A drive thru car wash can process cars at a rate of one every five minutes. The manager notices that during one particular day it takes cars an average of about 30 minutes in line to reach the car wash. What was the average number of cars in line on that day?

Question

Quizplus · Accepted Answer

Using Little's Law, which states that the average number of items in a queuing system (L) is equal to the average rate at which items arrive (λ) multiplied by the average time an item spends in the system (W), we can calculate the average number of cars in line. Given that it takes 30 minutes on average for a car to reach the car wash and a car is processed every 5 minutes, the arrival rate is 1 car per 5 minutes. Therefore, L = λW = (1 car/5 minutes) * 30 minutes = 6 cars. This means the average number of cars in line was between 4 to 6 cars.

A Drive Thru Car Wash Can Process Cars at a Rate