March 1, 2007

The wheels on the bus...

I just got internet access in my apartment around 6:30pm. So expect more blog posts from me. But right now, I will leave you with a puzzle...

When I get off the metro, there's a bus stop for the 309 bus, which I hop on to take back to my apartment. But there are often two 309 buses waiting at the stop. Now, even though cars can pass buses when they're stopped at a bus stop, buses can't pass other buses. Given that condition, what is the optimal passenger load for each bus? That is, in order to move things along in a timely, orderly fashion, how should the passengers arrange themselves on the two buses?

That's what consumed my thoughts for 5 minutes this evening.

5 comments:

patrick said...

The people waiting should split into two equal-sized groups such that everyone getting onto the front bus intends to ride further than everyone getting onto the back bus. That way, the front bus can go express through the first half (more or less) of the stops. The back bus will be busy stopping to let people off, so it won't need to pass the front bus.

That's my al-go-rith-m, and I'm sticking to it.

American Nationalist said...

or pile them all on the first bus so that it doesn't have to stop at the next stop, thereby holding up the emptier bus behind it.

only reason my way works better in real life is because people are stupid and couldn't sort themselves, though. mine is almost assuredly less efficient....

Kristina said...

Patrick's solution would work well if we wanted to space the buses. I think that if everyone who wanted to get off at an even stop got on one bus, and everyone who wanted to get off at an odd stop got on the other bus, both buses would more or less remain in sync without holding up the trailing bus.

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