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The Waiting Time Paradox, Or, Why Is My Bus Always Late?

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Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#31

Post by ikeboy »

ikken wrote: post #26

This reminds me the bet in the bitcoin community [1]. If on average bitcoin blocks are produced every 10 minutes, and you learn that 5 minutes ago someone found a block, what is the average time you will wait for the next block? It turns out it's 10 minutes, not 5 minutes as you would intuitively think. (it's a memoryless process, so average expected time till block is always the same - 10 minutes - no matter how man…

This is actually wrong. The average expected time till next block is almost never 10 minutes because hashpower goes on and offline all the time. It gets adjusted every 2016 blocks based on historical block timing so that if no changes occur then future blocks would be 10 minutes on average - but changes always happen so this is never accurate. As such, you do learn something by looking at prior block times.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#32

Post by LolWolf »

theoh wrote: post #29
bostonpete wrote: post #25

Earlier quoted context omitted.

Your use of "of course" seems to imply that there's some statistical reason that the probability of the next bus being inbound vs outbound wouldn't be equal. Is there? If so, it seems like it must be a different reason than the one in the article. What am I missing...?

It is impossible to catch more than one inbound bus on any given occasion, whereas any number of outbound buses might pass. BTW, on a slightly unrelated point, if there's no timetable, but the interval between buses is maintained reliably, the expected waiting time is uniformly distributed over that interval. If you have to get a second bus, you need to convolve two of those two uniform distributions to find out the…

Also, gaussians are great approximations for large n, too, since the convolution of any distribution with itself n times (for n "large enough") is close to gaussian (by the CLT. More generally, there are very nice error estimates for many distributions).

I suspect this analysis can be carried out and yield quite good results in the gaussian case (a careful analysis might even yield error bounds on the result).

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#33

Post by yhoneycomb »

stephengillie wrote: post #5

OneBusAway is surprisingly accurate, at least in my experience. Google Maps has very good transit support too. One reason buses are late is because a bus must travel a circuit. Cars provide linear transportation, so the delay can only happen in the direction of your travel. Since buses run a circuit, they are impacted by delays in the direction opposite of your travel as well. Your bus might be late because the retur…

> Google Maps has very good transit support too.

Where do you live? I'm guessing the bay area?

I was carless in DC for a year and Google Maps was ALWAYS wrong about when busses when arrive. My friend recommended an app called Transit which was right about 90% of the time, which was a godsend for me.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#34

Post by herodotus »

bostonpete wrote: post #25
herodotus wrote: post #8

Nice article. It reminds me of my year living in London, and taking the bus everyday to Imperial College from West End Lane in West Hampstead. There was a stop on both sides of the road - one for the outbound bus, and one for the inbound (the bus went from central London to a terminus and then returned mostly on the same route). Now we did not use schedules - way too inaccurate at rush hour, and the busses there were…

Your use of "of course" seems to imply that there's some statistical reason that the probability of the next bus being inbound vs outbound wouldn't be equal. Is there? If so, it seems like it must be a different reason than the one in the article. What am I missing...?

Because we might score -1, -2 or worse if 2 or 3 busses went in the other direction before ours came, but if ours came first, we score 1. We get on the bus and thus don’t know if another one or more arrives first on our side.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#35

Post by fjsolwmv »

ikeboy wrote: post #31
ikken wrote: post #26

This reminds me the bet in the bitcoin community [1]. If on average bitcoin blocks are produced every 10 minutes, and you learn that 5 minutes ago someone found a block, what is the average time you will wait for the next block? It turns out it's 10 minutes, not 5 minutes as you would intuitively think. (it's a memoryless process, so average expected time till block is always the same - 10 minutes - no matter how man…

This is actually wrong. The average expected time till next block is almost never 10 minutes because hashpower goes on and offline all the time. It gets adjusted every 2016 blocks based on historical block timing so that if no changes occur then future blocks would be 10 minutes on average - but changes always happen so this is never accurate. As such, you do learn something by looking at prior block times.

What you say is not a rebuttal of the parent comment. Parent explicitly said that average block times are 10mins in the assumption. The most recent block time doesn't change that.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#36

Post by fjsolwmv »

stephengillie wrote: post #5

OneBusAway is surprisingly accurate, at least in my experience. Google Maps has very good transit support too. One reason buses are late is because a bus must travel a circuit. Cars provide linear transportation, so the delay can only happen in the direction of your travel. Since buses run a circuit, they are impacted by delays in the direction opposite of your travel as well. Your bus might be late because the retur…

Not really. A bus a schedule usually has a built in delay between cycles.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#38

Post by stephengillie »

yhoneycomb wrote: post #33
stephengillie wrote: post #5

OneBusAway is surprisingly accurate, at least in my experience. Google Maps has very good transit support too. One reason buses are late is because a bus must travel a circuit. Cars provide linear transportation, so the delay can only happen in the direction of your travel. Since buses run a circuit, they are impacted by delays in the direction opposite of your travel as well. Your bus might be late because the retur…

> Google Maps has very good transit support too. Where do you live? I'm guessing the bay area? I was carless in DC for a year and Google Maps was ALWAYS wrong about when busses when arrive. My friend recommended an app called Transit which was right about 90% of the time, which was a godsend for me.

Seattle - Google Maps often suggests taking 2 buses for a 1 bus trip - to goto Tacoma on the 594, instead of going down the hill and taking the 594, it recommends going to the bus tunnel and taking another bus for about a mile, then transferring to the 594.

But it shows stop locations and plans routes quite effectively. Using the 2 apps in tandem creates a workable solution.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#39

Post by ikeboy »

fjsolwmv wrote: post #35
ikeboy wrote: post #31

Earlier quoted context omitted.

This is actually wrong. The average expected time till next block is almost never 10 minutes because hashpower goes on and offline all the time. It gets adjusted every 2016 blocks based on historical block timing so that if no changes occur then future blocks would be 10 minutes on average - but changes always happen so this is never accurate. As such, you do learn something by looking at prior block times.

What you say is not a rebuttal of the parent comment. Parent explicitly said that average block times are 10mins in the assumption. The most recent block time doesn't change that.

Parent is talking about bitcoin, where that is false. If they are assuming the average, then they're assuming something false.

Re: The Waiting Time Paradox, Or, Why Is My Bus Always Late?

#40

Post by [deleted] »

ikeboy wrote: post #31
ikken wrote: post #26

This reminds me the bet in the bitcoin community [1]. If on average bitcoin blocks are produced every 10 minutes, and you learn that 5 minutes ago someone found a block, what is the average time you will wait for the next block? It turns out it's 10 minutes, not 5 minutes as you would intuitively think. (it's a memoryless process, so average expected time till block is always the same - 10 minutes - no matter how man…

This is actually wrong. The average expected time till next block is almost never 10 minutes because hashpower goes on and offline all the time. It gets adjusted every 2016 blocks based on historical block timing so that if no changes occur then future blocks would be 10 minutes on average - but changes always happen so this is never accurate. As such, you do learn something by looking at prior block times.

[deleted]
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