As a way of dealing with high demand, the age-old practice of forming a long, orderly queue has something to be said for it: simplicity, transparency and equal treatment for all. But no matter how much the British are said to love a queue, you can have too much of a good thing. The UK’s public services are under strain in all sorts of ways and it is striking how many of the problems can be described as a gridlock of hidden queues.
Consider ambulance response times. Ambulances in England are supposed to arrive within a given target time, depending on how urgent the situation is. In “category 2” situations such as heart attacks and strokes (aka pretty damned urgent), the target is to respond in 18 minutes on average. The bad news is that the NHS isn’t hitting these targets: in November last year, the average response for category 2 calls was more than 32 minutes, the worst since last January. The good news is that things have been much worse than that in recent memory: at the end of 2022, the average response time was more than an hour. That’s the result of a queue that not even the British could love.
Why is this happening? The obvious explanation is that there are not enough ambulances, but the deeper problem is that ambulances themselves are being delayed in discharging patients into A&E units, which are themselves often overwhelmed: in the first quarter of 2014, 134 patients waited more than 12 hours in A&E before being admitted; 10 years later the figure was 141,693. The long delays in A&E are in part the result of the hospital beds all being full and that, in turn, is in part because hospitals sometimes struggle to discharge vulnerable patients into an overstretched social care system. All of these problems are a kind of queue and they all interact in a surprising way: you can die waiting for an ambulance because there aren’t enough nursing homes in your area.
What is striking is that the same pattern emerges in other parts of the public sector. For example, the prison system is full almost to capacity. That is partly the result of three decades of successive governments deciding that sentencing guidelines should be punitive, while also being unwilling to build enough prisons. But it is also the result of interacting queues: about one-fifth of the prison population is either awaiting a trial or awaiting a sentence, which means that delays in the court system feed into crowding in the prison system.
The study of queues dates back more than a century, with the initial spark coming from a mathematically gifted Danish telephone engineer named Agner K Erlang. Erlang combined his elegant mathematical ideas with a practical approach. He wandered around the streets of Copenhagen accompanied by a ladder-bearing assistant so that Erlang could descend through manholes to measure currents. (The unit of load on a queue-processing element, whether a telephone line, a supermarket checkout or a toilet cubicle in a theatre, is the erlang. So now you know.)
Since Erlang, the modelling of queues has blossomed, along with an alphabet soup of acronyms, including PQ (priority queuing), FCFS (first come first served — as any true Briton would advise) and the suspiciously continental-sounding SIRO (service in random order). The queuing literature has produced many ideas and, while some of the conclusions are obvious (queues form when there isn’t enough capacity to match demand), there are subtleties worth pondering.
First, when bottlenecks feed into bottlenecks, some strategic thinking is required to fix the system. There is often more than one bottleneck in a congested system and opening that bottleneck will sometimes mean the same queue builds up somewhere else.
Second, the optimum queuing time probably isn’t zero. In most cases, demand arrives at irregular intervals and it is likely to be impractically wasteful to have so much capacity (so many doctors, so many ambulances, so many crown courts) that even after a sudden surge in demand, nobody has to wait.
That said, the optimum queuing time should probably be kept quite short. Imagine a situation where an emergency doctor can see four patients an hour and patients arrive every 15 minutes. At first everything is fine: every patient can be seen immediately. Then something goes wrong. Perhaps there’s a sudden rush, when five patients unexpectedly arrive together. Perhaps the doctor takes an hour off for lunch. The waiting time suddenly increases from nothing to an hour, even though the doctor is still seeing four patients an hour and four patients an hour are still arriving.
The moral of this very simple story is that even if the capacity of the system is equal to the demand for it, queues can grow and then stay at unpleasant lengths. What’s needed is a little extra capacity to work through the inevitable queues that build up from time to time. Unfortunately, systems under intense pressure rarely have a little extra capacity hanging around.
Third, it can be hard to increase the capacity of a system. Let’s say that we have one million nurses and each nurse trains for two years before working for 20. Arithmetically, that requires 100,000 nurses to be in training at any given moment. What if it is decided that we need 1.1 million trained nurses and we need them as soon as possible? That would require an immediate recruitment boost, doubling the number of nurses in training.
Would that be possible? Even though the expansion in nursing personnel seems modest, it requires nursing courses to double in size and then to shrink again after a couple of years. An even more dramatic expansion will be needed at the advanced training colleges at which the teachers of nursing are themselves trained. It might be easier to persuade nurses to stay a little longer in the profession or to recruit from the Philippines.
This unpleasant arithmetic makes it all the more frustrating when the obstacles to capacity expansion seem unnecessary. My colleague Sarah O’Connor recently described the large stock of frustrated foreign-qualified dentists in the UK who cannot practice dentistry because they are waiting to take a registration exam. There are 8,000 dentists on the waiting list; 350 of them scrambled through the chaotic registration process in 2024. At this rate everyone now on the waiting list will be able to practise dentistry before 2050.
Queuing can be a fiendishly difficult problem to solve, but not always. Sometimes the free lunch is right in front of us, waiting to be eaten.
Written for and first published in the Financial Times on 7 Jan 2026
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