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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.
And here is the 3 pages long paper
I just found out there are three mathematicians have the same problem and they did come up with a paper for it this month.
here is the linkIn 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.
And here is the 3 pages long paper