24 January 2008

Should you wait for the bus?

Take the lazy way (from Agence France-Presse, via the (Toronto) Globe and Mail,): it is better to wait for the bus than to walk along the route of the bus and get on the bus when it catches up to you. This is intuitively obvious: whether you start walking or not, you end up arriving at your destination on the same bus (and therefore at the same time), and if you walk you risk that the bus will pass you between stops. The result is due to Justin Chen, Scott Kominers, and Robert Sinnott.

This was actually in the arXiv a couple weeks ago (0801.02979v2), but I didn't see it. Surprisingly enough, a newspaper article about mathematics in the mainstream news actually linked to the original research it was referring to! (This is surprisingly rare, and not just for articles about mathematics, but for just about anything.)

On a personal note, I walk to school and back each day even though there is public transit paralleling my usual route. This is contrary to the solution explained in the paper, but there are things that the paper doesn't include. First, by walking (a mile and a half each way) I get exercise, so I don't have to go to a gym. Second, I get frustrated if I wait for the trolley and it doesn't come. Third, I get a lot of my best thinking done while walking; the trolley is noisy enough and bumpy enough that I can't think well on it. Fourth, I'm cheap. Fifth, bus schedules around herre works of fiction anyway, and solving this problem correctly would require a more sophisticated probabilistic model, which I'm not going to go to the trouble of doing.

And the comments on this on fark.com are actually rather interesting.

7 comments:

Mike said...

What? How could this possibly not be true?

.mau. said...

Here in Italy the most important newspaper, Corriere della Sera, published an article about it citing the arXiv paper. Pity they did not manage to write the link correctly :-) (and they did not understand anything about it, not even the joke at the end)

jackv said...

I normally cycle, but when I can't, I often walk because I'd prefer it to a vehicle (eg. pleasant, exercise) and sometimes because I'd prefer it a bus (not grubby, predictable arrival time, can't be bothered checking bus times). However, the question seems to be, is it ever quicker to walk? When I'm deciding between walk and bus for quickness, it's generally because the bus is late and I expect it to go on being late, such that I could walk there before a bus comes, but if the bus does come I *might* be able to catch it on the way. Which is a tricky decision I've generally got wrong, because by the time you've spent half an hour waiting, if you'd known to start with, you could have set off, but now it might be too late. I haven't tried this since some bus stops have started having electronic arrival-time-boards (in Cambridge UK), that might make it better if they're accurate.

Rowboat said...

Sixth, standing takes more effort than walking (well, it does for me), so instead of standing around or nervously walking back and forth at the bus stop you might as well just walk wherever it is you're going. Depending on how far it is, of course.

I generally take the tram into town every morning (it would be over an hour on foot, so in that case it's worth it), but the stop is some 15 minutes away; by bus it's only 5 minutes, but normally I walk that part because it usually gets me there faster than waiting for the bus.

Walking halfway just means the bus will be late that day and I'll spend over five minutes waiting at the next stop, only to have the bus pass me shortly after I finally lose patience and continue walking.

michael said...

Years ago when I worked 7:15 p.m. to 2:45 a.m. I'd run home. That would get my daily run done [I ran marathons] and I'd easily get home faster than the subway. The ran across the Brooklyn Bridge was always beautiful.

Phil! Gregory said...

Back when I rode the bus, I would, on cold days, walk in opposition to the bus route (while keeping an eye on the road and being ready to run to the best stop one I saw the bus coming). It didn't get me to my destination faster, but it got me on the (heated) bus faster, and gave me (warming) exercise in the meantime.

OOppsy7 said...

I'll just post the obvious comment that it is also better to walk if the time between buses is longer than the time it takes to walk to the destination, even though the bus ride could be 10 times as fast.