Little's law calculator.

Worked example

Customers arrive at 10 per hour and stay 30 minutes (0.5 hour) on average. L = 10 x 0.5 = 5 customers in the shop on average. Reverse it: if on average 2 customers are at the counter and 10 arrive per hour, each spends W = 2 / 10 = 0.2 hour (12 minutes) there. Both examples appear in the Little's law reference.

How it works

Little's law (J. D. C. Little, 1961) says that for a stable system the long-run average number of items equals the long-run average arrival rate times the average time each item spends inside. It holds whatever the arrival or service distribution and whatever the service order, as long as the system is stationary and you measure arrivals and time over the same boundary.

Common uses: work in progress = throughput x cycle time, requests in flight = requests per second x latency, and people in a queue = arrivals x wait. In an overloaded system that keeps growing, the averages are not stationary and the law does not apply to them.

FAQ

What is Little's law?

L = lambda x W: the average number of items in a stable system equals the average arrival rate times the average time an item spends in it.

Do arrivals have to be random for Little's law to hold?

No. It does not depend on the arrival or service distribution, only on the system being stable over the period you measure.

Which arrival rate do I use if some items are turned away?

Use the rate of items that actually enter the system (the effective arrival rate), not the rate of attempts.

How do I use Little's law for web servers?

Requests in flight = requests per second x average latency in seconds. The requests-per-second to concurrency calculator applies this directly.