1 One queue, two cameras — census vs flow standards
Every waiting-time standard watches the same thing: a queue with referrals arriving at rate λ and patients leaving when treated. The standards differ only in where the camera points.
Census standards — RTT & DM01
A monthly photograph of the stock. Everyone still waiting is counted every month until they leave, so long waiters accumulate in the metric. RTT: 92% of the list under 18 weeks. DM01: <1% of the list over 6 weeks. You can run this standard because a register (the PTL) exists to photograph.
Flow standards — cancer CWT
A stopwatch at the exit. Each completed pathway is scored once, in the month it completes — then it leaves the metric forever. FDS: 80% told within 28 days. 62-day: 85% treated within 62 days. There is no published stock at all — only the timed cohort.
2 The unifying model — converting between the two
In steady state the two cameras are linked by two facts, and together they form a mental conversion recipe:
① Little’s Law: list size = demand × mean wait (L = λ·W)
② Memoryless queue: if selection is roughly random (not strict FIFO), both cameras
read the same number: % within T = 1 − e−T/W
So any standard — census or flow — can be translated into a mean wait, and via Little’s Law into a sustainable list size: W = −T / ln(1 − p). That is the conversion this model runs on: the RTT and DM01 modules apply it to the photographed stock, the cancer module applies it to the timed cohort — one queueing engine, two camera angles.
| Standard | Camera | Target | Window T | Implied mean wait W | Sustainable list per 100 referrals/wk |
|---|
Reading the table: a harder percentage or a shorter window forces a shorter mean wait, and via Little’s Law a smaller queue relative to demand. The cancer 62-day standard, read through the same lens, is far more demanding than RTT-92 — which is why cancer pathways run on booking disciplines and escalation rather than list management alone. (Flow standards have no published stock; the “list” column is what an equivalent census queue would look like.)
3 Same queue, two readings — when the cameras disagree
The equality in ② holds when waits are roughly exponential. Booking discipline changes the shape: strict FIFO makes everyone wait about the same time. Drag the shape slider from memoryless towards FIFO and watch the two cameras separate — the flow camera sees a sharp all-or-nothing step around the mean wait, while the census camera always sees a spread of ages.
Share within x weeks — flow (completions) vs census (stock) (vertical line = the standard’s window T)
Two rules of thumb. ① FIFO-like booking flatters the census camera at every threshold: the stock is a fresh, evenly-aged mix (at strict FIFO, uniform between 0 and the mean wait — the census reads ≈ T/W), while the flow camera sees an all-or-nothing step at the mean wait — a FIFO pathway whose mean sits just past the window reads near-zero on flow yet respectable on census. ② The reverse asymmetry is the stagnant tail (not shown by the slider): patients who never complete never appear on the flow camera at all, but sit in the census photograph month after month — so a long-waiter backlog drags the census while barely denting the flow. Neither camera is wrong; they answer different questions.
4 Same action, opposite optics — the clearance drive
The cameras also disagree in time. Here a queue with a heavy backlog runs a clearance drive: for six months, extra capacity treats the longest waiters first. Watch the same events through both cameras:
A backlog clearance drive, read by both cameras (% within 18 weeks)
During the drive the census reading climbs — long waiters are leaving the photograph. The flow reading collapses — this month’s completions are the long waiters. After the drive, both settle high. The same is true in reverse: a growing backlog shows up in the census immediately but poisons the flow metric only later, as those waits complete. Mental conversion: the flow camera is the census camera plus a lag — it reports on decisions the system made months ago, while the census reports on the stock as it stands. This is why a trust mid-recovery can show an improving RTT list while its 62-day cancer performance is still deteriorating — and why neither number alone tells the story.