Wait ages for a bus and then two come along at once
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Re: Wait ages for a bus and then two come along at once
#2I thought this was going to be a rehash of this 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.
Re: Wait ages for a bus and then two come along at once
#3Well seems like he is aggregating data across many lines, stops and times per day. Not very surprising that the result looks random.
Re: Wait ages for a bus and then two come along at once
#4Also worth reading: http://en.wikipedia.org/wiki/Bus_bunching
Re: Wait ages for a bus and then two come along at once
#5Interesting. 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.
Re: Wait ages for a bus and then two come along at once
#6Does 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).
Re: Wait ages for a bus and then two come along at once
#7The 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
Re: Wait ages for a bus and then two come along at once
#8Bunching 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.
Re: Wait ages for a bus and then two come along at once
#9Interesting. 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 t…
My 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.)
Re: Wait ages for a bus and then two come along at once
#10Well seems like he is aggregating data across many lines, stops and times per day. Not very surprising that the result looks random.
There 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.