← Notes

The cost a correct hold pushes into the queue

Every item a control holds for good reason becomes review work, and Little's law says how long that work sits still.

Discussions about automated controls tend to focus on the errors: what got through and shouldn't have, what was blocked for no reason. The correct hold — the item the control stopped with good reason — is counted as a success, and then disappears.

It doesn't disappear. It becomes work. An item held correctly has to be read by someone, judged, and either returned to the flow or discarded. Until that happens it is work sitting still, and the time it sits has a formula. Little's law states that "the long-term average number of customers (L) in a stationary system is equal to the long-term average effective arrival rate (λ) multiplied by the average time that a customer spends in the system (W)".

Rearranged, it answers the question that matters: average wait time is queue size divided by service rate. If the review queue holds ten items and whoever reviews gets through two a week, each item waits five weeks — regardless of the order they are reviewed in, because the law does not depend on the service discipline.

Two consequences follow. The first is that tightening a control has a cost even when it is right: more correct holds means more queue, and more queue means more waiting for everyone in it. The second is that review capacity, not control precision, is what determines whether held material circulates again — and that capacity is the variable almost never sized alongside the control.

A note on the source: the reference above is an encyclopedia with an editorial standard, not the original publication. The primary article is behind a subscription and was not opened.