Question

Given an arrival rate of 20 people per hour, a dropout rate of 2 people per hour, and a departure rate of 6 people per hour, what is the length of the queue?

Answer 1

The length of the queue grows by 12 people per hour, calculated by subtracting the combined departure and dropout rates from the arrival rate.

Step-by-step explanation:

To calculate the length of the queue, we need to consider the net rate of change of people in the queue. The net rate is calculated by subtracting the rate at which people leave (departure rate + dropout rate) from the arrival rate. Thus, the net rate = arrival rate - (departure rate + dropout rate) = 20 people/hour - (6 people/hour + 2 people/hour) = 12 people/hour. Therefore, over the course of an hour, the length of the queue will increase by 12 people. Assuming there are no other factors affecting the queue size, this is the rate at which the queue will grow per hour.