Saturday, February 6, 2010

Braess paradox, queuing (standing in line), and the Boston Globe

I was pleased to see James Parker's column in the Boston Globe on queuing, which he says is what separates man from beasts. He gives credit to anthropologists for noting that queuing represents stable cooperative equilibrium and then goes out to note the Braess paradox, due to Professor Dietrich Braess, which showed that the addition of a new road may make everyone worse off in terms of travel time in the network. However, in the column he misrepresents the Braess paradox by saying that it reflects that two lines are shorter than a single line or queue. In the Braess paradox, the addition of a new road results in multiple roads or links then being shared and these are not parallel roads of different lengths.

For the exposition of the Braess paradox, along with links to the original Braess article, which was published in German, as well as to the translation to English, which Braess and I did with my former doctoral student, Tina Wakolbinger please click here. We had the pleasure of hosting the visit of Professor Braess at the Isenberg School of Management at UMass Amherst in April 2006. Of course, if one can control the flow of traffic then such a paradox cannot occur. It also does not occur in the case of uncongested networks in which the travel time of the link is independent of the flow on the link.

Last week, when I was at the Transportation Network Design and Economics Symposium at Northwestern University, I asked Professor T. John Kim of the University of Illinois at Urbana what he thought of the removal of the downtown arterial in Seoul, Korea, to recover the river and to restore the surrounding parks. Professor Kim had, of course, visited that part of Seoul and had discussed the matter with the civil engineering professor who had done the study prior to this road removal (like the reverse of the Braess paradox). He and others consider this road removal a great success.

The New York Times last week ran an article on the closure of Broadway between 47th Street and 42nd Street and the full analysis of the impacts on the traffic flow and travel time should be out fairly soon. In any event, the closure of Broadway appears to have had a similar effect to that of congestion pricing in London.

Queuing is a topic well-known to operations researchers and management scientists so I was pleased to see this topic featured in the Boston Globe.