Queueing
How long will this backlog take to clear? There is an equation for that
Little's Law is usually taught on a factory floor. It works just as well on a hiring pipeline, and it answers the question everybody is arguing about in one line.
A recruiting team has forty roles open and is filling six a month. Somebody asks how long it will take to clear. The answers in the room range from four months to a year, and everyone has a reason.
There is no need to argue. The question has an arithmetic answer, and it comes from the same equation that governs a queue of parts in front of a machine.
The equation, on a pipeline
Little’s Law says the average number of items in a system equals the average arrival rate multiplied by the average time each one spends there. Rearranged for the question actually being asked:
| L | Roles currently open | 40 |
|---|---|---|
| λ | New roles opening, a month | 4 |
| μ | Roles being filled, a month | 6 |
| Months to clear, at 2 net a month | 20 |
Illustrative figures. The backlog does not clear at six a month, it clears at the difference between six and four. That is the number everybody in the room forgot, and it turns a seven month answer into a twenty month one.
Twenty months, not seven. The pipeline is not being drained at six a month, because four more arrive while those six are being filled. What clears the backlog is the net rate, and the net rate is two.
That single correction is the most valuable thing this equation does, and it applies to every backlog anybody has ever tried to clear: support tickets, planning applications, invoices, claims. The rate at which you close things is not the rate at which the pile shrinks.
What it tells you that a plan does not
How close the pipeline is to never clearing. At six filled and four arriving the margin is two. If hiring slips to five a month, the clearance time goes from twenty months to forty. If it slips to four, it never clears at all, at any horizon, and the backlog is permanent regardless of effort. That cliff is invisible in a plan and obvious in the arithmetic.
Whether the fix is throughput or arrivals. Two a month net can be doubled by filling eight instead of six, or by opening two fewer roles a month. They are worth exactly the same to the clearance date and they usually cost wildly different amounts. The second one is almost never discussed, because reducing arrivals sounds like doing less, and here it is precisely as effective as hiring harder.
How long a role sits, without a survey. Turn the equation the other way. Forty open roles at six filled a month means the average role sits about six and a half months. If the team believes their time to hire is ninety days, one of those two numbers is wrong, and the equation is not the one that is guessing.
The conditions, which are real
Little’s Law is almost unreasonably robust. It needs no assumption about distributions, arrival patterns or service order. It needs two things.
The system has to be roughly in balance over the window you measure. Not necessarily stable, but not mid-collapse. Measure across a period where the backlog was exploding and you get an average that describes nothing.
Everything has to be counted the same way. This is the one that breaks it in practice. A role that was opened, frozen, reopened and rescoped is either one item or three, and it has to be the same choice in all three quantities. Most first attempts fail here rather than on the mathematics.
What to do with it
Write down all three numbers for your own backlog this week. How many are in it, how many arrive a month, how many leave. Most teams track the third and not the second, which is why the estimates in the room vary so wildly.
Then compute the net rate and say it out loud. It is usually a lot smaller than the throughput figure everyone has been quoting, and it is the only one that predicts a date.
And check the margin, not the answer. Twenty months is a fact. What matters more is that a small slip in throughput doubles it, because that is the difference between a plan that is tight and one that is fictional.