Braess' paradox: adding a new road to a city can slow down traffic

Taken to the extreme, if you made such a dense network of roads that it was effectively just one giant paved surface, then I think it's obvious that it'd be inefficient since everyone is barging through trying to go in their own straight line and getting in each other's way. In that case, adding barriers and one-way lanes would intuitively speed up people's journeys. So perhaps Braess's paradox is only unintuitive for simple cases that are very close to our existing road networks.

I once saw a particularly interesting physical manifestation of this paradox (performed I believe by Chris Bishop), where a weight was suspended from two partially elastic ropes, both attached to the ceiling. These two suspending ropes were connected in the middle by another rope. The weight was analogous to the destination, and the ropes were the roads, with the total duration of the route being analogous to the distance of the weight from the ceiling. When we removed the central road (by cutting the connecting rope), the weight paradoxically went up instead of down.<p>I wish I had a video of this demonstration, it really hammered in the point (for me) that this is a real phenomenon and not just mathematical trickery or electrical weirdness.

The paradox does not take into account the rigidity of a roadway user&#x27;s route. If your current route to work takes x minutes amount of time to drive and a new roadway is about to be opened that will reduce the drive time by ten minutes (x-10). News announces the new route, ribbons are cut, and signage is put in place announcing the new roadway.<p>* The user is aware of the new roadway and utilizes the roadway.<p>* The user knows that the old route was 10 minutes more and was the current ideal.<p>* Other users utilize the route under the same 10 minute saving condition, driving up the amount of traffic over time, even when the new route ends up adding travel time to the original time.<p>* Users do not consider going back to the old route, even though it may be better now as the system builders had declared this route to be the best. There is also an internal feeling that if the new route was like this, what will the old route look like.<p>* When talking to people who drive, once a known route has been established, it takes a lot to get them to change. That is why accepting Waze provides such a great opportunity for balancing traffic and utilizing roadway capacity.

From my (mathematician&#x27;s) perspective, when the solution to the optimal transportation problem corresponds to a Nash equilibrium, this is called a Cournot-Nash equilibrium. This does not happen generically.<p>In other words, it is very unlikely to simultaneously minimize both the expected commute cost for the group and for each individual.<p>However, in the continuous case, you can fix this using taxes, tolls or incentives (in theory - in practice I don&#x27;t know. )<p>Blanchet and Carlier have some nice mathematical articles including<p><a href="https:&#x2F;&#x2F;www.ceremade.dauphine.fr&#x2F;~carlier&#x2F;blanchetcarlierfinal.pdf" rel="nofollow">https:&#x2F;&#x2F;www.ceremade.dauphine.fr&#x2F;~carlier&#x2F;blanchetcarlierfin...</a>

Networked traffic routing apps like Waze ought to nullify the Braess&#x27; paradox; if everyone used Waze, new roads would always have a positive marginal impact.

That reminds me another notion from The Mythical Man-Month; Brooks&#x27;s law: Adding manpower to a late software project makes it later.

My understanding of this is that you have a highway and a road (with a low speed limit). The highway gets congested if many people use it so they’ll all move slower. If everyone takes the highway, it’ll still be faster than the road, so everyone chooses to take the highway. On the other hand, if everyone spends half their time on the highway and the other half on the road, all of them will be able to travel faster (But there is no incentive to do so).<p>At Nash equilibrium, the highway is over-utilised while the road is under-utilised. So stripped to the core, this is an example of tragedy of the commons where if every single individual works for their sole interest, they will all lose out and yet nobody has an incentive to make a change.

Brian Hayes wrote a nice article about this a few months ago in American Scientist [1] and also wrote a little JS demo to tinker with linked from here [2].<p>1. <a href="http:&#x2F;&#x2F;www.americanscientist.org&#x2F;libraries&#x2F;documents&#x2F;201561716294611219-2015-07CompSciHayesRev.pdf" rel="nofollow">http:&#x2F;&#x2F;www.americanscientist.org&#x2F;libraries&#x2F;documents&#x2F;2015617...</a><p>2. <a href="http:&#x2F;&#x2F;bit-player.org&#x2F;2015&#x2F;traffic-jams-in-javascript" rel="nofollow">http:&#x2F;&#x2F;bit-player.org&#x2F;2015&#x2F;traffic-jams-in-javascript</a>

Anyone who wants to try this might consider playing or watching a video of the Cities: Skylines game. It&#x27;s said to be a pretty good &quot;traffic planner&quot; simulation.

Ah, I love this stuff. Tim Roughgarten&#x27;s work on selfish routing was my bible through an undergrad research project, it&#x27;s succinct and packed with excellent proofs. <a href="https:&#x2F;&#x2F;mitpress.mit.edu&#x2F;books&#x2F;selfish-routing-and-price-anarchy" rel="nofollow">https:&#x2F;&#x2F;mitpress.mit.edu&#x2F;books&#x2F;selfish-routing-and-price-ana...</a>

I remember reading a piece by WIRED that discussed this phenomenon in Southern California: <a href="http:&#x2F;&#x2F;www.wired.com&#x2F;2014&#x2F;06&#x2F;wuwt-traffic-induced-demand&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.wired.com&#x2F;2014&#x2F;06&#x2F;wuwt-traffic-induced-demand&#x2F;</a> (&quot;Building Bigger Roads Actually Makes Traffic Worse&quot;)

What fraction of the time does adding a new road slow down traffic? Or, equivalently, what fraction of the time does removing a road speed up traffic? If this fraction is high we should be experimenting with closing roads: that&#x27;s a very cheap way to improve infrastructure.

I learnt this as a part of a course I was doing on social networks. This was under the game theory module. Pretty interesting stuff.

Why does everything have to have a new &#x27;paradox&#x27; when perfectly good physics exists already:<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Kirchhoff%27s_circuit_laws" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Kirchhoff%27s_circuit_laws</a><p>It is not as if cars are equipped with some superior intelligence when compared to electrons in a circuit, the behaviour is identical and the normal laws of physics apply.

Are there any examples of this happening when a new internet link is added?

Why is paradox? Seem obvious to me. If person can explain, thank you.