Why the secret to speedier highways might be closing some roads: the Braess paradox | Hacker News Reader

Why the secret to speedier highways might be closing some roads: the Braess paradox

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50 pointspaulgb21 comments

This is why I like computers. You get to define what happens to achieve an optimal outcome given the inherent limitations. At least you get to define it more than normal.

Even really simplistically, how many of us have gotten annoyed when someone decides their time is more valuable and cuts in front of the line waiting for the exit? That makes everyone behind them's commute longer (as well as using more gasoline and putting more wear on queued vehicles, even if it's slight), but the cutter's commute shorter.

If we could control the situation, we could create more optimal outcomes not just because of "cheaters", but because there is an inherent lack of communication. For example, two people driving need to understand what the other is doing and there is a delay as people are cautious and don't want to die on the road. However, if the vehicles coordinated with each other (hopefully not in a Skynet way), that delay could be minimized. For example, entering an interstate from an on-ramp. In front or behind the other vehicle? Depends where the other vehicle is, how fast it's going, etc. That can all be done better in a more automated fashion.

Maybe this paradox is real, I don't know, but it seems quite contrived. I don't think congestion really changes based on T/constant. It's almost certainly a log function.

And try this:

If just one person goes from start to end it will take him 4.8 seconds (.08 minutes).

So just line everyone up, and let them go one at a time. The last person in line will have to wait 80 minutes, but the average travel time is 40.04 minutes!

So adding a road does make it faster - much faster, contrary to what the paradox says. All you need is someone to police them and make them go one at a time.

And you are even waiting till they finish the trip before sending the next person. Send two at a time (one for each leg, since they are independent after all), and it's twice as fast.

I say putting in the road was a great idea! You cut the average travel time from 70 minutes to 20.02004 minutes. And the max from 70 to 40.08.

If I'm right, this does bust the paradox, but even more than that it shows that T/constant is the totally wrong formula for calculating congestion. Put in a correct formula and I bet this paradox won't exist.

I think your example is a little too limiting for this paradox to take effect. The paradox is based on people guessing what others are going to do given a set of options, where your example basically sends them through in the most efficient manner possible by suggesting that one person is going to be willing to wait 80 minutes when that person knows that others are able to do the trip in less than 10 seconds.

Exactly, not everyone will willingly comply. You (ars) have found an optimal solution, but it is not a nash equilibrium - cars will cut out of the line to make it through faster.

The constants in the example are arbitrary and were probably chosen for simplicity, a (thankfully) common thing to do in these sorts of examples.

One of the more interesting highway behaviors I have seen was a huge backup on a 2 lane highway where truckers would block both lanes and prevent people from passing them. It's a slight cost the each trucker on the left but it significantly increased throughput.

In the blogs example one person 1 goes Start to A, then while person 1 goes B to end Person 2 goes start to A. etc. Worst case travel time is now faster after adding the new road and 2 agents can help this happen by limiting how fast people enter A.

Edit: with 2 people limiting traffic they can reduce their travel time by 25% (3x 1/2 vs 2 x 1) even if they are in the second group. 1/2 the cars do the first leg, then the other half do the first leg while the first set does the second leg.

PS: This is why we make traffic lights.

> All you need is someone to police them [...] If I'm right, this does bust the paradox.

You completely misunderstand the nature of the paradox. Yes, if you have an authority (the "police") compute and enforce the social optimum, then more roads can only ever decrease the average travel time. That's obvious, and pointing that out didn't "bust" anything.

The nature of the paradox is that optimization at the individual level leads to a suboptimal result at the social level. That's in contrast to certain results from economics, where free markets can be proved to guarantee optimal resource allocation (in idealized circumstances).

Your complaint about the T/constant formula is downright silly; I'm convinced that an equivalent paradox can be created for every reasonable formula you agree to. (Actually, I think I can prove that.) The only thing that would change is that the "lines" on the equilibrium diagram would become "curves".

>You completely misunderstand the nature of the paradox.

You are right - I did, but then it was not said anywhere, and this is the first I'm hearing of this.

I understand that it's a mathematical/game theory paradox, but it's listed as a real world paradox - and it's not.

> Your complaint about the T/constant formula is downright silly; I'm convinced that an equivalent paradox can be created for every reasonable formula you agree to. (Actually, I think I can prove that.) The only thing that would change is that the "lines" on the equilibrium diagram would become "curves".

I think you can't. If you modeled real traffic congestion for this the paradox would not exist. Maybe I'm wrong, but I don't think so.

The "real world" examples listed on the page were not because of this type of paradox, but rather because in the real world it takes time to merge, so removing a merge point makes things faster.

But a road paradox structured like this one? I don't think you can. The whole paradox is because the T/x does nutty things as T changes (nutty as compared to the real world).

At the minimum I want to see f()+c. And f() should be an s curve.

http://en.wikipedia.org/wiki/Braess_paradox

It would be interesting to contrast the blog with wikipedia. I haven't yet gone through the explanation, but I had to check wp first to get a grasp of the problem.

I was introduced to the paradox from Wikipedia, but I submitted this article instead. I found the Wikipedia version more precise, but Presh's explanation is a bit more accessible to those not versed in game theory.

I went and read the wikipedia article; I thought it was clearer. Thanks for submitting, though... I had never heard of this.

Tragedy of the commons. Simple solution: congestion prices. Singapore is an example. Any others?

Ayn Rand it and just allow private ownership of the roads everywhere. Totally ad-hoc, with non-standard markings, conventions, and traffic "laws" that would show up in your road contract. You would have to read the road contract everytime you drove through a new area with roads operated by a different company. That is until a savior road monopolist finally took over all the markets by getting the largest established base and then using his network effect advantage to lock out other roads until they all caved in. Said monopolist could just eliminate the congestion by fiat.

No offense but hypothetically if we had private ownership they would agree with a standard marking. Its naive to assume otherwise. I don't agree with ayn rand on all things but corporations have standards....

Countries have private ownership of their roads with respect to other countries, and they all have their own markings, traffic laws, etc.

Nope. Several countries in Europe use the same markings.

PS: There is a reason you can get an International Driver's License.

The EU practically is a country. There are plenty of other counter examples, mostly countries that were formally some part of an imperialist empire, or essentially still are (many countries in the Caribbean).

When your an island it's not that important but counties that share borders tend to have similar road markings, signs, stoplights etc.

The differences between countries' marking and traffic laws are small compared to the broad commonalities. Close countries tend to harmonize. And a network of interlinked but mildly competitive roads in a single country would have even stronger incentives to harmonize.

But also: a trend in traffic control is to reduce the markings, so that people pay closer attention, using their innate intelligence to drive cooperatively. (The idea goes by the names 'psychological traffic calming' or 'naked roads'.) Speeds go down a little; accidents go down a lot. It seems traditional markings lead to overconfidence -- a destructive abdication of personal responsibility to the authoritative sign-makers.

So even if a patchwork of private roads couldn't agree on any signage standards, and just tore out all the signs (as the safest, liability-reducing option), we might wind up better off. (But of course, freeways and major thoroughfares/intersections would just work the same as they do absolutely everywhere else, under any ownership system.)

Or you could use privatization and use a tiny, well-placed amount of carefully considered government intervention and have awesome results. Example: The East Side of Santiago de Chile. Tolls do not slow traffic because they are done by RFID tags and ... OK, I don't have that much data behind me, but the data point that is Daniel Cussen says the system is effective. People I talk to generally agree.

And the unwashed masses would put up with 10 different traffic sign symbolic paradigms and roadblocks by the local owners because they simply felt like blocking traffic for better prices...this wouldn't cause the slightest stir among the millions of people and commerce it would affect...would it?

Also London and Stockholm for downtown areas.

The 91 Express Lanes (http://en.wikipedia.org/wiki/91_Express_Lanes) in Orange County are an interesting case - instead of charging a fixed toll to enter an area, there is a variable toll on a 10 mile stretch of freeway. There are 4 free lanes in each direction and 2 reversible toll lanes that go with the rush. Tolls vary from free (at night) to $10 on Friday afternoon.

One concern about these variable toll lanes is that they would only be used by the rich, but studies of license plates of drivers showed that every demographic used them about once a week, rather than every day or never. Pretty cool what happens when people have the option to pay more for better service.

http://en.wikipedia.org/wiki/Congestion_pricing

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