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.
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.