From: Jean-Julien Fleck <jeanjulien.fleck@...>
Date: 2010-08-17T23:41:58+09:00
Subject: Re: can i do this in ruby? a simulation process

2010/8/17 Andrew Wagner <wagner.andrew@gmail.com>:
> Well, it may be interesting, but not in terms of the question originally
> asked. Actually, I'm not sure what you could ask to make it interesting if
> buses are going in both directions, as I would expect the average result to
> be no change in the number of people currently in either city.

Don't be fooled by the apparent simplicity of the question :o)
Random walks have many many interesting behaviors, one of which is
that they can go as far as you like from the origin in a time you can
estimate (from a probabilistic viewpoint).

The most simple realisation is the 1D random walk:
- choose an origin
- flip a coin to decide if you should go right or left
- go there
- flip a coin...
- etc.

For sure, as the problem is symetrical on right and left, the mean
value of the displacement is 0. But if you rather ask yourself the
question: "how far can I go from the origin" (either on the right or
on the left), then you can estimate how much time you need to achieve
this goal within a given probability.

In the OP problem, it would read: how much time do you need to
transfer 500 people either from A to B or from B to A with the given
set of rules.

Cheers,

-- 
JJ Fleck
PCSI1 Lycée Kléber