Little's Law

349. Little's Law

𝐿 = 𝜆 𝑊

Where:

$𝐿$ : average number of items (customers, tasks, etc.) in the system
$𝜆$ : average arrival rate (items per unit time)
$𝑊$ : average time an item spends in the system

Example

Bank where customers arrive at an average rate of 10 customers per hour ( $𝜆 = 10$ customers / hour). Each customer spends an average of 12 minutes in the bank ( $𝑊 = \frac{12}{60} = 0.2$ hours).

𝐿 = 𝜆 𝑊 = 10 \times 0.2 = 2

On average, there are 2 customers in the bank at any given time (includes being served and those waiting in line)