3 ms·

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 ine

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.

TeMPOraL 11y ago
It's a generally helpful technique to try and push a problem to both limits alongside some variable; it often reveals new solutions or insights.
- eru 11y ago
  Or at least it gives you easy special cases you can sanity check your general solutions against.
Certhas 11y ago
But that's not all there is to it. It really is a network phenomenon. Otherwise you wouldn't expect it to also appear in power networks: http://iopscience.iop.org/article/10.1088/1367-2630/14/8/083036/pdf http://iopscience.iop.org/article/10.1088/1367-2630/14/8/083...
- adekok 11y ago
  A standard physics question is to calculate the electrical flow between two points on an infinite square grid of resistors. Not surprisingly, the flow isn't large. The electricity takes many path through the circuit. Here, too, having fewer paths would result in large flow.
  - mikexstudios 11y ago
    But the equivalent resistance always decreases as the grid of resistors increase. I don't see how having "fewer paths would result in a large flow". See: http://physics.stackexchange.com/questions/2072/on-this-infinite-grid-of-resistors-whats-the-equivalent-resistance http://physics.stackexchange.com/questions/2072/on-this-infi...
- Asbostos 11y ago
  Wow, it seems like you can do it with a simple DC circuit too! That paper's a bit complicated but if you just make the road network with constant voltage drop diodes and resistors instead of constant travel time roads and time-proportional-to-traffic roads respectively, it looks like adding a link actually increases the voltage drop across the overall circuit for a constant current!!

TeMPOraL 11y ago

It's a generally helpful technique to try and push a problem to both limits alongside some variable; it often reveals new solutions or insights.

eru 11y ago
Or at least it gives you easy special cases you can sanity check your general solutions against.

Certhas 11y ago

But that's not all there is to it. It really is a network phenomenon. Otherwise you wouldn't expect it to also appear in power networks: http://iopscience.iop.org/article/10.1088/1367-2630/14/8/083036/pdf http://iopscience.iop.org/article/10.1088/1367-2630/14/8/083...

adekok 11y ago
A standard physics question is to calculate the electrical flow between two points on an infinite square grid of resistors. Not surprisingly, the flow isn't large. The electricity takes many path through the circuit. Here, too, having fewer paths would result in large flow.
- mikexstudios 11y ago
  But the equivalent resistance always decreases as the grid of resistors increase. I don't see how having "fewer paths would result in a large flow". See: http://physics.stackexchange.com/questions/2072/on-this-infinite-grid-of-resistors-whats-the-equivalent-resistance http://physics.stackexchange.com/questions/2072/on-this-infi...
Asbostos 11y ago
Wow, it seems like you can do it with a simple DC circuit too! That paper's a bit complicated but if you just make the road network with constant voltage drop diodes and resistors instead of constant travel time roads and time-proportional-to-traffic roads respectively, it looks like adding a link actually increases the voltage drop across the overall circuit for a constant current!!