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  • Subway-Train-System Geometries: Remarkably Similar

  • General discussion of passenger rail systems not otherwise covered in the specific forums in this category, including high speed rail.
General discussion of passenger rail systems not otherwise covered in the specific forums in this category, including high speed rail.

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 #1048937  by lpetrich
 
Journal of the Royal Society: Interface - A long-time limit for world subway networks by Camille Roth, Soong Moon Kang, Michael Batty, Marc Barthelemy
Preprint at arxiv.org: [1105.5294] A long-time limit of world subway networks
Where I learned of it: Study shows subway systems develop in remarkably similar ways - nontechnical

The authors started off with a graph of what percentage of cities in the world have subway-train systems as a function of population. It increases roughly linearly to 65% for 3 million people, then roughly linearly to 100% for 10 million people.

They then looked at subway-train systems in Beijing, Tokyo, Seoul, Paris, Mexico City, New York City, Chicago, London, Shanghai, Moscow, Berlin, Madrid, Osaka, and Barcelona. Since their growth patterns varied as a function of time, they instead decided to use the number of stations as their independent variable.

They found that subway-train networks converge onto a structure with a multiply-connected core and outward-radiating branches. The percentage of stations in branches starts off at 100% and goes down to about 45%. When a well-defined core forms, the branches' spatial extent converges on twice the core's spatial extent, and stays there. The number of branches increases as power 0.6 of the number of stations, close to the value of 0.5 if one expects the number of branches to be proportional to the core's perimeter.

Most systems' barycenters moved very little, with the exception of those of NYC and Chicago, which are constrained by various bodies of water.

The number of stations increases as the square of the distance from the barycenter while in the core, but increases more slowly outside the core -- Moscow has an exponent of about 1 outside the core, corresponding to evenly-spaced stations.


The authors did not address the question of what might be causing these patterns, so I will. I think that this core-and-branches structure is caused by something shared: where to put new lines. Do they feed into existing lines? Or do they stay separate from existing lines? Feeding into existing lines could cause subway traffic jams, while building separate lines would bring service to additional areas. So there are both operational and political reasons for making new lines separate.

Core regions typically have a lot of travel destinations, like major workplaces, while branches extend into residential areas, and there are not as many people traveling from one residential area to another.
 #1049009  by amm in ny
 
lpetrich wrote:They ... looked at subway-train systems in Beijing, Tokyo, Seoul, Paris, Mexico City, New York City, Chicago, London, Shanghai, Moscow, Berlin, Madrid, Osaka, and Barcelona.
...
Core regions typically have a lot of travel destinations, like major workplaces, while branches extend into residential areas, and there are not as many people traveling from one residential area to another.
I notice that all the cities they studied, or at least those I'm familiar with, have the urban development pattern that was common in the late 1800's and the first half of the 1900's, where jobs tended to be in the center and residences outside the center. BTW, this was encouraged by the presence of urban and suburban rail networks. In the past 50 years or so in the USA, most of the job growth has occurred outside the city centers, encouraged by the building of freeways that bypass the city centers and facilitate suburb-to-suburb travel (but only by car.)

I wonder what conclusions the authors would have reached if they had studied cities (or metropolitan areas) where most of the jobs are distributed around the outskirts, such as Atlanta, or which never had a single concentration of jobs (city center) to begin with, such as Los Angeles.
 #1049145  by lpetrich
 
They would have had to study the geometry of road networks, not rail ones.

To see what other urban-rail systems are like, I went to urbanrail.net > metro - subway - light rail, with its huge collection of maps. I found several other systems that fit the pattern of a core of crisscrossing lines surrounded by branching outward lines, like the Washington Metro. That pattern is evident even in many systems with only a few lines, like Boston, Philadelphia, Montreal, St. Petersburg Russia, etc.

So are there any exceptions among subway-train / rapid-transit systems? Apart from trivial ones like only one or two lines, an exception would have to have a lot of outlying lines without a core of crisscrossing lines, and that requires a lot of branching. The only such system I know of is BART. It has 4 branch points and no crossing points.

Turning to North American light-rail systems, some of the surviving older systems have a single urban-core line with several branches: Boston, Philadelphia, San Francisco. Most of the newer multiline ones have a lot of branching without crisscrossing, like in Dallas, Salt Lake City, and San Jose. Portland, OR is an exception, with some core crisscrossing.

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Commuter-rail systems are a different story. Most of the older multiline ones radiate out from stub-end terminals, having a lot of branching but no core crisscrossing. But over the last century, some cities have built connections between commuter-rail terminals, like Philadelphia, London, Paris, Madrid, Hamburg, Frankfurt, Munich, and Berlin. In fact, the Berlin S-bahn and the Paris RER have crisscrossing cores.
 #1049181  by amm in ny
 
Apparently in response to my comment:
amm in ny wrote:I wonder what conclusions the authors would have reached if they had studied cities (or metropolitan areas) where most of the jobs are distributed around the outskirts, such as Atlanta, or which never had a single concentration of jobs (city center) to begin with, such as Los Angeles.
lpetrich wrote:They would have had to study the geometry of road networks, not rail ones.
Why?

I can't think of a reason for ignoring the rail networks in LA and Atlanta in favor of studying the road networks that would not equally apply to the cities they did study.

All of the cities in the original study have extensive road networks, as well as urban/suburban rail networks. The roads in cities that I know of are set up to allow suburb-to-suburb travel without going through the core, just like LA and Atlanta.

Los Angeles and Atlanta both have subway systems in addition to their road networks. I don't know about LA, but Atlanta is apparently going with the suburbs-to-core model for its subways.
 #1049322  by lpetrich
 
So you have in mind studying the rail systems of places like Atlanta and Los Angeles.

It must be noted that there isn't much to study. Neither city has the complexity of NYC's or Chicago's systems.

Atlanta's MARTA system is two crossing lines, each of which has a branch. Most of it is within I-285, a highway that encircles Atlanta proper. Atlanta is now building a downtown streetcar that crosses MARTA's north-south line a little north of its intersection with MARTA's east-west line. It will go east-west, and does not have any other intersections with MARTA lines. For Now, Atlanta Opts to Promote Streetcar Starter Line Over Beltline « The Transport Politic

Los Angeles has a rather short subway system, though it does have a branch in it. Some light-rail lines radiate outwards, but only one of them has a branch. There is one crossing: the Green Line crossing the Blue Line in southern LA. The Crenshaw Line will connect the Green Line and the Expo Line, and may continue northward to the Purple Line, a branch of the LA subway. So it's mostly branching.