Braess's Paradox
en.wikipedia.org
en.wikipedia.org
Adding a route to a road network does not itself reduce total capacity, of course. It's actually a queueing theory issue--misusing a road as a dysfunctional queue by putting more cars on it than can get through causes head-of-line blocking and allows cars taking the congested, shorter route to obstruct the clear, longer route. (this is concealed in the Wikipedia article by describing the travel time as Travellers/100, the latency of a fast, very wide road queueing into a narrow intersection.)
Cutting the route can "solve" the problem by eliminating that particular congestion source, but only in the case of an extra, redundant shortcut route.
Other options -- like rate-limiting at the start point, or queueing separately for the shortcut route (an express lane), or forbidding queuing on the main road for the shortcut at all, both fix the general case and this case in specific.
The general version of the issue is: When you build a network, never queue in the core. Either drop traffic early and often at the point of congestion, or rate limit as close to the source as possible. Or change links at random and hope your network reconverges into a less broken state, I guess.
More recently 76 has implenented variable speed limits to prevent backups - though it's entirely ignored unfortunately - you can't safely follow a 30mph limit when everyone is going 65 speeding their way into a jam
It's impossible to google, though, because the results are all about how to reduce the tension in your life and people's weight going up.
However, I'm blanking on how the analogy to traffic flow works, and on how exactly the blue and red lines are connected to make this work or how stiff they are assumed to be. (I thought they had to be infinitely stiff for this to work but the math on that doesn't work in my quick calculation.) Edit: the German says the three linkages are infinitely stiff (hart) I'm confused because that would make the parallel case infinitely stiff.
Edit: Okay I had that wrong, the extra linkages are indeed infinitely stiff. In the parallel case, that doesn't make the system infinitely stiff because each one is in series with a finite stiffness spring. And in the analogy stiffer = shorter travel time, and any road system with a fixed travel time is thus infinitely stiff.
Fascinating.
If you have 2 roads and close one and change absolutely nothing besides everyone switching to the open one, of course things get worse.
City and traffic planning is perceived as a pure "requirements implementation" project. Citizens say they want X, so let's build them X.
Truth is more complex. Individuals don't frequently know what is best for the community at large. So City planning needs to influence people's behaviour as much as people's behaviour needs to influence city planning.
There were essentially no other ways to travel, as in N+M notation (N = river crossing capacity, M = spare capacity) Warsaw has been long time operating at below required capacity. Closest example of adding more crossings not reducing congestion involves a bridge which couldn't take up increased traffic because the roads to it were congested...