Interesting Math Problem

It is a real problem I also encounter almost every morning: Shall I wait for the bus or just walk to the subway station. For those live in Flushing or Queens, you will know I mean :wall

I just found out there are three mathematicians have the same problem and they did come up with a paper for it this month.

In this recreational mathematics note, we address a simple, yet instructive question:
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.
We model Justin's decision constraint and completely solve the model in a special case. The answer is intuitive: the optimal strategy is the laziest.
here is the link

And here is the 3 pages long paper


  • Lazy_Walk_0801.0297v2.pdf
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Bastian Gross

German Mathquant
that is some easy game theory stuff.
In traffic science it is also well-known, that to be caught up in a traffic jam beats to drive detour.
I think this could be related.

So I wait this evening for the bus :yawinkle:
That problem is part of New Yorker's daily life. But most of us won't bother to think of it.
Indeed, I am walking to subway station in the morning at least twice a week. And most of the time I beat the buses. :) That translates I am losing money on my Metro Card. LOL

Bastian Gross

German Mathquant
but you need more food and less gym-workout. ;)
Lazy mathematicians......Really!!!

Now I read the paper some days back and actually found the article to contain a lot of "errors "(though the final result as expected is correct). I had written to the authors but they haven't responded. I am attaching the clarifications I had demanded.
Since they haven't responded I wanted to confirm whether I have understood the problem correctly and cross check my "maths". If not, then the mathematicians who wrote the paper are indeed lazy ( ;) )


  • Lazy_Mathematician_Clarifications.pdf
    57.2 KB · Views: 19