Graph Theory Subway Trains

Monday, September 7th, 2009

U-Bahn.svgBeen to Berlin recently? Noticed how everything seems to flow particularly smoothly when you navigate the subway system (the U-bahn) there? But that’s just because it’s Germany, right? I mean, seemingly in exchange for exhibiting certain, shall we say, strict and humorless character-traits, and sustaining themselves on Sauerkraut and other tasteless food (at least according to popular imagination outside of the country), Germans can at least be sure that their trains run on time.

Actually, not really. I don’t mean that the subway-trains don’t run on time in Berlin, it’s quite likely that they do. Rather, it seems that they have recently addressed the entire issue of U-bahn efficiency – especially the problem of minimizing transfer times between one line and another – with a bit of higher mathematics, as Holger Dambeck recounts for us in Der Spiegel (Waiting faster).

Consider: you pull into a transfer-station in your one subway train and cast an anxious eye across the platform to where you rather hope the other subway-line to which you want to transfer has a train already waiting there for you. Of course, it’s rare that you’re so lucky; usually you’ll need to get out and wait for some period of time before that follow-on train ever arrives. And sometimes – oh, the frustration! – you do see the train there across the platform as your first train pulls into the station, yet the other train-driver can’t even wait a minute and instead pulls out of the station just as you are arriving! (more…)

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