Queues
Rationing by Waiting, and Who It Quietly Favours
Introduction
There is never enough of some things. Kidneys. Social housing. Appointments with a specialist. Places at a good school. Permission to live in a country. Something has to decide who gets them and in what order, and there are really only two devices in wide use. You can charge, and let price sort the queue. Or you can make people wait.
Waiting is the device societies reach for when charging feels wrong. Nobody wants an auction for donor organs. Most people are uncomfortable with a market in school places. So we form a line instead, and the line feels like the fair option, because it does not obviously favour the rich.
The thing worth understanding is that the line is not neutral either. It has its own winners, its own costs, and its own black market. None of the three gets discussed much, partly because a queue looks like the absence of a policy rather than a policy. The page below is about what a queue actually does: what it costs, who it advantages, what grows up beside it, and why every way of ordering it contains a judgement about who deserves to go first.
Two Ways to Hand Out What There Is Not Enough Of
Price and waiting do the same job by different means. Both take a scarce thing and decide who gets it. Both work by making people give something up - money in one case, time in the other. The difference is what happens to what they give up.
When allocation runs on price, the thing given up moves. The buyer's money becomes the seller's revenue, and that revenue does something afterwards: it pays wages, funds more supply, gets taxed. The payment is a transfer. It leaves one pocket and arrives in another, and the total is unchanged.
When allocation runs on waiting, the thing given up disappears. An hour spent in a waiting room does not arrive anywhere. The clinic does not receive it. It is subtracted from one life and added to none. This is the single most important structural fact about queues and the one least often said out loud: a price moves value between people, and a queue destroys it.
That is why economists tend to dislike queues, and the objection is real. But it is not the end of the argument, and treating it as one is where the economic case usually overreaches. The money in a price system moves toward whoever already has money, and the whole reason the queue was chosen was a decision that this particular thing should not follow money. A queue is expensive in a way a price is not. It is also refusing to do something that a price does automatically.
Why Waiting Gets Chosen
Queues appear in a recognisable set of circumstances, and noticing the pattern makes them easier to think about.
When charging is thought improper. Some goods carry a widely-held sense that money should not decide the outcome. Organ transplantation is the clearest case: almost every country prohibits payment for organs, so the American list of just over 103,000 people is ordered by medical criteria and time waited rather than by willingness to pay. Around seventeen people on that list die each day. Nobody proposes fixing this with an auction, and the reluctance is not irrational - it is a judgement that some allocations would corrupt the thing being allocated.
When supply is fixed by law rather than by cost. The clearest example is immigration. The United States caps employment-based permanent residence at 140,000 a year, a figure set in 1990 and unchanged since, and adds a rule that no single country may take more than 7% of the total. Applied to India, a country with roughly a sixth of the world's people, that produces a backlog of more than 1.2 million and waits measured in decades for some applicants. No shortage of anything physical is causing this. The queue is manufactured directly by the arithmetic of the rule.
When the price is set below the clearing level on purpose. Rent controls, subsidised childcare, and free-at-point-of-use healthcare all deliberately price below what would balance supply and demand. The gap does not vanish; it reappears as a list. England's health service holds an elective waiting list of around 7.1 million treatments - the lowest in three and a half years, and still a number that only exists because access is not rationed by price.
And when nobody chose at all. Many queues are not policy. They are what happens when a system runs close to its capacity, which is a separate mechanism with its own arithmetic: past a certain level of fullness, waiting times stop rising gently and start rising steeply. A queue of this kind is a symptom rather than a decision, and treating it as an allocation problem when it is really a capacity problem produces a great deal of wasted effort.
Who Wins a Queue
The appeal of a line is that it treats everyone the same. It does, in the narrow sense that the rule is identical for all. But the same rule does not cost everyone the same, and the differences run in a consistent direction.
Flexible time beats scarce time. An appointment offered at eleven on a Tuesday is nearly free for someone who sets their own hours and expensive for someone paid hourly who must ask permission to leave. Both waited the same number of weeks. One of them paid far more for it.
Knowing how the system works beats not knowing. Most queues are not a single line but a set of them, with rules about transfers, priority categories, appeals and alternative routes. People who understand the structure route themselves better, and understanding it correlates strongly with education, with having navigated bureaucracies before, and with knowing someone who has done it already.
Being able to absorb uncertainty beats needing certainty. A queue gives you a place but rarely a date. Someone who can hold their life loosely while they wait is in a different position from someone who must know whether the operation is in March, because a job, a lease or a family arrangement depends on it. The second person often leaves the queue and buys the thing privately, which is one of the main ways a public queue quietly turns into a private market at the edges.
None of this means queues are secretly worse than prices for poorer people. Often they are much better, which is exactly why they are used. It means the fairness is partial rather than complete: a queue removes the advantage of money and replaces it with the advantage of time, information and stability. Those are distributed unevenly too, just along different lines and less visibly.
The Market That Grows Beside It
Wherever a queue allocates something below its market value, a second system appears alongside to sell the position. This happens reliably enough to be treated as a property of queues rather than as a scandal about particular ones.
The mildest form is professional line-sitting, which is a real occupation: people paid by the hour to stand in a queue and hand over the place when it reaches the front. It exists for court hearings, congressional committee seats, product launches and restaurant tables. It is legal, openly advertised, and it converts a time-rationed good back into a money-rationed one for anyone willing to pay.
The middle form is resale. Tickets priced deliberately below what the market would bear are bought by people who intend to sell them, and the difference between the two prices is captured by an intermediary rather than by the artist, the club or the theatre that set the low price on purpose. The queue was meant to give fans access at a fair price. What it produced was a transfer from fans to resellers.
The severe form is corruption. Where the queue governs something essential and the state is weak, positions in it are sold by the officials who administer it. This is one of the most common shapes petty corruption takes, and it is worth noticing what it does: the good still goes to whoever pays most, exactly as under a price system, except that the payment goes to an official rather than to the provider, and nothing about supply improves as a result.
The common thread is that a queue only holds if the leaks are closed, and closing them takes continuous work. A queue with an open side door is not an alternative to allocating by money. It is allocation by money with extra steps, worse information, and the proceeds going to whoever runs the door.
Every Ordering Rule Is a Judgement
Once a queue exists, something has to decide the order. There is no neutral option. Each available rule optimises for a different thing and sacrifices a different group, and the choice is a moral one dressed as an administrative one.
First come, first served is the rule that feels fairest and takes the least account of need. It rewards whoever could get in line earliest, which is a fact about their circumstances rather than about their claim. Its real virtue is that it is hard to corrupt and easy to verify, and in low-trust settings that can matter more than getting the order right.
Triage reorders by urgency and was formalised by Napoleonic army surgeons, who noticed that treating in order of arrival killed people who could have been saved. It is plainly better in an emergency room. It also means that someone who has waited all day is passed over repeatedly by people who arrived later and are sicker, which is correct and does not feel like it.
Shortest job first is the rule that gets the most people through. Take the quick cases before the slow ones and average waiting time falls, which is why supermarkets have express lanes and why some clinics separate simple from complex work. The cost is hidden in the average: the longest, most complicated cases are pushed back indefinitely, and those are usually the people in most difficulty.
Priority categories try to encode judgements directly - by need, by dependants, by contribution, by vulnerability. This is the most honest approach, because it says out loud what the others decide silently. It is also the one that invites the most gaming, since any category worth having is a category worth claiming, and the people best at claiming it are the ones who understand the rules.
The useful discipline here is to read an ordering rule as a statement of values and ask whether anyone would defend it if stated plainly. "We serve the least sick first because they are quicker" is a real policy that gets implemented often and defended almost never.
Two Things Worth Knowing About Any Queue
The first is a piece of arithmetic that lets you work out a wait nobody has told you. The second explains why two queues of identical length can feel completely different.
The length divided by the rate is the wait. This is Little's Law, proved by John Little in 1961, and it is unusually powerful for something so simple. The average time something spends in a system equals the number of things in it divided by the rate at which they arrive or leave. It holds regardless of how the queue is ordered, how variable the arrivals are, or what the service looks like inside.
The practical use is that organisations almost always publish the two numbers you need and almost never publish the one you want. A list of 60,000 people that clears 1,000 a month is a five-year wait, whether or not anyone has said so. If the list is growing, the answer is worse than it looks: the divisor is the rate at which people leave, not the rate at which they join. Do this sum on any queue you are in. And note that a stated target date is a claim about future throughput, not a description of the present one.
How long a wait feels is a separate variable from how long it is. David Maister set out the regularities in 1985 and they have held up. Unoccupied time feels longer than occupied time. Unexplained waits feel longer than explained ones. A wait of unknown length feels much longer than the same wait with a stated end. Waiting alone feels longer than waiting in company. And a wait feels far worse when it seems unfair, which is why one person served out of order does more damage to a room's mood than an extra twenty minutes.
This is why the ticket display exists. It converts an uncertain wait into a known one and costs nothing in throughput. It is also why some airports moved baggage reclaim further from the arrival gates: the total time to bags was unchanged, but more of it was spent walking and less standing, and complaints fell. That story is often told as a trick played on passengers. It is better understood as a real improvement to something real, since the discomfort of waiting is not less genuine for being psychological.
The two findings pull in different directions and both are true, which is worth holding onto. Making a queue feel better is cheap and worth doing. It also does nothing whatever to the number of people who will not be treated this year, and it is entirely possible to spend years improving how a wait feels while the wait itself gets longer.
Working Practically With Queues
A few things follow that are worth knowing when you are the one waiting.
Find out which queue you are actually in. Most systems that look like one line are several, with different rules and different speeds, and the single highest-value action is usually establishing which one applies to you rather than waiting faster in the wrong one. Ask what the priority categories are and whether your circumstances place you in one. This is not gaming the system; it is the system working as designed, and the people who never ask are subsidising the people who do.
Treat a long queue as information about capacity, not about your luck. A wait that keeps growing is telling you the system is running above the level where it can absorb variation, and that it will not recover on its own. Plans that assume the list will clear are usually wrong, because nothing about a full system clears a backlog without either more capacity or fewer arrivals.
And when you are designing rather than waiting, be suspicious of the instinct to keep the rule simple. First come, first served is the easiest rule to administer and the one least connected to who needs the thing. Sometimes that trade is right, particularly where trust is low and the appearance of fairness is doing important work. It should be a decision rather than a default.
A queue is a decision not to let money settle something, and it is a real decision with real merits. It is also expensive in a way a price is not, because the hours it consumes arrive nowhere, and it is less equal than it looks, because time and information and stability are unevenly held. Neither of those makes the queue the wrong choice. What they make is a queue something to design deliberately rather than to arrive at by default - knowing what it costs, who it favours, what will grow up beside it, and what the ordering rule is saying about whose claim comes first.
