Thread by @Ghoshal_G

Given the news that NYC is going to adopt congestion pricing—following the lead of Singapore, London, Milan, Stockholm and Gothenburg—thought it will be a good time to re up our article in @NatureComms on the spatial patterns of congestion. 1/15
nature.com/articles/s4146…

This follows from trials such as the famous shutting down of Broadway to counterintuitively improve traffic (with mixed results). 2/15
cityroom.blogs.nytimes.com/2010/02/11/a-c…

Where does all of this come from? Roughly speaking, it follows from an observation from German mathematician Dietrich Braess, where alterations to road networks (such as adding connectivity) to improve traffic flow, has the unintended effect of making things worse. 3/15

This is called Braess’s paradox, which more specifically, is a statement on the difference between Nash Equilibrium and optimality. You can read about in the excellent paper by Tim Roughgarden and Eva Tardos 4/15
theory.stanford.edu/~tim/papers/ro…

Loosely speaking it can be interpreted as, perturbations to existing infrastructure (in terms of removal) can actually improve its efficiency. For a network context, in terms of food webs see the paper by Sahasrabudhe and @adilson_motter 5/15
nature.com/articles/ncomm…

Our paper adds to this mix, by suggesting that quite apart from dynamics on the network, or human behavioral choices, the structure of the street network on which traffic propagates also matter, but not quite how you would think. 6/15

The first thing to note is that street networks are planar graphs. In planar graphs, standard network metrics such as degree distributions and clustering are irrelevant, given the strong constraints imposed by planarity 7/15
en.wikipedia.org/wiki/Planar_gr…

Instead global measures such as the betweenness centrality, a measure of load and congestion on nodes conveys more information. 8/15
en.wikipedia.org/wiki/Betweenne…

Here’s the rub, we show that the statistical distribution of the betweenness centrality across a 100 cities globally is roughly identical once one accounts for city size and boundary effects! 9/15

This is due to the majority of flow occurring on the scaffold of the network, known as the spanning tree, with the rest, accounted for by loops, corresponding to shortcuts or bypasses. Instead, the real information is in the spatial distribution of the high load nodes. 10/15

Here is a figure which shows that as we build more roads in the network, the regions of high congestion develop spatial correlations and coalesce towards the city center as the network gets denser. 11/15

To get wonky about it, this is due to planar graphs starting to behave like geometric graphs above a critical level of connectivity. In the latter the centrality has a spatial correlation, that monotonically decays from the barycenter 12/15 en.wikipedia.org/wiki/Random_ge…

Thus, once again we arrive at the counterintuitive result that building roads beyond a critical capacity has the effect of concentrating congestion towards the city center. Blocking of roads/instigating congestion pricing diffuses traffic more evenly across the city. 13/15

The results also suggest a geometric limit to urban planning. An analysis of 200 years of central Paris, corresponding to the famous Hausmann intervention, suggests limitations to the “the build your way out of” approach to controlling traffic. 14/15

Instead, investments in multimodal transportation systems, building overpasses and underpasses, in addition to smart policies such as congestion pricing may be the way forward. Thanks for reading! 15/15