An article to think about. I downloaded it from: http://arxiv.org/abs/0801.0297

Walk versus Wait: The Lazy Mathematician Wins
Authors: Justin G. Chen, Scott D. Kominers, Robert W. Sinnott
(Submitted on 1 Jan 2008 (v1), last revised 27 Jan 2008 (this version, v3))
Abstract: 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's a comment for the article:

January 29, 2008, 2:18 pm
Further Adventures in Bus Stop Strategy
By Stephen J. Dubner

Now, this is disappointing: three mathematicians go to the trouble to model bus waiting strategy — is it better to wait or to walk to the next forward stop? — and conclude that waiting is the best option.
Because they didn’t even consider an alternative bus waiting strategy discussed earlier on this blog: walking backward one stop.

I downloaded the comment from: http://freakonomics.blogs.nytimes.com/