The idea of this lesson is to introduce, in a simplified manner, the so-called Braess Paradox by providing simple examples to clarify that the addition of some new roads to a network does not always lead to an improvement in the liquidity of the traffic; in some cases it might even increase the time required to get from one point to another if all drivers are selfish. The educational objectives for this lesson can be summarized as follows: providing a practical application of mathematics; indicating the importance of scientific research; training the students on methods of counting and surveying all the possibilities in a given problem; and introducing Nash Equilibrium and Braess Paradox in a simplified manner by visual examples. The time required for the implementation of this lesson is about 50 minutes divided equally between the video and classroom activities. I was keen not to include examples that involve equations that are difficult to handle. All a student needs to know is how to solve two linear equations in two variables by substitution (or omission), and therefore it is suitable for students of intermediate and secondary schools. The rest is simple calculation. Implementation of the lesson does not need any special equipment as it can be carried out in any regular class, subject to the availability of a computer or a devise to play the video which can be downloaded from the MIT BLOSSOMS website via the Internet. The video consists of seven sections.
Dr. Abuhlail is an Associate Professor in the Department of Mathematics and Statistics at King Fahd University of Petroleum and Minerals (KFUPM) in Dhahran, Saudi Arabia. He is from Palestine and his major area of study and teaching is Algebra. Dr. Abuhlail’s interests include applications of mathematics in the real world, eLearning, the History of Mathematics, and Math Olympiads (regional and international). Dr. Abuhlail is also the Associate Managing Editor of AJS-Mathematics, a section of the Arabian Journal for Science and Engineering (AJSE).
An excellent article in the Scientific America magazine that discusses the topic of this lesson.
A site with numerous valuable links on the Braess Paradox and on Dietrich Braess, sponsored by the Virtual Center for Super Networks at the University of Massachusetts where Professor Braess lectured in 2006.
This site provides a Wikipedia overview of the Braess Paradox.
This site provides a Wikipedia overview of the Nash equilibrium.
|Selfish Drivers: The Braess Paradox and Traffic Planning (Arabic, mp4)||Arabic||MPEG 4||Download|
|Selfish Drivers: The Braess Paradox and Traffic Planning (Arabic, QuickTime)||Arabic||Quicktime||Download|
|Selfish Drivers: The Braess Paradox and Traffic Planning (Arabic-English Subtitles, mp4)||Arabic-English SubtitlesArabic-English Subtitles||MPEG 4||Download|
|Selfish Drivers: The Braess Paradox and Traffic Planning (Arabic-English Subtitles, QuickTime)||Arabic-English SubtitlesArabic-English Subtitles||Quicktime||Download|