Sample frameDay 185·Operations · Measurement

Morning. Three numbers describe every queue you've ever stood in, and you already hold two of them.

Operations.

Little's Law

5 min read·Apply by lunch

The question

How many pieces of work are sitting open in your business this morning — live deals, unbilled projects, unanswered tickets, orders not yet shipped — and how many new ones arrived in an average week? Divide the first by the second before you read any further.

The idea

John Little trained as a physicist at MIT and became one of the founding figures of management science there. In 1961 he published a short paper in Operations Research under the flattest title in the literature: A Proof for the Queuing Formula: L = λW. The formula wasn't new. What Little supplied was the proof, and the proof is what makes it usable, because it holds under conditions almost nothing else in queueing theory survives. The average amount of work in a system equals the average rate at which work arrives, multiplied by the average time each piece stays. It doesn't care whether arrivals are steady or lumpy, whether you serve first-come-first-served or by whoever shouts loudest, or how many people are working the queue. It asks one thing only: that the system is roughly stable across the window you measure, meaning about as much came out as went in. Grant it that and you never have to measure all three numbers. Count what's open, count what arrives, and the time a customer waits falls out of the arithmetic — no stopwatch, no survey, no argument about whose estimate is fairer.

The framework

01
Why measure the number that's hardest to get?
Work in progress is a count you can take this morning: open deals in the CRM, jobs on the board, tickets unresolved, invoices unpaid. Arrival rate is a count you can take from any four-week window: new enquiries, new orders, new tickets, divided by four. Both are cheap and both are already recorded. Flow time — the number your customer actually experiences and the one nobody tracks — is the expensive one to measure directly, which is exactly why you shouldn't try. Take the two cheap numbers and stop arguing about the third. What to do about the answer comes later; today the job is to know it.
02
The units and the boundary have to match.
The law is arithmetic, so it punishes sloppiness. All three numbers must refer to the same flow unit, the same boundary and the same time base. If you count open deals as work in progress, then arrivals must be new deals rather than new leads, and the answer comes back in whatever period you counted arrivals in. Draw the boundary explicitly — where a unit enters the count, where it leaves — before you count anything. Half the disputes about a flow-time number aren't disputes about flow time at all; they're disputes about where somebody put the line.
03
What happens when the window isn't stable?
Little's proof needs the system roughly in balance across the window you measure. If your open work doubled during the four weeks you were counting, the number you get describes nothing much. That isn't a reason to abandon the law; it's a reason to take all three numbers on the same day each month and read the direction rather than the point. Work in progress creeping up while arrivals hold flat means your flow time is quietly lengthening, and customers will feel that a month before any dashboard mentions it. It doubles as a lie detector for quoted lead times.

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