Cartographer (and artist) Daniel Huffman is drawing river systems as subway maps.  He insists it’s just for fun, but these maps push an important button for me.

Leigh Holcombe’s email pointing to Huffman’s work is fascinating timing, because I was just about to write a section of the book on how branching dissipates frequency.

Really, these fanciful maps are a bit reminiscent of some real transit maps, aren’t they?

Metlink’s map of the Melbourne train network has important things in common with a river system map.  First, both networks are radial, which means that all lines converge to flow to a single point (New Orleans for the Mississippi River, the City Loop for Melbourne’s trains).  And necessarily, both maps are full of branching:

But branching always divides frequency.  The Melbourne map gives a superficial impression that Lilydale, Boronia and Ringwood all have the same kind of transit service.  They certainly all have train stations, but the branching means that Ringwood has to have more frequent service than either branch, and that may be the difference between a service that can be used spontaneously and one that requires you to build your life around a timetable.

It’s interesting to speculate how transit policy might change if everybody was trained to be suspicious whenever they see this …

… because this always means one of three things.  Either (a) points beyond the branching point have less frequent service or (b) one of the branches operates as a shuttle, requiring a connection, or in a few rare cases (c) the train itself comes apart, with some cars proceeding along one branch and some along the other.  Geometrically, it has to mean one of those things.  And before you decide whether the service is useful to you, or whether you support a proposed transit project whose map looks like this, you should ask which of those it is.

I’ve always been partial to mapping styles where a branch is rendered as a wide line splitting into two narrow lines, such that the width of the two narrow lines adds up to the width of the main line.  In my presentation “A Field Guide to Transit Quarrels,” I used that approach to clarify one of the possible branching patterns of BART’s San Francisco Airport line (though this is not the pattern that runs today.)

Because in that respect, transit lines really are like rivers.  Just as two converging rivers combine their volume of flow, two converging transit branches combine their frequency.

36 Responses to what rivers teach about transit

1. Edward February 16, 2011 at 6:38 pm #

You’re right as a general rule. Where I live in Adelaide though, although the main line before the branch has more trains, they do not all stop at the same stations. It is only the larger stations that have the higher frequency.
Where I grew up in the UK, what would sometimes happen would be for two separate unit trains to be coupled together until the junction station and then split.

2. Zoltán February 16, 2011 at 6:57 pm #

Incidentally, in London, the particular Branch of the Northern Line that you’ve used a picture of (if I’m right about this, the branch to Mill Hill East) runs as a shuttle now, and is shown as a disconnected line of the same colour on maps.
Occasionally, there’s useful potential to remedy the problem with branching by turning one branch into a larger orbital line, with good transfers to the remaining radial line. When considering a big subway project that involved splitting off the Myrtle Avenue el from the Brooklyn Broadway el (JMZ trains) and extending both ends, I noted that it would have the benefit of allowing more frequent trains all the way along Broadway.
Though that example was more of a thought experiment than anything practicable, it’s a tactic that could prove of use in various places.

3. In Brisbane February 16, 2011 at 7:08 pm #

“But branching always divides frequency. The Melbourne map gives a superficial impression that Lilydale, Boronia and Ringwood all have the same kind of transit service. They certainly all have train stations, but the branching means that Ringwood has to have more frequent service than either branch, and that may be the difference between a service that can be used spontaneously and one that requires you to build your life around a timetable.”
I have a prickly prickly question. Do you have any comments on cutting off the branches and running a shuttle service to the mainline station? Good idea? Bad idea?

4. Tessa February 16, 2011 at 7:23 pm #

Do you have any examples of cities where a metro train actually splits and different cars go down different branches of a line? That is amazing and I would love to see posts on that and how applicable it is to elsewhere.

5. Jarrett at HumanTransit.org February 16, 2011 at 7:33 pm #

@ In Brisbane.  Running branches as shuttles can work off-peak and especially evening, if you're disciplined about creating good cross-platform connections.  But it's an idea that needs to be understood when the line's being built.  Otherwise, the shuttles end up being invented belatedly to solve problems that should have been solved in the original design.  See the Almaden extension of the San Jose light rail system, for example.  In Brisbane, Tennyson used to be served a Corinda-Yeerongpilly shuttle, which I believe finally died of its own absurdity.

6. In Brisbane February 16, 2011 at 7:59 pm #

Since my post I’ve tried to look for examples where this happens at all times and the best I can come up so far is Toronto’s Sheppard subway (locals call it ‘Stubway’ which runs every 5-6 minutes all day and feeds the Yonge-University-Spadina line (YUS).

7. Leigh February 16, 2011 at 9:12 pm #

@ In Brisbane: The new timetables for Melbourne (due to kick off in May) will run a shuttle between Newport and Laverton (Werribee line) creating a kind-of spur that connects back onto itself to increase/match frequencies on this section where there’s mostly single track.
The Lilydale line does actually run shuttles between Ringwood and Lilydale (after 8:30pm) to meet with trains operating on the Belgrave line, hence creating an even frequency.
This idea has also been floated around by enthusiasts for Belgrave (not Lilydale) Cranbourne and Williamstown (see: http://transporttextbook.com/?p=1080 ), though given the recent media beat-up about the inconvenience of having to transfer to achieve the convenience of frequency increases (without anyone having actually SEEN the new Metro timetables) it may be some time before the public accepts these concepts. Maybe once they’ve all embraced smartcard ticketing?
Also, the Carlingford line in Sydney operates as a segregated branchline from Clyde (with this interchange the main use of the station as most passengers use nearby Granville).

8. Leigh February 16, 2011 at 9:24 pm #

PS – the map in that link does go a small way to indicate frequency increases where the different lines converge at Footscray, North Melbourne, Richmond, South Yarra, Caulfield, and Burnley.
Difficult to create for Melbourne, as some mainlines would be drawn thicker than others, or combine multiple express lines to cope with the inconsistent stopping patterns

9. Wad February 16, 2011 at 9:55 pm #

You know, the Melbourne map reminded me of the Stockholm, Sweden, metro map hilariously translated to English.
http://strangemaps.files.wordpress.com/2007/06/stockholmmetro.jpg
Here is the real map to compare:

10. In Brisbane February 16, 2011 at 9:58 pm #

Thanks for this. The media might have had a beat up about transfers but is this a “cultural feedback effect” springing from their bad interchange experiences where the connection wasn’t frequent or timed? I wonder.

11. anonymouse February 16, 2011 at 11:02 pm #

Jarrett, a minor correction: the branching pattern you show actually does run today, during the day only though. At night and on weekends, it’s San Bruno to Millbrae via SFO (with a reversal at SFO). Which in itself is pretty confusing and customer-unfriendly.

12. Jarrett at HumanTransit.org February 16, 2011 at 11:05 pm #

Anonymouse.  Thanks, corrected.

13. anonymouse February 16, 2011 at 11:24 pm #

Also, a Melbourne actually used to have circumferential railway lines, including the Inner Circle from Royal Park to Rushall/Merri and the Outer Circle from Fairfield via East Camberwell, then including the Alamein branch, and continuing via East Malvern to Hughesdale. Both of these are now abandoned, though the right of way is mostly preserved as bike trails.

14. Sdier February 16, 2011 at 11:50 pm #

BART uses that pattern until 7pm, so its still in, just not after 7pm.
After 7 all trips are via SFO terminating and starting in millbrae [at least for millbrae bound and leaving trains].

15. Sdier February 16, 2011 at 11:52 pm #

[and thats on weekdays, not weekends]

16. Jack Horner February 17, 2011 at 1:56 am #

@Tessa: example of where trains split.
In the 1970s this used to happen at Staines, southwest London, the two halves continuing to Windsor and Weybridge. I don’t think they do it any more, presumably becuase it’s a hassle operationally.
@ In Brisbane: whether a branch should be run as a shuttle: depends how much you want extra frequency on the downstream combined route section.

17. Stephan February 17, 2011 at 5:31 am #

Tessa:
Do you have any examples of cities where a metro train actually splits and different cars go down different branches of a line?
The S1 in Hamburg splits at the airport-branch junction.

18. PhilC February 17, 2011 at 8:14 am #

Splitting hairs maybe, but the Mississippi, like most river basins is more arborescent than radial, unless it has a huge delta comparable to the catchment area, in which case its still arborescent with a big root structure…
Not quite a metro but regional commuter trains BOB (Bayerische Oberlandbahn) south of Munich also split up to serve 3 branches.

19. EngineerScotty February 17, 2011 at 8:51 am #

The Amtrak Empire Builder splits into two trains (while headed west) at Spokane, with one branch going to Seattle and the other to Portland.
Of course, that’s long haul rail service, not intracity transit…

20. francis February 17, 2011 at 9:49 am #

With trains that divide, doesn’t that mean for part of the trip there’s an extra set of staff? Or do they just board at the branch off point?

21. Winston February 17, 2011 at 12:26 pm #

Another example of splitting trains is what used to happen on the Muni Metro in San Francisco where trains were coupled in a tunnel shared by several lines and then split when the lines split on the surface.

22. JJ February 17, 2011 at 5:47 pm #

Holy cow, I JUST saw that Mississippi River map in person today at the Wisconsin Land Information Association conference!

23. rhywun February 17, 2011 at 6:23 pm #

@Winston
I was just going to add the example of San Francisco… they don’t do it anymore? I only lived there for one year in 1996, and they were doing it then. It seemed kind of pointless to me at the time. Unless there was some small savings to be had by using only one driver in the tunnel? But it was so hugely annoying for riders to sit there at West Portal while the train uncoupled. But then the whole operation of the Market Street tunnel (and Muni in general) was so notoriously chaotic at the time – things can only have improved since then. I would hope.

24. Ed Sanderson February 17, 2011 at 7:40 pm #

Rivers were our first transit systems and this brilliant map explains why. I followed the link to the creator’s Web site and I posted a message expressing my desire that he publish his creations in a book. I hope that you who love transit systems, maps and graphics design, like I do, do the same.

25. Edward February 17, 2011 at 8:14 pm #

Tessa,
Another example of splitting, and one that is close to Jack Horner’s example, was a train made up of two units that used to leave London Waterloo and then divide at Woking. One half would go to Alton while the other went to Basingstoke. They would join up at Woking when going the other way.
These days on Sundays, South West Trains runs trains from Waterloo that split at Eastleigh. Half goes to Portsmouth while the other continues towards Southampton and Bournemouth. Here is the timetable. See pp12-13. Trains marked with “D” split:
Cheers,
Edward

26. In Brisbane February 18, 2011 at 12:38 am #

What happens when the river floods? Is that a good analogy with too many cars?

27. anonymouse February 18, 2011 at 12:58 am #

@rhywun, I think they did it because of the extremely limited capacity at the Embarcadero terminal. The turnback track past Embarcadero and the extension to 4th/King has largely fixed that bottleneck. That and apparently when they tried running more than two Bredas in a train, they tripped the breakers at the substations. It might be possible to achieve a similar increase in capacity by double-berthing trains at the nice long platforms on Market, but unfortunately, the crufty old Seltrac system doesn’t support that.

28. Dexter Wong February 18, 2011 at 1:10 am #

@winston,@rymun,
I lived in San Francisco from 1955 to 1989 and took Muni Metro from its beginning in 1980 until 1985, then off and on until 1989. Muni’s big dream was to have trains of JN and KLM cars leave Embarcadero and split off at Duboce and West Portal. It started off OK, but the time it took to un-train and separate the cars slowed things down. Coordinating the link-up of LKM cars annoyed people who had to wait for a train to form, or traffic kept the proper cars from showing up in time, so dispatchers would send a solitary car ahead to keep up the schedule. Eventually, the whole scheme was discarded. However, this causes people to say that the subway is underutilized. (Damned if you do, damned if you don’t.)

29. anonymouse February 18, 2011 at 10:15 am #

Of course, all this is made worse by the fact that Muni has to pay the driver extra when their train is switched from a K to an M or whatever, which makes it much more important for the trains to go into the subway in the right order.

30. David M February 18, 2011 at 12:28 pm #

So true. In Vancouver there is a combined line from downtown Vancouver to Columbia in New Westminster – there the line splits. On the combined line, trains run every 108 seconds in the peak. On the branches, one gets 4-5 minute peak service and the other roughly a 2-3 minute peak service. Late at night (after midnight to the last trains) the combined line has trains every 4 minutes and each branch sees a train every 8 minutes. Still frequent but you get the idea.
It’s interesting to note that in London the newest Underground lines have no branches (Victoria, Jubilee). In fact, when Jubilee was originally opened it took over one of the Bakerloo Lines branches, reducing the Bakerloo to a branchless line also.
For real complications, look at Camden Town on the Northern Line in London, England. Just south of this station is a complex deep underground junction that lets trains from any two of the branches south of Camden to simultaneously run on any two of the branches to the north. It is a marvel of engineering, but it is also an operational nightmare with trains run from any branch to any branch – one train runs late and it can cause problems on all of the branches. London has wanted to simplify the operations by spliting the line into two and requiring an interchange at Camden Town. There are four platforms at Camden Town but the interchange passages are insufficient to handle the expected interchange traffic – so for now, it is cheaper to suck it up and deal with the operational issues.
There is an interesting effect of this interchange. Going south, both branches serve Euston Station before heading off to cross London on two different lines serving different areas of the core. You can get on one train at Camden, stop at Mornington Crescent and at Euston. You could get on the following train at Camden and arrive at Euston without passing through Mornington Crescent. The reason is that Mornington Crescent is on only one of the two branches, the other just bypasses the station. It makes for fun time when trying to get to Mornington Crescent.

31. Tessa February 20, 2011 at 12:02 pm #

Thanks to the other commenters for the links. I do get the impression from the video that it could be tough to manage on high-frequency lines, though it is pretty cool.

32. anonymouse February 21, 2011 at 8:26 am #

I think the splitting/joining of trains is a good idea in highly branched networks, like the lines radiating from London, and you go the split or join not on the highest frequency section but somewhere after the first or second branching point, where you’re not as constrained by track capacity. It helps when you’ve got a mainline rail network, because those tend to have extra platforms at stations that can be used for this sort of thing.

33. Alon Levy February 21, 2011 at 10:12 am #

In addition to splitting, you can shorten trains beyond some point, if the frequency is too low for having some trains short-turn. It’s done on a couple of lines in Greater Tokyo.

34. James A February 22, 2011 at 7:07 am #

Germany has too many examples of trains that are split partway through their journeys to name here. But since I’m in Munich I’ll name the local examples: the S1 regional rail line runs on a 20 minute headway and splits in Neufahrn, with one section going to the Airport and one to the suburb of Freising; the Bayerische Oberlandbahn runs three-unit DMU trains on a one-hour headway, with the sections splitting at two different points and ultimately continuing to Bayerischzell, Lenggries and Tegernsee; the Fugger-Express regional express line runs from Munich on a one-hour headway, splitting in Augsburg, with one section continuing to Ulm and one to Donauwörth.
In Franconia (northern Bavaria, up near Nuremberg) there are dozens of splitting schemes, such as the trains between Lichtenfels, splitting in Neuenmarkt-Wirsberg into sections to Bayreuth and Hof. In the 2009 timetable (haven’t checked since then), there was even one daily train that left Nuremberg with 4 DMUs, each going to four different destinations! The first split happened IIRC in Hersbruck, just 15 minutes from Nuremberg!
And these are just some examples (the through carriages on the night trains are even more complicated). The lesson: it’s more common than some think, and always be sure to check the destination of the section of train you are boarding when in Germany!

35. Jarrett at HumanTransit.org February 22, 2011 at 1:24 pm #

@ James.  Does staff for half the train board/alight at the branch point, or ride all the way through the common segment?  If the former, how long does the splitting action take before both trains are ready to depart?  Jarrett

36. Thewhitefolder.blogspot.com June 7, 2011 at 9:48 am #

Is there some rule of thumb for how many stations, trains, or passengers justify building a new branch? If there’s only one or two stations, it seems like you should just people into a station on the main line – be that by bus, auto park-n-ride, people-mover, etc.