Question

Suppose your company has a simple service process. Customers arrive at the rate of 48 per hour, and they are served at the rate of 60 per hour. What is the utilization, average waiting time for service to begin, and the average number of people in the system?

A) Utilization: 80%, Average Waiting Time: 0.2 hours, Average Number of People: 12
B) Utilization: 20%, Average Waiting Time: 0.5 hours, Average Number of People: 15
C) Utilization: 80%, Average Waiting Time: 0.5 hours, Average Number of People: 12
D) Utilization: 20%, Average Waiting Time: 0.2 hours, Average Number of People: 15

Answer 1

Utilization: 80%, Average Waiting Time: 0.2 hours, Average Number of People: 12.

Step-by-step explanation:

Utilization: Utilization is defined as the ratio of the average service rate to the average arrival rate. In this case, the average arrival rate is 48 customers per hour, and the average service rate is 60 customers per hour. Therefore, the utilization is 60/48 = 1.25 or 125% (option A and C are incorrect).

Average waiting time for service to begin: The average waiting time is calculated using Little's Law, which states that the average number of customers in the system multiplied by the average time a customer spends in the system is equal to the arrival rate. The average number of customers in the system is the utilization (1.25), and the arrival rate is 48 customers per hour. Therefore, the average waiting time for service to begin is 48/1.25 = 38.4 minutes, which is 0.64 hours (option D is incorrect).

Average number of people in the system: Again, using Little's Law, we can calculate the average number of people in the system. The arrival rate is 48 customers per hour, and the average waiting time for service to begin is 38.4 minutes or 0.64 hours. Therefore, the average number of people in the system is 48 * 0.64 = 30.72, which is 31 people (option B is incorrect).

Therefore, the correct answer is option A: Utilization: 80%, Average Waiting Time: 0.2 hours, Average Number of People: 12.