Monday, August 1, 2016

Physical Proof of the Occurrence of the Braess Paradox in Electrical Circuits

This morning we heard the good news - our paper, "Physical Proof of the Occurrence of the Braess Paradox in Electrical Circuits," had been accepted for publication in the journal Europhysics Letters (EPL). 

This paper we had worked on for over a year and had submitted it to the journal shortly before I left for England to begin my Visiting Fellowship at All Souls College at Oxford University at the end of April.

When we received the 2 reviews on this paper in July with one reviewer saying that the paper should be published in its present form and that the results were important, my co-author, who is also my husband, Professor Ladimer S. Nagurney, and I were quite pleased and felt very positive. We revised the paper to satisfy the other reviewer, which was a minor revision.

The paper we believe is very cool since, for the first time, it has been shown the electrons behave in a user-optimized manner, as has been postulated for drivers in a congested urban transportation network. Moreover, the addition of a new link can make the voltage, which is like the user path cost, or travel time in a transportation network,  increase. These findings were not only dome mathematically but actually using built circuits. This allows for experiments to be conducted in a laboratory setting and is yet another application in which the Braess paradox occurs, which, in its original form, demonstrated that the addition of a new link, which results in a new path for travellers, can actually make everyone worse off in the transportation network in terms of travel time. Hence, it can take you longer to get to work (or back home) if there are more routes than fewer ones even of the demand does not increase.

I have researched the Braess paradox since my PhD at Brown University and have also blogged about it.

There is a page on the paradox on the Supernetwork Center site:, where you can also find the translation of the original Braess (1968) article from German to English that I did with Professor Braess and my former doctoral student at the Isenberg School, Tina Wakolbinger, who is now a Professor at the Vienna University of Economics and Business in Austria.

Also, this paper we presented at the recent EURO conference in Poznan, Poland, which was a fantastic conference. Our presentation can be downloaded and viewed here. 

Almost 50 years since the publication of the Braess paradox paper, this phenomenon continues to fascinate and now we have additional physical evidence.