The transit trilemma - by Benedict Springbett

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The transit trilemma<br>The fundamental trade off all railways face

Benedict Springbett<br>Jul 24, 2025

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Thank you to Matthew Bornhoult for introducing me to this way of framing the problem.<br>In macroeconomics, there is a concept called the impossible trinity. It is impossible for a country to have all three of a fixed foreign exchange rate, an absence of capital controls, and an independent monetary policy. You can pick two, but not all three.1<br>There is a similar concept in transit. A railway line can pick two of frequent services, reliable operations where the trains run to the timetable, and complex service patterns – expresses, branching and sharing tracks with other services. I’ve alluded to this concept on several occasions, but it is fundamental enough that it deserves its own blogpost.<br>Edit: In response to one of the comments, I should explain why complexity can be a good thing. I think that expresses are self-evidently useful. Track-sharing with freight and intercity trains is good because it lowers construction costs. And complicated branching can be useful for passengers: I used to live on the Northern Line, and it was really useful to be able to get a direct train to either the City or the West End. All else being equal direct trains are preferable. But this passenger convenience comes with a trade off, which is what this post is all about.<br>For more posts like this, please subscribe!

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The trilemma explained

Anybody who has got the Victoria Line at rush hour will have witnessed a train leaving the platform, and another coming onto the platform only 30 seconds later, almost like a conveyor belt. The Victoria Line runs 36 trains per hour (tph); some transit lines like Line 14 of the Paris Métro get up to 40 tph.<br>This is what happens when you have a very simple service pattern. On both the Victoria Line and Line 14, every train stops at every station (and they also take the same amount of time to travel between the stations). The only limit to frequency is imposed by the signalling system, which means that in practice you can have a train every 90 seconds (or 100 seconds on the Victoria Line) and both lines are reliable.<br>The Victoria line therefore chooses frequency and reliability, but trades off complexity. Every train stopping at every station2 is the simplest service pattern possible.<br>What happens, however, if we introduce some complexity? Suppose we want to have a branch. The diagram below shows a flat junction: the line branches off, but the branch line crosses over the main line on the same plane. This means that trains from B to A have to cross the path of those running from A to C, and vice versa.

Two trains, about to crash into one another.<br>Maintaining 2-minute intervals between trains (Paris Line 14 is exceptional for its 90 second headways), in theory we can operate the junction like this. By repeating this pattern like this, these parallel moves enable us to get 30 tph through the junction.

But there is an obvious problem – the entire dance has to be co-ordinated perfectly in order to work. If one of the trains is delayed, then everything else will have to wait for it. Frequency combined with complexity mean that reliability suffers.<br>Likewise, consider what happens if we add an express service (red) that only stops at the important stations, on the same tracks as some stopping trains (blue). We are again maintaining a 2-minute spacing between trains, which is shown in the lighter shading.

This service pattern works – so long as nothing goes wrong. If the 11.01 stopping train is delayed at Station 9, it will delay the 11.09 express. We have once more traded off reliability in favour of frequency and complexity.<br>Exactly the same logic applies if we have intercity or freight trains on the same tracks, or if we are using a tram-train which shares space with road traffic. A final form of complexity is joining and splitting trains, so that one train can serve two destinations – but the more trains we try to run in this way, the more instability we introduce into the timetable.<br>For the third option, suppose we want to run a reliable, complex service. The only way to do that is to ensure that the services do not run too often. Continuing with the example above, if we trim the blue service down to quarter-hourly, then the timetable will be more robust, with fewer chances of delays:

To be clear, all of this is assuming competence. Deutsche Bahn and the New York City Subway both show that it is possible to have complex services, which are neither frequent, nor reliable. In both cases, the root cause of the poor reliability is under-investment, which is exacerbated by the complex service patterns they try to run.<br>Which limb to trade off?

Given that we have to trade off one of these three desiderata, which is it to be?<br>It is almost always a bad idea to trade off reliability. For one, it...