This is the so-called Pigovian Tax. Also named for Arthur Pigou is a road traffic thought experiment much like Braess's ("Pigou's example").
So if I understand it, adding road signs before the new route adding estimated travel times (that take congestion into account) will fix things? The paradox arises from considering only route length, and not congestion?
No, the problem comes from considering only your travel time, and not how your choices impact other drivers. The example given in the wiki demonstrates that even road signs with estimated travel times, will still not fix the above problem.
I wonder if any this applies to that experiment about adding obstacles in front of an exit speeding up exit times by slowing down individuals (especially in the case of an emergency - where sometimes the exits become blocked by the masses all trying to exit the same way - and perhaps even ignoring another route that would lead to a quicker exit)?
However the example have a road that takes 45 minutes regardless of how many drivers go through it, that is not very realistic is it. nowdays we have apps that can tell us in real time how long each path will take according to current traffic, and the time is never constant.
It's actually pretty realistic for very lightly congested roads. At those levels of congestion, the primary bottleneck is the distance and speed-limit. Marginally increased traffic will have minimal impact on travel time.
In contrast, for heavily congested roads, the primary bottleneck is the congestion itself. Hence, marginally increased traffic will have a proportional impact on travel time.
How does one car impact another? Wouldn't the drivers gravitate to the least congested/long road, and hence distribute across capacity?
Presumbly, adding a temporary speed-limit to a road would have a similar effect.
It's been well proven in economics that externalities, if unregulated, will produce sub-optimal outcomes. That the way to restore optimal outcomes is to impose a tax that's proportional to the negative externality imposed on others. In an ideal high-tech world, this can be achieved by having differential prices that each driver has to pay, to use each road/highway. In a low tech world, narrowing/closing a road is akin to imposing a tax on certain routes, which explains why it can counter-intuitively help us get to a more optimal outcome.