The queue is part of the price.

Picture a small paper ticket from a service counter, the kind a machine by the door hands out. It says 47 in large type. Under the number it says the fee for the service is $12.00, and a clerk will stamp it paid. On the back, in pencil, someone has kept a record the ticket does not: took the ticket at 9:04, the board showed 31; called at 10:21; out the door at 10:33. (The ticket, the counter and the times are invented for this essay. They describe no real office.)

The ticket is an honest receipt for one part of the transaction. It records twelve dollars. It has no line for the hour and seventeen minutes, though the customer gave those up as surely as the money, and could not have been served without them. A morning off work, a parking meter, a child collected late from school: the costs of that hour land on the customer, and on nobody's books.

My argument is that the price of being served has two parts, the money paid and the time spent waiting, and that a service should be judged on both. When capacity is scarce and the money price is held low, the line does the rationing: whoever can afford to wait gets served. A service can be cheap to buy and expensive to use. This does not mean that charging more is fairer, or that every wait should be engineered away. Waiting is sometimes the best available rule, and spare capacity costs money. The claim is narrower: every way of handing out a scarce service is an allocation choice, and the choice should be made in the open, with the time on the bill.

What a line is for

A queue looks like a failure, a sign that something has gone wrong. Often it is doing a job. When more people want a service than the service can handle at the price it charges, something has to decide who is served and in what order. A higher price would do it by turning some people away. A line does it by making everyone pay in time, until enough people decide the service is not worth the wait.

The economist Yoram Barzel worked out the logic in 1974. When a good is handed out at a price below the one that would clear the market, waiting takes over the job the price would have done, and the line grows until the time cost of the last person willing to join roughly matches the gap the low price left open.¹ The lower money price is real, but much of the saving is paid back in hours. And unlike the money, which at least goes to the seller, the hours go to no one. They are simply used up.

How much is that time worth to the people giving it up? A well-known natural experiment gives one answer. Robert Deacon and Jon Sonstelie studied drivers who could wait in line for cheaper gasoline at one station or pay a higher price, with no wait, at another. Their choices implied a value of time roughly equal to their after-tax wages.^2,3 Deacon and Sonstelie went on to argue that the gas lines of the 1970s price controls cost consumers more than the controlled prices saved them, which is Barzel's point in a single sentence.⁴ A 2022 study of ordinary gas station choices found a value of the same order: about $27.50 an hour, or 89 percent of the median wage in its sample.³

Two cautions keep that number in its place. A wage is a rough proxy for what an hour is worth to the person giving it up, not a measure of the person, and an hour taken from a parent, a shift worker or someone in pain may be worth far more to them than any pay rate says. And the burden is not spread evenly. A queue serves people whose time is cheap or flexible: the retiree, the salaried worker who can step out, the person with someone to hold their place. It turns away people who cannot leave a job at ten in the morning, whatever the service is worth to them. A price rations by wealth; a line rations by schedule. Neither is neutral.

The free service with a six-week lead time

The same mechanism runs inside companies, where it is harder to see because no money changes hands. Consider a shared analytics team, or an internal platform group, whose work is free to the business units that use it. There is no chargeback, no budget line, no invoice. There is a request form, and a lead time of several weeks.

The price of that service has not disappeared; it has moved. It shows up as delayed launches, decisions made without the analysis, and projects that wait for a dependency. It shows up as workarounds: a spreadsheet maintained by someone in finance, a contractor hired on a business unit's own budget, a tool bought on a credit card because the official route would take a quarter. And it shows up as requests that are never made, because people have learned the answer is "get in line." That last cost is the hardest to see, since a request that is never submitted never appears on any report.

The first step toward seeing the queue is to measure it, and here a result from operations research helps. In 1961 John Little proved that, for any system in a steady state, the average number of items in the system equals the average rate at which they arrive multiplied by the average time each one spends there.⁵ In symbols, L = λW. Fifty years later, he noted that the law holds under remarkably general conditions: it does not depend on how arrivals are spaced, how long service takes, or the order in which items are served. Its practical value, he wrote, is that "if you know two of {L, λ, W}, you can quickly calculate the third."⁶

Apply it to the shared team. Suppose 20 requests arrive each week, and on an average day 60 are in the system, counting from the moment a request is submitted to the moment its work is delivered. Then the average request spends 60 ÷ 20 = 3 weeks in the system. The units have to match (requests, requests per week, weeks), and the boundary has to be stated: a clock that starts at "work begins" rather than "request submitted" will report a shorter wait and hide the queue. Little's Law also counts something else useful. At any moment, those 60 requests are each accumulating a week of delay every week. The organization is carrying 60 request-weeks of waiting per week, and somebody, somewhere, is paying for it.

What the law does not do is say whether the wait is too long, or what to do about it. Little himself was careful about this: the law relates averages and does not tell managers how to handle trade-offs.⁶ Nor does it predict how the wait will respond to more staff. That takes a model of the service itself, and queueing theory's main lesson there is that a team running near full capacity sees waits rise steeply, so modest added capacity can shorten the line a great deal.⁶

Three ways to change a line

An organization with a long internal queue has three broad responses, and each one changes who gets served and who bears the cost.

• Add capacity. Hire, automate, or remove work that should not be in the queue at all. This shortens the wait for everyone, and it costs money that someone has to budget. It also means some capacity will sit idle in slow weeks, which is the price of having it in busy ones.
• Change the admission rule. Triage, appointments, reserved slots for urgent work, limits on how much any one team can submit. These change the order of service without adding capacity. They can direct the wait toward the requests that can best afford it, which is often fairer than first come, first served. But they move waiting rather than remove it, and someone has to decide what counts as urgent.
• Charge for priority. An internal fee to jump the line. This turns part of the time price back into a money price, and it rations by budget: the teams with money to spend get served first. The fee itself is a transfer inside the company. It buys a better place in line, not more capacity, unless the revenue is spent on capacity.

Pricing has a better theoretical case than its reputation suggests. In 1969 the operations researcher P. Naor studied customers who look at a queue and decide for themselves whether to join. Each one weighs their own wait, but not the delay they add for everyone who arrives behind them. Customers deciding this way may join even when, from the social point of view, everyone would be better off if they did not.⁷ Naor showed that a toll on arriving customers can frequently bring the system to the social optimum.⁸ A small price can deter requests that are worth less than the delay they impose. The same price also deters valuable requests from teams with no budget, which is why the choice of rule is never purely technical.

The worksheet below puts the three responses side by side for the shared team. It shows money and waiting separately first, because they are different things. Only then does it convert waiting into dollars, using a value of delay that you set and that is plainly an assumption.

Start with the money row and the waiting row before touching the dial. Doing nothing costs nothing on the budget and carries 60 request-weeks of waiting every week. Adding an analyst costs $4,000 a week and cuts the waiting by two thirds. Triage costs nothing and leaves the total wait where it was, but changes who carries it: urgent requests are through in under half a week while routine ones wait almost four. The priority fee also leaves the total unchanged. Its $3,000 a week is real money to the teams that pay it, and real income to the service, but the organization as a whole is no richer or poorer for it. What changes is that two urgent requests a week, from teams without the budget to pay, now wait longer than they did when the service was free.

Now move the dial. At a very low value of delay, doing nothing is cheapest: if a week of waiting costs almost nothing, there is no case for spending money to shorten it. As the value rises past about $60 a week for a routine request, adding capacity overtakes doing nothing, and past about $130 it overtakes triage as well. Triage beats the fee at every setting, because it reserves the fast lane for urgent work while the fee gives it to whoever pays. None of these crossover points is a fact about any real organization; they follow from the invented numbers. The point of the worksheet is the procedure: write the time down, decide what it is worth and to whom, and only then compare.

Objections, considered

"Charging for priority just lets the rich jump the line." It can, and that is the strongest case against it, inside companies as much as outside them. But a free queue is not egalitarian either. It favors people whose time is cheap or flexible, and inside a company it favors teams with the slack to wait or the budget to work around the line. The honest comparison is between two rationing rules, each with its own losers, not between a fair queue and an unfair price.

"Some services should never be rationed by price." Agreed. Emergency care, public safety and many basic services should be allocated by need. The argument here does not favor fees. It favors counting the wait, which matters most precisely where a money price is ruled out. Where price is off the table, the choice is among waiting, triage, appointments and capacity, and those choices still decide who is served.

"Triage and appointments solve this without money or waiting." Often they do it better than either. Reserved capacity for urgent work and booked slots that let people plan around a wait can serve fairness and efficiency at once. But they are rules someone writes, and they can be gamed: if urgent work goes first, every request becomes urgent. A triage rule needs a definition, an owner and an occasional audit, like any other measure.

"Spare capacity is waste." Idle staff and empty slots are costly, and a service run with no waiting at all would be expensive to the point of absurdity. Some queue is usually the right answer. The question is how long, borne by whom, and whether the people deciding can see the cost. A service that looks efficient because it runs at full utilization may be efficient only because its customers are absorbing the difference.

A service is not cheap because its price is low; it is cheap when the price and the wait are both low.

Back to the ticket

Before deciding that a service is cheap, a leader can ask four questions.

• Which apparently cheap service imposes the longest unrecorded wait? Count the requests in the system and the arrival rate, and let Little's Law give you the time.
• Who absorbs the wait? Name the teams or customers, and what they give up or work around while they wait.
• Who never gets in line? Look for the requests that are not made, and the people the schedule or the price turns away.
• Would a different rule improve access? Compare more capacity, a better admission rule and a price for priority, with the time and the money both written down.

Look again at the ticket. There is nothing wrong with what it prints: twelve dollars, stamped paid. What it needs is the line written on the back, carried onto the front. With both on the page, the money paid stops posing as the whole price, and the time spent waiting becomes something an organization can count, assign and decide about, instead of something its customers quietly pay.