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7:56. A train pulls into the station in front of me, right on schedule. As I stepped through the door, I wondered, “How on earth do trains and buses arrive at their destination within +/- a few minutes of the indicated time?” It seems like a pretty unlikely event – there are just so many variables!

First, there’s the number of people who get on and off the train/bus. Maybe there’s an old lady, or a guy in a wheelchair that takes like 3 minutes to get on. Maybe there’s 100 people going to a party and they all need to squeeze off at the same time. Maybe there’s nobody on the bus and nobody at the stations, so the bus just keeps on going. Since this is a big variable that is kind of random, it’s hard to imagine how a train/bus can arrive in +/- 2 minutes over 90% of the time.

Furthermore, trains and buses usually never arrive early. Most of the time, we see them going as soon as people get off. Occasionally, there may be a long pause due to construction delays or something, but we just don’t seem to see the bus/train stop at one spot just because they’re early. Sure, at the final stop the bus/train heads out at the right time, but how often have you seen a bus just sitting there waiting for the right time to leave? Given this, how can a bus/train pretty much never arrive early? (I cannot recall a single instance when this has happened in my life) If they arrive on time normally, and there are times when there are no people on the train and they don’t stop, it doesn’t seem to make logical sense.

Thirdly, there are traffic lights all over the place (yes, the light rail here in California does stop for traffic lights)! If someone takes 20 seconds to get on vs. 15 seconds to get on, that could mean an additional minute or two of waiting time. Given that a bus (more than a train) crosses so many streets, it seems that this would be a significant variable in how long the bus would take to get to the next stop. Wouldn’t it hit all green lights sometimes and all red lights at other times?

Lastly, there are all sorts of accidents, breakdowns, etc. that may significantly impact the schedule. This is actually the most common reason why trains are late in my experience, which is pretty amazing to me. Almost all the times I’ve been late on trains, it’s because some train is going out of service or something is blocking the track.

Given all of these variables and the fact that during busy hours, the “scheduled time” is only 15 minutes apart, it seems like the times on the schedules shouldn’t mean anything. The best you can do would be to say, “Okay, there’s going to be a bus/train around every 15 minutes”. Yet, between 7:55 and 7:58 on over 95% of the mornings, my train seems to arrive.

I am aware that train bus/train schedules have different intervals for different parts of the day and different schedules for weekdays and weekends, perhaps partially accounting for these variables. Still though… within a 3-4 minute window most of the time?

Maybe people’s traffic patterns are much more predictable than I’m thinking. Maybe traffic lights are more predictable than I think too. Maybe trains and buses do arrive early sometimes and I just don’t notice.

It seems like a lot of maybes though.

Then again, the train is there on time so…

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3 Responses to “The Strange Accuracy of Bus And Train Schedules”

  1. thom on November 23rd, 2007 1:16 pm

    I’m a transportation engineer. Trains don’t arrive on-time very often. What area are you in?

  2. thom on November 23rd, 2007 1:18 pm

    On traffic lights: They’re normally not that intelligent. Although some transit systems have things like street-car or bus overrides, which cause the lights to extend the “green time” longer to let the transit vehicle through.

    On the unpredictability of people/etc: Drivers are normally responsible for compensating for the schedule. So if they’re behind, they speed up (if possible). If they’re ahead, they might wait an extra few seconds at a stop.

  3. Warren on November 23rd, 2007 1:32 pm

    I’m in the San Jose area and I’m mostly referring to the airport shuttle and the light rail.

    Ohhh, that’s interesting about the extra “green time” thing! Hmmm… what if two buses approaching from two directions both want it to be green?

    Yeah, so how do they get past the traffic light thing without the override? Just seems like that’s kind of random :)

    Hmm I see – so it seems like the drivers compensate a lot for the schedule. It’s weird though, since I’ve never seen them waiting at a stop for no particular reason. It’s usually like “this train is stuck, so we need to wait 5 minutes”. And yet, even with all these delays, even like at night, the train still arrives within +/- 5 minutes of the indicated time!!