I’ve been taking buses for a long time. One thing I noticed is that the buses are fullest in the city centre.

Now that’s kind of obvious. After all, most people who take the bus are going either to or from the city centre. It makes sense the buses are packed full of people there.

But that’s not the only effect at play here. There’s another, much simpler reason for the buses being packed full of people in the city centre. It’s the middle of the bus route.

To show how this works, I made a very simple model, shown below:

In my model, there are 10 bus stops. From every bus stop, one person wants to go to each of the other bus stops. So on the first stop, there will be 9 people getting on, while on the 7th stop, there will be 6 people getting off and only 3 people getting on, because there are only 3 stops left.

The blue bars show how many people arrive at each bus stop, whil the red bars show how many people leave each bus stop.

Actually, after I drew the diagram, I was surprised by how flat the distribution seemed around the centre. It looked like only the first two and last two steps were really empty, and otherwise the bus contained pretty much the same amount of people. So just for the kicks, I decided to build the same model with 30 bus stops:

Again, the distribution is very flat around the “city centre”.

Now that I think of it, that’s pretty much what you see in the real world. The bus is more or less constantly full around the city centre, then it slowly starts emptying, and suddenly on the last 3 or so stops, you see a right old exodus!

Hmm, if I spent a bit more time thinking about this, I could probably come up with a lot more examples of this phenomenon. Like cities having a more or less constant population density around the centre, and then quickly dropping the density at the edges. Or mushrooms having a more or less constant height around the centre and dropping off quickly at the edges. This phenomenon would be named Vlad’s Bus Stop Principle, and I would become rich and famous because of its numerous applications…

Ok, maybe not :).

1. Hubert Says:
   February 20th, 2009 at 11:25 am

   Great post once more! Your blog is great and i really enjoy its read! Many thanks!
   But what about the octonion analysis… :p

2. Vlad Says:
   February 20th, 2009 at 3:24 pm

   @Hubert:
   Hmmm, I guess I sparked some curiosity with my blurb about octonion analysis :). You’re not the first one who’s asking.

   I’ll probably include it as an endnote the next time I write a post here. So stay tuned!

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