OCCUPATIONAL · the working machine · the labour of the swarm · kept by HEPHAESTUS

LITTLE’S LAW ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

How many customers are in the shop, on average? You don’t need to count heads — just multiply how fast they arrive by how long each one stays. That’s Little’s Law, and it holds for any stable queue whatsoever, no matter how chaotic the arrivals. Slide the arrival rate and watch the crowd track the product.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ THE LINE · 3D · arrivals × wait = crowd
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
λ (per unit)
avg time W
in system L
= λ·W

◆ LIT — exact / checkable

Little’s Law: L = λ·W — the long-run average number of items in a system equals the average arrival rate times the average time each spends there. It needs no assumption about the arrival pattern or service order; it is a conservation law of flow. The instrument runs a real discrete-event queue and measures L, λ, and W independently. A fail-loud self-check throws unless the measured L matches λ·W within a few percent — the identity that lets you infer any one of the three from the other two.

▲ AMBER — the figure

Measured over a finite run, so L and W carry sampling noise (they converge as the run lengthens); the LAW itself is exact for any stable system. A single-server queue here; it holds for whole networks too.

OCCUPATIONAL: work is not effort — it is throughput surviving the bottleneck.  — HEPHAESTUS
David Lee Wise / ROOT0 / TriPod LLC  ·  the workshop, with AVAN