Walk versus Wait: The Lazy Mathematician Wins
  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. 
Justin G. Chen, Scott D. Kominers, Robert W. Sinnott