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 four minutes per customer, and average arrival rate is 36 customers per hour. It is expected that the new bank will have similar characteristics.
How many spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars?
A)10
B)11
C)12
D)13
E)14

Question

Quizplus · Accepted Answer

To find the number of spaces needed, we use the M/M/3 queue model. The arrival rate (λ) is 36 customers per hour, and the service rate (μ) is 15 customers per hour per teller (since 60/4 = 15). The traffic intensity (ρ) is λ/(3μ) = 36/(3*15) = 0.8. Using queuing theory tables or calculations for M/M/3, we find that to have a 96% probability of accommodating all waiting cars, 12 spaces are needed.

A Bank Is Designing a New Branch Office and Needs