Question

In the library, students arrive randomly at the help desk, which is staffed by 3 employees (all of them answer inquiries from students). The time required for inquiry varies from student to student. Arrivals have been found to follow a Poisson process (i.e., exponentially distributed inter-arrival times), and the service times follow an exponential distribution. The average arrival rate is 14 students per hour, and the average service rate is 13 students per hour. What is the utilization of the help desk? Note: 1. Provide your answer as a percentage, but do not include the % mark. 2. Keep two decimal places.

Answer 1

The utilization of the help desk is 108%.

Step-by-step explanation:

To find the utilization of the help desk, we need to calculate the ratio of the average arrival rate to the average service rate. The utilization is given by the formula: Utilization = Arrival rate / Service rate.

Given that the average arrival rate is 14 students per hour and the average service rate is 13 students per hour, we can calculate the utilization as: Utilization = 14 / 13 = 1.08.

Therefore, the utilization of the help desk is 108%.