The mathematics of waiting for a bus

We all use math (sic) everyday! - so says the intro to the geek fantasy that is Numb3rs, the US maths/FBI/unrequited love show. Apparently we should, according to Chen et al., when experiencing the irksome decision of "shall I wait for a bus or just walk there?".

For those of you who find this a challenging decision to make, there's an easy answer. Simple solve this funtastic equation:

Working from the assumptions that a) you need to get to your destination as fast as possible (usually true), b) getting the bus is faster than walking (very debatable) but it only arrives at the stops sporadically and c) you're lazy enough that you'd rather get the bus than walk if possible (likely) they run through a test case or two to come up with the above.

The Poorhouse loses track of the maths after page 1, but luckily an article in the New Scientist interprets it for us.

When both options seem reasonably attractive, the formula advises you to choose the "lazy" option: wait at the first stop, no matter how frustrating.

and there is certainly no point - in a perfect bus-world - in walking to anything but the first bus stop before waiting. That would just be silly.

The advice does break down under extreme circumstances though, says Scott Kominers, a co-author, such as "when the time interval between buses is longer than an hour, for example, and your destination is only a kilometre away."

So there we go, you're usually quicker to get a bus to reach a far-away bus-stop than walk there, unless the buses don't come very often and the journey is only a very short distance away. You read it here first. Well, second maybe.


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