Understanding Queuing Theory: Average Queue Size and Waiting Time Explained

[Chadlee88]

hey, I was reading my lecture notes and I'm stuck trying to understand this example.

A checkout operator can deal with 10 customers per hour. We assume it takes exactly 6 minutes to service each customer.

The shoppers arrive in groups of 10, every hour. (Average arrival rate of 10/hr)

Q1. How many people are in the queue on average?
A. 4.5

Q2. What's the average waiting time in the Queue?
4.5 * 6 = 27 minutes.

Could someone please explain how these answers are derived.

Thanks :)

 

[Valkarie]

Answer 1: The average number of people in the queue is derived by calculating the rate of arrival and the rate of service. Since there are 10 customers arriving every hour and the checkout operator can serve 10 customers per hour, the average number of people in the queue is (10 arrivals per hour - 10 services per hour) / 2 = 4.5 people in the queue on average. Answer 2: The average waiting time in the queue is calculated by multiplying the average number of people in the queue (4.5) by the average time it takes to serve each customer (6 minutes). Therefore, the average waiting time in the queue is 4.5 * 6 = 27 minutes.