Week 4: The Cost of Waiting

1Multiply it out

800 applications × 90 minutes is 1,200 hours of human life per day, at that one office. Over a working year, about 300,000 hours — roughly a hundred and sixty people’s entire working lives, spent sitting in a room.

Neither number required anyone’s cooperation. Last week’s arithmetic produced both of them from outside the building:

So here is the room, with the bill drawn underneath it.

2Why that changes behaviour

When the cost of waiting sits entirely outside its accounts, the rational internal decision is nearly always to push the queue rather than the budget: run at 97% utilisation, cut the counter from four windows to three, add a verification step that costs the office thirty seconds and the queue forty minutes.

That middle one is the control at the top of this page, and it is worth doing by hand. At fourteen applications an hour, going from four open windows to three takes the average wait from sixteen minutes to forty-eight and the day’s waiting from 28 person-hours to 86. The office saves $304 a day and the room loses $2,303 — seven and a half dollars of somebody else’s time for every dollar saved, and not one line of it in the office’s ledger.

Watch the mechanism rather than the numbers, because it generalises past passport offices. Three windows instead of four is a small change in ρ and a large change in ρ/(1−ρ) — week 2’s table, with a public counter on it. The manager did not make a large decision. The curve made it large for them, and the curve was not on the report.

None of these are failures of management. Each is a correct decision given the information the manager is scored on. The failure is upstream, in what gets measured — which is why “the staff are lazy” is almost always the wrong diagnosis of a long queue, and why week 1’s instinctive answer, not enough staff, is the wrong one too.

The general form is worth naming, because you will meet it in every remaining week of this course. An externality is a cost borne by somebody outside the transaction that produced it. Pollution is the textbook case. Waiting is the same structure, paid in hours instead of particulates, and with one extra feature that makes it worse: the people paying it are assembled, in a room, in front of the organisation, and it still does not appear.

3How an hour gets priced, when anybody bothers

It would be reasonable to think that $40 figure is made up. It is not arbitrary, and the way it is arrived at in practice is worth knowing, because your hour is already being priced — just not by the people making you wait.

Transport economics does this routinely and at enormous scale. Every national appraisal guidance for road and rail publishes standard values of travel time savings: a schedule of what an hour saved is worth, per person, by journey purpose. Those numbers decide which motorways get built. A scheme that shaves four minutes off two hundred thousand daily journeys is justified, or not, on exactly the arithmetic you did at the top of this page.

Two features of that practice matter here.

The value depends on the purpose, not the person. Business travel is typically valued at or near what the employer is paying for that hour, on the argument that the time is genuinely lost output. Commuting and leisure travel are valued lower, and derived from what people actually do — how much extra they pay for a faster route, how far they will drive for cheaper fuel — rather than from their wage.

The numbers are published and argued about. Not perfect, not uncontested, but on the page, where somebody can object to them.

Set that against the passport office, which has implicitly priced its queue at zero and published nothing. The contrast is the lecture: this is not a hard problem that nobody has solved. It is a solved problem that this particular organisation has no reason to apply, because the hours are not its hours.

4Now the uncomfortable arithmetic

Say we accept that waiting should be costed. At what rate?

Price each hour at what that person would pay to avoid it. This is the economically orthodox answer, and it gives a defensible number. It also gives the result that a barrister’s hour is worth forty times a pensioner’s — so any system allocating on that basis will serve the barrister first, with a rigorous efficiency argument for doing so.

Price every hour identically. This is what most people’s instincts prefer. It is not a measurement. It is a moral commitment wearing a spreadsheet, and it should be defended as one rather than smuggled in as arithmetic.

Price it at zero. This is what the passport office is doing right now, and it is the option that produced the 300,000 hours.

There is a fourth answer, and it is the one worth carrying into Act II: price it differently depending on what the queue is for. An hour lost at a passport office and an hour lost in an emergency department are not the same object, and a single exchange rate for time cannot express the difference. Week 7 is about a queue where the thing being traded is not hours at all, and where that is precisely why everybody consents to a rule they would resist anywhere else.

5The part that is not hours

Everything so far has treated a wait as a quantity of time and nothing else. That is a useful simplification and it is badly incomplete, because the experience of waiting is not proportional to the clock.

The classic statement of this is David Maister’s, from the mid-1980s, and it is a short list of propositions that anyone who has run a service will recognise immediately:

• Unoccupied time feels longer than occupied time. Hence magazines, mirrors by the lifts, and the menu board positioned where the queue can read it.
• Waiting before a process starts feels longer than waiting during it. Being seated and ignored beats standing at the door, even for the same total wait.
• Anxiety makes waits feel longer. Did my form go through? Is this the right line?
• Uncertain waits feel longer than known, finite waits. Ten minutes you were told about beats five minutes you were not.
• Unexplained waits feel longer than explained ones. “We are one staff member down today” is worth several minutes of actual time.
• Unfair waits feel longer than equitable ones. One person served out of turn poisons the entire line, and everybody in it can tell you exactly how many minutes it cost them, which is never the true figure.

Perceived waiting and measured waiting are different quantities, and only one of them is on the dashboard.

Take this the right way round. It is not a licence to leave the wait alone and manage the feeling instead — that is a real and common abuse, and week 11 takes it apart. It is a warning that the 300,000 hours is a lower bound on the damage, and that two systems with identical L, λ and W can be experienced as completely different places.

6Who is actually in the room

Look at who is standing in that passport queue at 10am on a Tuesday. It is disproportionately people who cannot pay to avoid it, cannot send somebody else, cannot take the appointment at 2pm on a Wednesday, and cannot do it online.

The queue is not a random sample of the population. Any rule you apply to it lands on that population, not on an average one — and the rules that look most neutral in the abstract are often the ones that land hardest, because neutrality is exactly what stops them noticing who is there.

There is a sharper version of this, and it changes what the 300,000 hours means. An hour is not equally available to everybody. A salaried worker with flexible hours spends an hour. A shift worker on an hourly contract spends an hour and the wages for it, plus possibly the shift. A single parent spends an hour and a childcare problem. Researchers on administrative burden separate out three costs that a citizen pays to obtain something they are entitled to: the learning cost of finding out how, the compliance cost of doing it — of which queueing is the purest form — and the psychological cost of being processed.

All three fall hardest on exactly the people most likely to need the service. Which produces the result that should end any argument that a queue is politically neutral: raising the hassle of a service reduces its take-up, and reduces it most among the people it was designed for.

7When the wait is the point

Now the uncomfortable extension, and it is not hypothetical.

Economists have a name for a barrier deliberately placed in front of a benefit so that only those who really need it will bother: an ordeal mechanism. The argument is genuinely clever. If you cannot observe who is truly in need, make the benefit costly to obtain in a currency the needy are more willing to spend than the non-needy — and time is the obvious candidate, because it cannot be borrowed, transferred or counterfeited. A queue, on this reading, is a means-test that requires no paperwork and cannot be lied to.

It sometimes works. It is also, quite often, exactly backwards.

You should not leave this beat thinking every queue is a conspiracy. Most are not. But when you find a wait that nobody has tried to shorten despite it being cheap to shorten, the possibility that the wait is doing a job for somebody belongs on your list of hypotheses. It comes back in week 8, where the job it is doing is making a fast lane worth paying for.

8What Act I gave you

Four weeks, four tools, and they compose.

Week 1. A queue is a designed object with four parts, and the fourth one — who goes next — is a rule somebody chose. Name the rule before you judge it.

Week 2. Queues are made of variability, not load, and the cost of load is non-linear: W ≈ V × U × T. Look at the spread before you look at the average.

Week 3. L = λW lets you measure any queue from outside, and the boundary you draw around it is the claim you are making. State the box before you state the number.

Week 4. The wait has a price, the organisation causing it cannot see that price, and the people paying it are not a random sample. Find out who is holding the bill.

Put them together and you can walk into a building, watch a line for ninety seconds, say why it is there, estimate what it costs, and name who is paying. That is the toolkit, and it is entirely diagnostic: not one of those four weeks told you what the system should do.

From next week we start turning the knob that actually decides the outcome — and we begin by taking apart the rule you have believed in since you were four years old.