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Wait for Bus or Walk January 24, 2008

Posted by Andre Vellino in Logic.

Here’s a(small) question to which I’ve always wanted to know the answer: is it more effective to wait for the bus or walk to the next bus stop?

The Globe and Mail informs me that some mathematicians at CalTech have given it some thought. Here’s the abstract to their paper on Arxiv.org:

Justin has to travel a distance of d miles along a bus route. Along this route, there are n bus stops i, each spaced at a distance of d_i from the starting point. At each bus stop, Justin is faced with a choice: to walk or to wait. If he walks on, he can still catch a bus at the next bus stop–but if a bus passes him while he walks, he is almost assured a longer wait.


1. Daniel Lemire - January 24, 2008

It is intuitively clear that walking to the next bus stop is useless unless you want the workout.

2. Andre Vellino - January 24, 2008

Yes, that seems to be everyone’s intuition. But according to the paper, it depends on the frequency of the bus and the distance to the next stop.

I often try to calculate this probability and weigh it against – how bad the weather is and how important it is for me to be on time. If the negative value of being just a few minutes late = the negative value of being many minutes late, I’ll often choose to walk (to where I change buses) because the distance to that destination is ~ 1K.

It’s comforting to know that my brain is mathematically rational (at least as far as buses are concerned.)

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