Transit+Networks

=Transit Networks / Braess' Paradox= Author: Tom Hayden (thayden@gmail.com) Date: 5/5/2011

The students had just completed a unit on acceleration/velocity and other misc physics concepts. I wanted to connect those ideas to ideas about networks and ideas about transit networks seemed to be the easy way to do it. Unfortunately, many of the ideas from the study of transit networks (particularly flow) were too complicated for a short lesson on traffic and networks. I do think someone should try to teach this notion to students, though, it is probably the most important idea in the study of traffic and network design.

As a pre-requisite, I recommend reading the [|wikipedia page on Braess' Paradox].

Presentation Component (20 mins)
In the presentation, I wanted to cover the following things:
 * We can model traffic and transit systems as a big network, much like how we modeled other others (hip hop, electricity networks)
 * These networks have interesting properties and we can do cool algorithms on them - such as depth-first-search or other quick pathfinding algorithms. This is how websites like Google Maps or your GPS are able to determine the shortest path for you.
 * For the sake of time and to keep it interesting, I moved into a conversation about something called Braess' Paradox. The paradoxical result is this: adding a road to a traffic network, in some specific cases, may actually make overall traffic worse! Included was a link to a youtube video with the same paradox but in a physics setting (there is good coverage of this physics example in the book: "The Pea and the Sun: A Mathematical Paradox" by Leonard Wapner.

Note: the presentation here also includes material from the lesson(s) on hip-hop networks. The second half the presentation concerns that unit, so feel free to skip that or ignore it. The first half covers the content that I wanted to speak to the students about with regards to traffic networks. [|Transit Network Powerpoint]

Worksheet / Activity Component (20 mins)
I attempted to design a worksheet to go along with the ideas about Braess' Paradox and some basic notions of traffic/flow networks. I didn't think this worksheet went over very well but I am providing it here such that it may be a good place to start if someone is looking to teach a lesson on the paradox or flow networks. The second half of the worksheet involves using a traffic simulation tool, which is really cool, but hard to build a solid lesson out of.

Paradox Activity (note: this link is incorrect - does anyone have the Paradox Activity worksheet they can upload?)