In mathematical queueing theory, Little's law (also result, theorem, lemma, or formula[1][2]) is a theorem by John Little which states that the long-term average number L of customers in a stationary 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.
The only requirements are that the system be stable and non-preemptive[vague]; this rules out transition states such as initial startup or shutdown.
In some cases it is possible not only to mathematically relate the average number in the system to the average wait but even to relate the entire probability distribution (and moments) of the number in the system to the wait.
[6][7] The form L = λW was first published by Philip M. Morse where he challenged readers to find a situation where the relationship did not hold.
However, because a store in reality generally has a limited amount of space, it can eventually become unstable.
If the arrival rate is much greater than the exit rate, the store will eventually start to overflow, and thus any new arriving customers will simply be rejected (and forced to go somewhere else or try again later) until there is once again free space available in the store.
[14] Little's law is widely used in manufacturing to predict lead time based on the production rate and the amount of work-in-process.
[15] Software-performance testers have used Little's law to ensure that the observed performance results are not due to bottlenecks imposed by the testing apparatus.