[HN Gopher] Braess's Paradox
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Braess's Paradox
Author : Tomte
Score : 55 points
Date : 2021-05-16 14:09 UTC (8 hours ago)
(HTM) web link (en.wikipedia.org)
(TXT) w3m dump (en.wikipedia.org)
| infationtukaway wrote:
| Related! Housewife-knowledge: In a curious particular case a
| manufacturer lowered the volume of a dish soap from 600ml to
| 500ml. After a shit-storm the producer resumed offering the old
| 600ml plastic bottle, but not without written '+20% free' on his
| plastic bottles.
| istjohn wrote:
| "[T]hey showed that adding a path for electrons in a nanoscopic
| network paradoxically reduced its conductance. That was shown
| both by simulations as well as experiments at low temperature
| using as scanning gate microscopy."
|
| Fascinating.
| celias wrote:
| Up and Atom has a video about Braess's Paradox
|
| https://www.youtube.com/watch?v=cALezV_Fwi0
| billytetrud wrote:
| Only semi related, I'm super annoyed that popular culture seems
| to love the idea that adding more lanes to a road makes traffic
| worse. There's tons of problems with that idea, like the fact
| that it generally isn't true (but the surprising times it is true
| makes the news), or the fact that increasing capacity of a road
| obviously will make more people want to use that road vs the
| other roads who's capacity has not increased.
| bcoates wrote:
| I think the way this is presented (including in the Wikipedia
| article) is overly confusing and leans too much on irrelevant
| game-theory issues.
|
| 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.
| calvinmorrison wrote:
| Philly has this! Our newest highway - the blue route runs wide
| around the city and connects the turnpike to close to Delaware.
| It has a queue system which only let's on X cars per minute,
| preventing a heavy merge area from slowing everything down.
| Basically it's a stop sign with a red light at the on ramp. It
| goes green for a second, two cars go, it goes red. Interesting
| concept.
|
| 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
| alimw wrote:
| As a game theorist I find your description utterly impenetrable
| :)
| xenadu02 wrote:
| This is what the Bay Area highway on-ramp traffic lights do.
| They rate limit traffic merging onto the highway thereby
| avoiding stop and go jams. That results in an overall increase
| in throughput on the highway at the cost of forcing vehicles to
| queue at the ramps. The overall travel time is lower despite
| the time spent waiting in the on-ramp queue.
| bollu wrote:
| Nice explanation, I hadn't t heard this perspective, and it
| makes it a lot more intuitive! What's your favourite way to
| learn queueing theory? I feel like I'll get cool insights from
| this :D
| the-dude wrote:
| Adding programmers to your team slows you down ( Mythical Man
| Month )
| The_rationalist wrote:
| If find the contrapositive paradox even more striking: _Removing_
| a road can reduce congestion /traffic time!
| raldi wrote:
| This writeup would be greatly improved by a detailed real-world
| example.
| davikrr wrote:
| https://en.wikipedia.org/wiki/Braess%27s_paradox#Traffic
| mrow84 wrote:
| The "Possible instances of the paradox in action" section,
| "Traffic" subsection, has several examples.
| bradrn wrote:
| I mentioned in another comment that I once read a book which
| mentioned this paradox. That book gave the example of a major
| street in Manhattan which was closed for a while; this
| surprisingly made traffic generally better. Unfortunately, I
| can't remember the street, or when this happened, though it
| might be possible to look it up. (I'd like to know!)
| rossdavidh wrote:
| Funny thing is, in actual real cities in which I have lived,
| construction (or a bad wreck) closing a road never, ever, ever
| has led to an improvement in the traffic situation. It may be
| theoretically possible, but I have never seen it happen in my
| actual lived experience.
| deanCommie wrote:
| Well, no, not in the short term, and without any other
| adaptation.
|
| 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.
| simonh wrote:
| The paradox has been known since 1968 and I assume modern
| traffic planners are well aware of it, so it seems unlikely to
| me than many of our road networks will still be flawed by
| design in this way.
| billytetrud wrote:
| You overestimate humanity
| bradrn wrote:
| I've known about this phenomenon for a long time, ever since I
| read a book in primary school which mentioned it, but I
| completely forgot the name and have been unable to read more
| about it. Thank you for submitting this!
| raldi wrote:
| I once saw a diagram of a weight suspended from system of string
| where cutting one of the strings would actually increase the
| tension on the weight and make it move upwards.
|
| 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.
| twic wrote:
| That's in the second figure on the linked wikipedia page -
| captioned "Comparison of Braess's paradox for road and spring
| networks".
| [deleted]
| thunderbong wrote:
| It's on the same Wikipedia page under Example[0]
|
| [0]: https://en.wikipedia.org/wiki/Braess's_paradox#Example
| rmetzler wrote:
| The German page of the Braess Paradox has a description for
| this. https://de.wikipedia.org/wiki/Braess-
| Paradoxon#Mechanisches_...
| SilasX wrote:
| Ah, okay, that helps! So basically, you have a system where
| two springs are in parallel, thus resulting in effective
| stiffness being equal to the sum of their stiffnesses (K = k1
| + k2). However, the extra linkage makes them act in series,
| which reduces total stiffness. (1/K = 1/k1 + 1/k2, like
| parallel resistors).
|
| 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.
| praptak wrote:
| It is possible to Google:
| http://web.mit.edu/tsg/DemoPage/B/B17/B17.htm
| lixtra wrote:
| Nice https://m.youtube.com/watch?v=ekd2MeDBV8s
| raldi wrote:
| What were your terms?
| praptak wrote:
| spring paradox
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