rel:: [[Resilient Software Engineering MOC#Queuing Theory]]
# Little's Law
> [!wikipedia]
> In [queueing theory](https://en.wikipedia.org/wiki/Queueing_theory "Queueing theory"), a discipline within the mathematical [theory of probability](https://en.wikipedia.org/wiki/Probability_theory "Probability theory"), **Little's result**, **theorem**, **lemma**, **law**, or **formula** is a theorem by [John Little](https://en.wikipedia.org/wiki/John_Little_(academic) "John Little (academic)") which states that the long-term average number _L_ of customers in a [stationary](https://en.wikipedia.org/wiki/Stationary_process "Stationary process") system is equal to the long-term average effective arrival rate _λ_ multiplied by the average time _W_ that a customer spends in the system.
>
> [wikipedia source](https://en.wikipedia.org/wiki/Little%27s_law)
$
L = λW
$
| | |
| --- | ------------------------------------------ |
| $L$ | number of queued items |
| $λ$ | long-term mean arrival rate |
| $W$ | average queue time |