Walk versus Wait: The Lazy Mathematician Wins
Justin G. Chen, Scott D. Kominers, Robert W. Sinnott
Justin G. Chen, Scott D. Kominers, Robert W. Sinnott
(Submitted on 1 Jan 2008 (v1), last revised 10 Jan 2008 (this version, v2))
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.
from:https://arxiv.org/abs/0801.0297
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