It's one of those eternal questions: Wait or walk?
You're standing at a bus stop, but there's no bus in sight. Should you start walking - hoping to beat the bus but risking it fly by you while you're between stops - or simply grit your teeth and wait?
Now three top mathematicians in the United States have addressed this age-old problem and come up with the answer: Take the lazy option and wait for the bus rather than hoofing it.
Justine Chen of the California Institute of Technology, and Scott Kominers and Robert Sinnot, both of Harvard University, have drawn up a formula to calculate whether waiting or walking is the best option for those facing a sporadic bus service.
Their equation has these variables: n, for the number of bus stops spaced along the bus route; d, for the distance along the bus route; Vb, being the bus speed; Vw, the walking speed; and p(t), being the probability in time that a bus will show up.
Their verdict: Stick around and wait for the bus at the first stop. If you set off walking, there is a comparatively greater risk that the bus will pass you before you reach the next stop on the route.
"The answer is intuitive: the optimal strategy is the laziest," the mathematicians conclude.
Walking becomes the smarter option, though, if the distance to be travelled is less than a kilometre and there is at least an hour between buses, the investigators say.
If you do choose to walk, you should make your decision before you start waiting, Mr. Kominers told the New Scientist. You will still reach your destination later than the bus you'd have caught, but it will be much less frustrating than waiting for a while and then watching the bus roar by.
"Many mathematicians probably ponder this on their way to work, but never get around to working it out," he told the magazine. "It certainly has changed the way I travel."
For those of you of a mathematical inclination who would like to read the full paper, point your web browser to xxx.arxiv.org/abs/0801.0297 on the open-access library of New York's Cornell University and download it. It'll make for good reading on the bus.
