← Silokillersilokiller.com
Field guide

The laws of flow

Five laws explain most of why work gets stuck between silos. They hold in a factory, an IT department, a kitchen and a hospital. Each one comes with everyday examples and a small model you can play with.

  1. LittleWIP and lead time
  2. KingmanUtilization and variation
  3. BrooksAdding people
  4. GoldrattThe bottleneck
  5. ParkinsonWork expands
Law 1 · John Little, 1961

Little’s Law

Lead time = WIP ÷ Throughput
WIP
Work in progress: everything started but not finished.
Lead time
How long one item takes from start to finish.
Throughput
How many items are finished per unit of time.

The law holds for any stable system, on average. It sounds obvious, but it has a hard consequence. If you can’t finish things faster, the only way to shorten lead time is to have less going on at once.

Want faster delivery? Stop starting, start finishing.

Everyday

The coffee line

You walk into a café. Twelve people are ahead of you and the barista finishes about two drinks a minute.

12 ÷ 2 per min = 6 min

You can estimate your wait before you join the line, without a stopwatch.

Software / IT

The backlog

A team has 60 open tickets and closes about 10 a week. Every new ticket joins the back.

60 ÷ 10 per week = 6 weeks

Adding a “quick” request doesn’t make it quick. It waits behind 59 others.

Public sector

The permit office

An office has 900 building permits in process and approves 150 a month.

900 ÷ 150 per month = 6 months

Each case may only take a few hours of real work. The rest is waiting in piles.

Try it
60 10

Law 2 · John Kingman, 1961

Kingman’s formula

Wait ≈ (Ca² + Cs²) ⁄ 2 × u ⁄ (1 − u) × ts
Ca, Cs
Variation in when work arrives and in how long it takes.
u
Utilization: how busy the resource is, from 0 to 1.
ts
The time the work itself takes.

Little’s Law works with averages. Kingman explains what happens when reality varies. The middle term is the trap: it isn’t a straight line. As utilization approaches 100%, waiting time shoots toward infinity, and more variation makes it happen sooner.

Planning people or machines for 100% utilization guarantees long queues. Short lead times need slack.

Traffic

The motorway at rush hour

At 60% of capacity, one car braking hard changes nothing. At 95%, the same braking creates a queue that lasts an hour after the cause is gone.

IT operations

The fully booked team

A support team is planned at 100%. Then one urgent incident arrives. There is no slack to absorb it, so everything else slides, and the queue never quite recovers.

Manufacturing

The utilization bonus

Managers are rewarded for keeping machines busy. They run large batches and start everything early. Utilization looks great. Lead times and inventory explode.

Try it
85%

TypicalLow variationHigh variation
Law 3 · Fred Brooks, 1975

Brooks’s Law

Channels = n × (n − 1) ⁄ 2

In The Mythical Man-Month, Fred Brooks argued that adding people to a late software project makes it later. Two things happen at once:

Talk
Every new person adds lines of communication. The number of pairs grows much faster than the team.
Training
The experienced people have to stop and teach the new ones, so capacity drops before it rises.

Don’t throw people at a bottleneck. Reduce dependencies and protect the team you have.

Software

The rescue squad

A project is three months late, so five consultants join. For the next six weeks the original team spends its days explaining the system. The delay grows.

Restaurant

Too many cooks

A kitchen gets two extra cooks for a busy Saturday. They don’t know where anything is, they ask constantly and block the stove. Service gets slower.

Organization

The steering group

A decision needs sign-off from six departments. That is 15 pairs who need to agree. Add two more departments and it becomes 28.

Try it
5

Law 4 · Eliyahu Goldratt, 1984

The bottleneck rules

Goldratt’s The Goal introduced the Theory of Constraints. A system can never produce more than its narrowest step allows.

Before
Improving a step before the bottleneck only builds a bigger pile in front of it.
After
Improving a step after the bottleneck is waste. It will sit waiting for work.
At
An hour lost at the bottleneck is an hour lost for the whole system.

Find the bottleneck. Never let it stand still. Make everything else follow its pace. Then lift it.

The Goal

Herbie on the hike

In the book, a scout troop hikes in a line. The whole troop can only move as fast as Herbie, the slowest boy. Put him at the front and lighten his backpack, and everyone arrives sooner.

Travel

Airport security

The airline adds more check-in desks. Passengers get through check-in faster and then stand longer at security. The trip to the gate takes exactly as long.

Office

The one approver

Every purchase over a limit needs sign-off from one manager who travels a lot. Faster forms and smarter systems do nothing while that inbox is the narrowest step.

Try it: improve a step and see what the system delivers

Law 5 · Cyril Northcote Parkinson, 1955

Parkinson’s Law

Work expands to fill the time available for it. Parkinson wrote it as satire about bureaucracy, but anyone who has had a long deadline knows it’s true.

In flow terms, generous deadlines and big batches create hidden waiting. Short cycles, small pieces of work and a steady rhythm keep attention on what creates value.

Shrink the box: smaller pieces, shorter cycles, a fixed rhythm.

Meetings

The hour-long meeting

The calendar default is 60 minutes, so meetings take 60 minutes. Book 25 and most of them finish in 25.

Budgets

December spending

Units that don’t use their budget lose it next year. So money that wasn’t needed in October gets spent in December.

Projects

Padded estimates

Everyone adds safety margin to their task. Then each task starts late and uses its full margin, so the project is still late.

Putting it together

Three rules for flow

Kingman · Parkinson

Make batches smaller

Smaller pieces of work vary less and wait less. They also give feedback sooner.

Little · Goldratt

Limit work in progress

Set a cap on what is started. Queues shrink, lead time falls, and the bottleneck becomes visible.

Kingman · Brooks

Plan for slack

Don’t plan people for 100%. Spare capacity is what absorbs variation and keeps lead times short.

A note on the curves: waiting time near full utilization isn’t technically exponential. It grows as 1 ÷ (1 − u), which goes to infinity at 100%. Communication channels in Brooks’s Law grow with the square of team size, not exponentially. Both are bad enough.