Little Things That Matter: Interchange Siting
I’ve written a lot about the importance of radial network design for urban metros, for examples here, here, here, here, and here. In short, an urban rail network should look something like the following diagram:
That is, every two radial routes should intersect exactly once, with a transfer. In this post I am going to zoom in on a specific feature of importance: the location of the intersection points. In most cities, the intersection points should be as close as possible to the center, first in order to serve the most intensely developed location by all lines, and second in order to avoid backtracking.
The situation in Berlin
Here is the map of the central parts of Berlin’s U- and S-Bahn network, with my apartment in green and three places I frequently go to in red:
(Larger image can be found here.)
The Ring is severed this month due to construction: trains do not run between Ostkreuz, at its intersection with the Stadtbahn, and Frankfurter Allee, one stop to the north at the intersection with U5. As a result, going to the locations of the two northern red dots requires detours, namely walking longer from Warschauer Strasse to the central dot, and making a complex trip via U7, U8, and U2 to the northern dot.
But even when the Ring is operational, the Ring-to-U2 trip to the northern dot in Prenzlauer Berg is circuitous, and as a result I have not made it as often as I’d have liked; the restaurants in Prenzlauer Berg are much better than in Neukölln, but I can’t go there as often now. The real problem is not just that the Ring is interrupted due to construction, but that the U7-U2 connection is at the wrong place for the city’s current geography: it is too far west.
As with all of my criticism of Berlin’s U-Bahn network layout, there is a method to the madness: most of the route of U7 was built during the Cold War, and if you assumed that Berlin would be divided forever, the alignment would make sense. Today, it does not: U7 comes very close to U2 in Kreuzberg but then turns southwest to connect with the North-South Tunnel, which at the time was part of the Western S-Bahn network, running nonstop in the center underneath Mitte, then part of the East.
On hindsight, a better radial design for U7 would have made it a northwest-southeast line through the center. West of the U6 connection at Mehringdamm it would have connected to the North-South Tunnel at Anhalter Bahnhof and to U2 at Mendelssohn Park, and then continued west toward the Zoo. That area between U1/U2 and Tiergarten Park is densely developed, with its northern part containing the Cold War-era Kulturforum, and in the Cold War the commercial center of West Berlin was the Zoo, well to the east of the route of U7.
Avoiding three-seat rides
If the interchange points between lines are all within city center, then the optimal route between any two points is at worst a two-seat ride. This is important: transfers are pretty onerous, so transit planners should minimize them when it is reasonably practical. Two-seat rides are unavoidable, but three-seat rides aren’t.
The two-seat ride rule should be followed to the spirit, not the letter. If there are two existing lines with a somewhat awkward transfer, and a third line is built that makes a three-seat ride better than connecting between those two lines, then the third line is not by itself a problem, and it should be built if its projected ridership is sufficient. The problem is that the transfer was at the wrong location, or maybe at the right location but with too long a walk between the platforms.
Berlin’s awkward U-Bahn network is such that people say that the travel time between any two points within the Ring is about 30 minutes, no matter what. When I tried pushing back, citing a few 20-minute trips, my interlocutors noted that with walking time to the station, the inevitable wait times, and transfers, my 20-minute trips were exceptional, and most were about 30 or slightly longer.
The value of an untimed transfer rises with frequency. Berlin runs the U-Bahn every 5 minutes during the daytime on weekdays and the S-Bahn mostly every 5 minutes (or slightly better) as well; wait times are shorter in a city like Paris, where much of the Metro runs every 3 minutes off-peak, and only drops to 5 or 6 minutes late in the evening, when Berlin runs trains every 10 minutes. However, Parisian train frequencies are only supportable in huge cities like Paris, London, and Tokyo, all of which have very complex transfers, as the cities are so intensely built that the only good locations for train platforms require long walks between lines.
New York of course has the worst of all worlds: a highly non-radial subway network with dozens of missed connections, disappointing off-peak frequencies, and long transfer corridors in Midtown. In New York, three-seat rides are ubiquitous, which may contribute to weak off-peak ridership. Who wants to take three separate subway lines, each coming every 10 minutes, to go 10 kilometers between some residential Brooklyn neighborhood and a social event in Queens?
Pedestrian Observations 
Good post, Alon. I’ve never been to Berlin but I have suffered a similar kind of painful back-tracking and three-seat-riding in Madrid*, worsened by summer headways. Still the longest transfer I remember was in Paris (between M5 and the TGV at Gare du Nord, IIRC).
I’d like to raise a couple of (small) additional points:
1) Station depth: even if the tunnels cross at a convenient location, the transfer might be complicated by the vertical distance between the platforms. For example, in Madrid the cut-and-cover L1 crosses the deep-bored L10 at Tribunal, but the transfer is laughably labyrinthine. In non-flat cities, do you think it’s worthwhile to make two radial lines cross somewhat further out so as to stcak the tracks just on top of each other (or even have them parallel for a nice cross-platform transfer)?
2) Major destinations along the circle line: even if the main purpose of circle lines is to take pressure away from the central interchanges, there might be important destinations close enough to the optimal alignement to justify a detour. I think this was the case in Moscow, where the northern portion of the Koltsevaya line was built further out than originally planned (under the Garden Ring, like the southern portion) so that it could hit all the mainline rail terminals. I haven’t seen this tradeoff discussed in the posts you link at the beginning – apologies if you’ve covered this already!
*Madrid is funny in an infuriating way because it superficially resembles your ideal network but, if you zoom a little in, it becomes a mess of awkward one-sided radials (which usually force a 3-seat ride), radial-circumferential lines and plenty of pairs of lines crossing either more than once or not at all.
Even in Alon’s idealized diagram, it’s a three seat ride to get between the southern ends of the red, yellow, or orange lines. Similarly with the north ends of the blue and turquoise lines. All these lines do have direct transfers, but the direct transfer requires another 8 or so stops of traveling, which makes transferring to the circle line for 1 or 2 stops pretty appealing.
I just looked at Madrid and I don’t really think it’s worse than Alon’s ideal. Seems that the only lines that miss each other geographically are 3 and 9. Lines 1 and 7 cross each other but without a transfer (should be easy to add a subsurface station on 1, no?).
Bad transfers are an issue. But given the expense of building underground lines and the historical accidents that occur over a long history of city development, they are to some extent unavoidable.
Who wants to take three separate subway lines, each coming every 10 minutes, to go 10 kilometers between some residential Brooklyn neighborhood and a social event in Queens?
That is one of the compromises you make when you rent the cheap apartment. It’s one of the reasons it’s cheap.
So the apartment is cheap because it’s got bad transit mobility. That is true. But just because it’s true, doesn’t mean it *should* be true. It’s a failing of the transit planners of the past that the apartment is bad in this way.
Many places you can’t have a three seat ride because there aren’t three seats.
They had different priorities a century ago, people had less of an urge to go to out there because it hadn’t developed yet.
There is this wonderful invention that gives you a one seat ride almost everywhere you’d want to go, an automobile. One can even rent one with an operator supplied.
I mean, the concept of a radial metro was only invented for real in the 1930s in Moscow with British assistance (though London had a less clean version of the same emerging from a bunch of different private lines by 1907).
The NYC Subway is radial. It’s just that the center has expanded. Even with the bigger center it’s still radial.
“Cheap.”
What are your thoughts on the optimal distances from the center for rings?
I’d be curious how you’d design a network where some factor forces you to have a lot of three seat transfers. (Would imagine beyond history, geography would be a likely culprit. IE a mega-city with a large mountain or bay separating different sub-centers.)
Do you mean something like this?
Sort of – although I guess less the examples of Paris / NYC (where the water barriers are small and thus don’t really preclude treating the city differently than one without water) and more so something like Tokyo, Istanbul, SF. Ie somewhere that the geography would impede building between any given points A and B.
I suppose the question is perhaps too theoretical to be interesting, but what would an ideal network, from the ground up, look like in a city with that sort of geography?
New York’s waterways are really wide!
In both SF and Istanbul, urban rail should be thought of as a single trunk with branches. The trunk can have more trunks – there are two in each city and there should be more, and the exact paths of the trunks may differ somewhat, but there should be transfer stations to all the trunks at or near the landfall points. See for example my SB 827 crayon for SF.
A number of Asian systems are good examples of this. For example Hong Kong, Shenzhen, Busan.
Hong Kong is particularly bad given the high mountains in the New Territories and Victoria Harbor. They’re attempting to fix some of that, but the entire saga is basically what Alon loves to rail about, down to cost overruns, cutting corners, and the government having to call a board of inquiry…
In the meantime, Jarrett Walker managed to find a *six* seat ride: https://humantransit.org/2012/08/hong-kong-metro-five-transfers.html
Sort off-topic, but Copenhagen’s new ring is going to run (fully-automated) trains on 100 second headways. Maybe another way to get really fast service is not to be a big city, but a rich small one
Yeah, I saw, Copenhagen’s new-build Metro is really fascinating. That said, Paris runs driverless trains even more frequently: M1 and M14 run every 85 seconds, and M1 is so far the only driverless metro line that used to be have a driver (M14, Vancouver, Copenhagen, etc. were built driverless). This is something Paris truly is the global leader in. Only other place I know of that is planning to convert lines with a driver to driverless ones is Tokyo.
I guess that really depends. You might be able to get away with low dwell times as a small city, but when you go to something on a larger scale, perhaps the only thing that really works are larger trains that arrive a bit less frequently since crowding drives dwell times and headways up.
We’re learning this the hard way in Singapore with our medium-capacity Circle and Downtown lines being perpetually rammed at peak hours.
Nuremberg runs trains on the shared U2/U3 trunk (all driverless) every 100 seconds…
But to be fair it’s a rather short trunk of only six stops…