What is the implied service rate at a bank teller's window if demand is 26 customers per hour and the bank staffs are 3 tellers with an average utilization of 80%?
A) Less than 5 customers per hour
B) More than 5 but less than or equal to 10 customers per hour
C) More than 10 but less than or equal to 15 customers per hour
D) More than 15 but less than or equal to 20 customers per hour

Question

Quizplus · Accepted Answer

Utilization is defined as the ratio of time a server is busy to the total time they are available. In this case, the average utilization of 80% means that on average, each teller is busy serving customers for 48 minutes out of every hour (since there are 3 tellers, the total available time is 180 minutes per hour). This means that there are 12 minutes per hour that each teller is not serving customers, and therefore the combined implied service rate for the 3 tellers is (26 customers per hour) / (3 tellers) = 8.67 customers per hour per teller. Taking into account the 80% utilization, each teller can actually serve (8.67 customers per hour) / 0.8 = 10.84 customers per hour, which is closest to option C.

What Is the Implied Service Rate at a Bank Teller's