

Why the secret to speedier highways might be closing some roads: the Braess paradox - paulgb
http://mindyourdecisions.com/blog/2009/01/06/why-the-secret-to-speedier-highways-might-be-closing-some-roads-the-braess-paradox/

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mdasen
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.

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ars
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.

~~~
foulmouthboy
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.

~~~
Retric
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.

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Herring
<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.

~~~
paulgb
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.

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

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newt0311
Tragedy of the commons. Simple solution: congestion prices. Singapore is an
example. Any others?

~~~
anewaccountname
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.

~~~
zitterbewegung
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....

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

~~~
Retric
Nope. Several countries in Europe use the same markings.

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

~~~
captainobvious
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).

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

