4 ms·

The WBEZ article below alludes to the true dynamics problem, but doesn't explain it. The problem is that say you normally run in 10 minute intervals. For what

The WBEZ article below alludes to the true dynamics problem, but doesn't explain it. The problem is that say you normally run in 10 minute intervals. For whatever reason, double parked car, helping a disabled person on the bus, etc, you get a minute behind schedule. Now suppose at the next stop typically 10 people are waiting. They arrive at the bus stop at one per minute all day. Since you're a minute late, there will be 11 people, which will take slightly longer to load. Furthermore, now the buss is a little bit fuller, so it takes people a little longer to get to and from the doors. Now you get a little more behind schedule. The bus behind you now has the opposite happening. The extra guy you picked up should have been his passenger, and so he makes his stops more quickly, until he catches up with you. You can try to fix this in a few ways. 1. You can reduce the perturbations to the system, for example, offboard payment, dedicated lanes, stricter double parking enforcement, quicker entry/exit systems for disabled passengers. 2. You can reduce the feedbacks, or provide a counter-feedback, for example, frequent scheduled waiting stops to resynchronize, don't collect fares when the bus is full, traffic light priority when the bus is full

foobar2020 12y ago
This is a nice analysis, but the data in the article actually disproves it, at least to the degree show in the last plot (quite reliably in my opinion). The distribution of the waiting time is exponential, is a Poisson process, which means that buses do not influence each other.
- stdbrouw 12y ago
  The existence of one plausible explanation (good model fit) does not automatically invalidate another plausible explanation (mechanism of action).
  - foobar2020 12y ago
    It does if the explanations are contradictory. In this case this means one of two things: 1) The "first bus collects delay" theory is responsible for a part of the difference between the data and the model, after all there is some. 2) There is another mechanism at action that statistically reverses the effect of the "first bus collects delay" theory, not necessarily in the same bus runs. Number 1) is coherent with Occam's razor.
- barrkel 12y ago
  The mechanism is real and I've seen it in action, to the point that two buses can end up leap-frogging one another as they make their way along a route, the later bus becoming the earlier bus, but getting bogged down on the next stop, and so on. Glommed together like that, they rarely come apart. If the data doesn't support that - and I haven't the time to analyze the analysis to determine if it doesn't - it's probably due to actions TfL take to counter it. Buses don't stop as often to "even out gaps in the service" as the tube does, but standing at bus stops, I frequently see buses "disappear": two buses look like they're going to arrive at the same time, but one of them turns into a different bus, like it's been reallocated.
- fragmede 12y ago
  http://en.wikipedia.org/wiki/Bus_bunching http://en.wikipedia.org/wiki/Bus_bunching is a real, studied thing.
meej 12y ago
I like to summarize this with a riff on Brook's Law: "Adding people to a late bus makes it later."
thaumasiotes 12y ago
The first thing I'd want to know, to see whether this is true, is "when two buses clump, do they both arrive between the scheduled arrival time for bus 1 and bus 2, or do they both arrive on time for bus 2?" The only time I've personally experienced bus clumping, they were both late (for the bus 2 time). That doesn't suggest that bus 2 was being sped up relative to expectation.
- unreal37 12y ago
  If buses don't generally pass each other (for reasons of both practicality of doing so the way stops are laid out, safety and policy), bus 2 making their schedule is dependent on bus 1. So if bus 2 is late, it can be bus 1's fault.
  - thaumasiotes 12y ago
    But they do pass each other. Look at quarterto's comment: > I've noticed that in the "two come along at once" scenario, the second bus often leapfrogs the first, skipping a stop while the first bus picks up passengers.
    - unreal37 12y ago
      That may be true in some cities, and not true in others. As a car driver in a big city, I've rarely seen a bus pass another bus, but I have seen buses all bunched together. I suspect there is no incentive for a bus driver to pass another bus. He's not the one in a rush to get anywhere.
TrainedMonkey 12y ago
Or you can detect that and let empty bus pass full one.
acomjean 12y ago
This happened to me this year. In our first blizzard this year in boston I just missed the 1 bus. Imagine my surprise to see a second half full 1 about 2 minutes later. By the time the bus went over the river to Boston we could see the first bus just a couple blocks ahead. Very few people (if any) at our stops.
soperj 12y ago
couldn't this be easily solved by making the fuller bus in front no longer stop at any stops unless a passenger requests a stop? And the emptier bus behind pick up all the passengers? -Full bus would get farther ahead by not stopping to pick people up and the bus behind would fall behind as it picked more people up.

foobar2020 12y ago

This is a nice analysis, but the data in the article actually disproves it, at least to the degree show in the last plot (quite reliably in my opinion). The distribution of the waiting time is exponential, is a Poisson process, which means that buses do not influence each other.

stdbrouw 12y ago
The existence of one plausible explanation (good model fit) does not automatically invalidate another plausible explanation (mechanism of action).
- foobar2020 12y ago
  It does if the explanations are contradictory. In this case this means one of two things: 1) The "first bus collects delay" theory is responsible for a part of the difference between the data and the model, after all there is some. 2) There is another mechanism at action that statistically reverses the effect of the "first bus collects delay" theory, not necessarily in the same bus runs. Number 1) is coherent with Occam's razor.
barrkel 12y ago
The mechanism is real and I've seen it in action, to the point that two buses can end up leap-frogging one another as they make their way along a route, the later bus becoming the earlier bus, but getting bogged down on the next stop, and so on. Glommed together like that, they rarely come apart. If the data doesn't support that - and I haven't the time to analyze the analysis to determine if it doesn't - it's probably due to actions TfL take to counter it. Buses don't stop as often to "even out gaps in the service" as the tube does, but standing at bus stops, I frequently see buses "disappear": two buses look like they're going to arrive at the same time, but one of them turns into a different bus, like it's been reallocated.
fragmede 12y ago
http://en.wikipedia.org/wiki/Bus_bunching http://en.wikipedia.org/wiki/Bus_bunching is a real, studied thing.

meej 12y ago

I like to summarize this with a riff on Brook's Law: "Adding people to a late bus makes it later."

thaumasiotes 12y ago

The first thing I'd want to know, to see whether this is true, is "when two buses clump, do they both arrive between the scheduled arrival time for bus 1 and bus 2, or do they both arrive on time for bus 2?" The only time I've personally experienced bus clumping, they were both late (for the bus 2 time). That doesn't suggest that bus 2 was being sped up relative to expectation.

unreal37 12y ago
If buses don't generally pass each other (for reasons of both practicality of doing so the way stops are laid out, safety and policy), bus 2 making their schedule is dependent on bus 1. So if bus 2 is late, it can be bus 1's fault.
- thaumasiotes 12y ago
  But they do pass each other. Look at quarterto's comment: > I've noticed that in the "two come along at once" scenario, the second bus often leapfrogs the first, skipping a stop while the first bus picks up passengers.
  - unreal37 12y ago
    That may be true in some cities, and not true in others. As a car driver in a big city, I've rarely seen a bus pass another bus, but I have seen buses all bunched together. I suspect there is no incentive for a bus driver to pass another bus. He's not the one in a rush to get anywhere.

TrainedMonkey 12y ago

Or you can detect that and let empty bus pass full one.

acomjean 12y ago

This happened to me this year. In our first blizzard this year in boston I just missed the 1 bus. Imagine my surprise to see a second half full 1 about 2 minutes later. By the time the bus went over the river to Boston we could see the first bus just a couple blocks ahead. Very few people (if any) at our stops.

soperj 12y ago

couldn't this be easily solved by making the fuller bus in front no longer stop at any stops unless a passenger requests a stop? And the emptier bus behind pick up all the passengers? -Full bus would get farther ahead by not stopping to pick people up and the bus behind would fall behind as it picked more people up.