8 ms·
Wait ages for a bus and then two come along at once
- FLGMwt 12y agoI thought this was going to be a rehash of this http://www.wbez.org/series/curious-city/why-buses-arrive-bunches-110941 http://www.wbez.org/series/curious-city/why-buses-arrive-bun... but then I saw maths. I'd love to see more articles/analyses like this.
- im2w1l 12y agoWell seems like he is aggregating data across many lines, stops and times per day. Not very surprising that the result looks random.
- foobar2020 12y agoThere are different kinds of randomness. The exponential distribution of the waiting time is a nice, mathematically pleasing result. Although not a very nice one to the commuter.
- im2w1l 12y ago"Random" was poor wording on my part. What the exponential distribution means is that bus arrivals are completely independent. The time since the last bus came doesn't affect the probability that a bus will come anytime soon.
- natnat 12y agoAlso worth reading: http://en.wikipedia.org/wiki/Bus_bunching http://en.wikipedia.org/wiki/Bus_bunching
- evo_9 12y agoInteresting. He should look at data from Japan, along with other countries. When I was in Tokyo the trains and buses were all spread out and things ran on-time; you can literally watch the train arrive as the est. time of arrival clicked down to zero. Buses were similarly on-time and never bunched up. Not once did I see this pattern while I travelled around Japan for 15 days. When I arrived back in Denver the first thing I noticed were 2 light-rail trains that arrived about 5 seconds apart from each other. Buses also get similar bunched up. Denver isn't anywhere near London's density; I wonder if this is more related to the system in place and ethnocentric factors such as the pride that Japanese operators seemed to have at running everything as precisely as possible.
- lotharbot 12y agoMy dad always causes a ~90 second delay for the Denver light rail, because the operator has to activate the wheelchair ramp for him. How do they handle that sort of thing in Tokyo? (Also, I often see multiple light-rail trains bunched up after sporting events.)
- screwedup 12y agoI'd imagine that the platform on most light-rail trains is built so that a ramp is unnecessary?
- lotharbot 12y agoThere's a ramp inside the train that needs to be deployed to bridge the gap to the ramp at the platform.
- reverius42 12y agoSounds like a strange design to me. On most of the train-based public transit I've seen (and even some of the "rapid" buses), the floor of the car is aligned with the floor of the boarding area, such that ramps are unnecessary.
- lotharbot 12y agothey're aligned, but there's a small gap that needs to be bridged.
- warfangle 12y agoFrom what I found in a cursory investigation is that many stations: A station attendant will They will ask about your destination and escort you from the ticketing area to the appropriate platform and set up the ramp (if necessary) ahead of time. When arriving at a station, there will be an attendant there with the ramp set up for you to disembark. They also have wheelchair accessible escalators - an attendant will halt the escalator and merge several steps into one flat one, with a lip.
- cozzyd 12y agoDoes 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).
- quarterto 12y agoLondon buses are cashless. Either you use an Oyster or contactless payment card, or buy a ticket or pass in advance.
- thaumasiotes 12y agoSo, pay as you board.
- lmm 12y agoNot in a way that delays you - the driver doesn't count change or anything.
- pimlottc 12y agoThere's still a small delay as each passenger waits to scan their card at the single machine at the front of the bus.
- cozzyd 12y agoAlmost nobody in Chicago uses cash to board, but if there are 20-30 people boarding a bus, it can still take over a minute as they all have to go through the front door and tap their cards (and of course, it doesn't always work the first time for some reason).
- cameldrv 12y agoThe 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 agoThis 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 agoThe existence of one plausible explanation (good model fit) does not automatically invalidate another plausible explanation (mechanism of action).
- foobar2020 12y agoIt 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.
- dragon88 12y agoBunching 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.
- bentcorner 12y agoAnother 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".
- omegant 12y agoOr set a dropoff only stop 50 yards from the designated stop. That way the people from the stop don't try to board.
- quarterto 12y agoI'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.
- simonster 12y agoAnother, very different pattern of bus arrival times evidently arises when buses slow down to prevent bunching: https://www.quantamagazine.org/20130205-in-mysterious-pattern-math-and-nature-converge/ https://www.quantamagazine.org/20130205-in-mysterious-patter...
- rawnlq 12y agoIf we accept the exponential waiting time model, then another term for this phenomenon is Poisson clumping: http://en.wikipedia.org/wiki/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'
- mungoman2 12y agoThis sounds interesting, but I don't understand. "if someone walks in, you are more likely to currently be in a long streak and have stuff clump afterwards" What does that mean?
- dnautics 12y agoit'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.
- warfangle 12y agoInterestingly enough, I ran into an extreme of this on Saturday; while I wasn't inconvenienced by it (the bus showed up 2 minutes after I arrived at the stop), I overheard the bus driver talking to riders he seemed to know as regulars. This bus was on time, but there hadn't been a bus for over a 45 minutes; the schedule defined the interval as 1 bus / 7 minutes. There were seven busses on the same route directly behind us.
- erik_p 12y agoAt least with SF Muni the bunching of busses issue is more human/contractual/process related. When the bus runs late (because stuff happens) and thereby completes it's route late and turns around, and is basically right up against the "next" bus... they send them both out BECAUSE the thought of paying a muni worker to wait for 10 minutes to create a sane space between busses is unthinkable in a penny wise, results foolish budgeting process.
- dylansal 12y agoGreat article. And here's some academic research that models the dynamics of bus bunching and proposes a decentralized control scheme to minimize a combination of passenger wait time and travel time: http://www.its.berkeley.edu/publications/UCB/2011/VWP/UCB-ITS-VWP-2011-1.pdf http://www.its.berkeley.edu/publications/UCB/2011/VWP/UCB-IT... ...And here's a product we created to commercialize this research: https://www.youtube.com/watch?v=YQXZybHO52A https://www.youtube.com/watch?v=YQXZybHO52A Full disclosure: I am a co-founder along with the authors of the above paper of Via Analytics: v-a.io