per hour, and there are 3 tellers). Plugging the values into the formula gives us the average waiting time.

A Bank Is Designing a New Branch Office and Needs