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Wait ages for a bus and then two come along at once

jasmcole.com

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Re: Wait ages for a bus and then two come along at once

#11

Post by foobar2020 »

cameldrv wrote: post #7

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 wi…

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.

Re: Wait ages for a bus and then two come along at once

#12

Post by quarterto »

cozzyd wrote: post #6

Does London use pay as you board or proof of payment for buses? Here in Chicago, I think boarding delays significantly contribute to bus bunching (or at least make it worse).

London buses are cashless. Either you use an Oyster or contactless payment card, or buy a ticket or pass in advance.

Re: Wait ages for a bus and then two come along at once

#13

Post by bentcorner »

dragon88 wrote: post #8

Bunching happens a lot when one delay causes one bus/streetcar/train to hold up all the ones behind it. Best solution is letting transit vehicles going the opposite direction to turn ahead ahead of the bottleneck and serve the passengers waiting at the stations in front of the delay area.

Another solution would be to have the lead bus skip pickup at a stop (or two).

You'd need clear and solid signage to assuage people waiting though. Something like "Behind schedule, dropoff only. Next bus arrives in 2 minutes".

Re: Wait ages for a bus and then two come along at once

#14

Post by quarterto »

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. I've no intuitive idea whether this would smooth out the flow more than waiting behind the first bus though.

Re: Wait ages for a bus and then two come along at once

#15

Post by stdbrouw »

foobar2020 wrote: post #11
cameldrv wrote: post #7

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 wi…

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.

The existence of one plausible explanation (good model fit) does not automatically invalidate another plausible explanation (mechanism of action).

Re: Wait ages for a bus and then two come along at once

#16

Post by foobar2020 »

stdbrouw wrote: post #15
foobar2020 wrote: post #11

Earlier quoted context omitted.

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.

The existence of one plausible explanation (good model fit) does not automatically invalidate another plausible explanation (mechanism of action).

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.

Re: Wait ages for a bus and then two come along at once

#18

Post by rawnlq »

If we accept the exponential waiting time model, then another term for this phenomenon is Poisson clumping: http://en.wikipedia.org/wiki/Poisson_clumping.

I think one intuitive way to explain it is if you're flipping some biased coin continuously, then if someone walks in, you are more likely to currently be in a long streak and have stuff clump afterwards. For exampling flipping a coin with probability 1/60 of heads each minute for an hour (so average wait time should be 10 mins):

    > ''.join('H' if random.randint(1, 10) == 10 else 'T' for i in xrange(60))
    'TTTHTTTTTTTTTTTTTTTTTTTTTTTTTTHTHTTTTTTTTTTTHTTTTTTTTTTHTTTH'

Re: Wait ages for a bus and then two come along at once

#19

Post by meej »

cameldrv wrote: post #7

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 wi…

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

Re: Wait ages for a bus and then two come along at once

#20

Post by dnautics »

it's worth noting that this measures the distribution of bus intervals. The distribution of wait times will be more extreme because there will be more passengers waiting at a bunched stop, so the 'bunched' experience will be more common than the 'unbunched' experience. Moreover, the hours when the bunching phenomenon occurs are probably biased to high commute volume times.
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