
Braess’s paradox - unhammer
https://en.wikipedia.org/wiki/Braess%27s_paradox
======
cousin_it
Simple explanation: when you win five minutes by switching from road A to road
B, other drivers on road B might lose more than five minutes in total from the
extra congestion you cause. So the total time spent by all drivers will
increase, and so will average time (if number of drivers is constant). So
removing some connections from the road network, to prevent some drivers from
optimizing their route, can reduce average driving time.

~~~
mannykannot
Furthermore, when a driver chooses to take the new route, this does not create
any opportunity for the drivers disadvantaged by this choice to do better for
themselves (they also have the option of switching to the new route
themselves, but that opportunity was created by the creation of the new route,
not by the responses to it by other drivers.)

This paradox may have some relevance to the effect of navigation apps,
especially those that attempt to route around congestion, as they effectively
create routes in the sense that the vast majority of drivers would not have
considered using them without the app.

~~~
hota_mazi
I wonder if current navigation apps are smart enough to only propose a new
route to a portion of the total number of drivers in that location.

Ultimately, the only way to have optimal flow is to delegate all itinerary
decisions to a central authority...

~~~
toast0
Have you noticed how good the time estimates have gotten? Clearly they're
streering other traffic out of or into the way to keep it even.

~~~
ashtonbaker
I started noticing this very abruptly - that Google no longer redirects me
from congested roadways to low-traffic parallel roads. Now, as soon as I take
the exit to a less congested road, my estimated drive time might drop by 5-10
minutes, so clearly Google knows that it isn't sending me down the optimal
route. I don't think this used to be the case.

~~~
mannykannot
Interesting - I noticed recently, for the first time, that when I modified a
'fastest' proposed route using local knowledge, I found the predicted time
dropped, and that has happened several time since.

This may be the result of better predictive modeling, and particularly in
recognizing that dumping a lot of traffic into a low-capacity route is
pointless. It is probably also a political response to the fact that
residential areas don't like having a lot of traffic routed through them, and
are pressing for the power to regulate it.

Better predictions could also explain toast0's observations even when global
optimization is not being attempted.

------
dvh
In transport tycoon (openTTD) when train station started to become congested
adding more tracks usually didn't solve the problem, best way was having two
uninterrupted tracks almost into station then spread out into 15-wide station
(or whatever max was allowed) with short buffers before and after station.

~~~
Cthulhu_
TTD is great for modeling systems like that; what I like(d) to do was just
create a loop track, two tracks wide (one for each direction), with stop
lights every x tiles, making sure to have the same length trains at all times.

------
crazygringo
This is fascinating. The book Traffic [1] talks a great deal about how adding
road capacity (e.g. more lanes) can result in zero change in congestion
because more people choose to take more trips.

But this paradox appears to hold traffic constant, and uses game theory to
show how more _connections_ (not lanes) can result in worse congestion too.

It really is amazing how something as simple-seeming as roads and traffic,
where it feels like simple common sense ought to apply, winds up being so
deeply and fundamentally counter-intuitive.

[1] [https://www.amazon.com/Traffic-Drive-What-Says-
About/dp/0307...](https://www.amazon.com/Traffic-Drive-What-Says-
About/dp/0307277194)

~~~
ProblemFactory
> adding road capacity (e.g. more lanes) can result in zero change in
> congestion because more people choose to take more trips

This is not the paradox nor even an argument against adding road capacity
though.

Even if congestion or travel times stay the same, now more people are able to
travel to places they want to go. Traffic might not have improved, but some
measure of quality of life did.

~~~
X6S1x6Okd1st
Depends on the impact of sitting in traffic on quality of life.

~~~
dsfyu404ed
You can still forgo the trip though. It's up to each individual participant to
decide whether or not they want to make the trip. The ability for more people
to take the trip at the same opportunity cost. Adding a lane or a road is
little different than increasing the frequency of trains on a subway.

Peak demand will always saturate whatever capacity you have but the amount of
stuff you move at peak capacity is greater so you spend less time fully
saturated

~~~
X6S1x6Okd1st
> Peak demand will always saturate whatever capacity you have but the amount
> of stuff you move at peak capacity is greater so you spend less time fully
> saturated

That doesn't follow.

------
moultano
I believe this paradox applies to any congested highway with a robust network
of side streets around it. If everyone could agree to take side streets for
half of their trip, the side streets could easily absorb the extra traffic
without slowing down, and the highway would be able to flow freely, shortening
everyone's total commute time. But no single person can improve their commute
by switching to the side streets alone.

~~~
SilasX
What? It's usually the first switcher who benefits the most from using the
side streets, because they see zero congestion, and, if anything, it's more of
a problem (for the cut-through neighborhoods) of too many people switching.

~~~
moultano
If the side streets are currently faster than the congested highway that's
true. I'm talking about situations where it isn't, where the fixed cost of
stoplights and speed limits ensures it they will never actually be faster than
the congested highway.

------
dang
A discussion from 2009:
[https://news.ycombinator.com/item?id=929362](https://news.ycombinator.com/item?id=929362)

~~~
QML
Another relevant discussion, albeit from a more game theoretic view:
[https://news.ycombinator.com/item?id=17741641](https://news.ycombinator.com/item?id=17741641).

Beyond two submissions sharing the same subject-title, do you think it'd be
possible to find all "relevant" discussions -- say, back-links or forward-
links -- as well and post them?

------
Sharlin
I’m not sure how this is different from the concept of induced demand? BTW,
the ”See also” section is awesome. A serious time sink.

~~~
ajuc
Induced demand is when more people drive, or they drive more often, or longer
routes because of added roads.

This is when the same amount of traffic is distributed less optimally because
of adding new edges on the graph.

~~~
Sharlin
Ah, right. Thanks!

------
epx
I think that some changes in traffic aim to optimize the instantaneous speed,
while it should aim to minimize the door-to-door time. Driving 1km@10km/h
takes 6 minutes, while driving 5km@30km/h takes 12 minutes, and you might end
up driving 5km@1km/h at rush hour because the longer distance keeps you in
traffic for more time.

This actually happened in my home city, some areas implemented "improvements"
that made it very difficult to reach some destinations, you need to follow
long detours intended to "improve flow", they might improve flow for whoever
is just passing by, but traffic that originates or terminates in that area, it
is hell.

------
kevlar1818
This might not be the exact manifestation of the paradox, but I think it's at
least a supporting anecdote.

The latest Sim City had its problems, but I definitely experienced this
phenomenon in its traffic simulation. Adding more roads created more
intersections which -- using a computer analogy -- created more context
switches between competing cars (threads). Intersections would become clogged,
potentially backing up nearby intersections. The best traffic systems in Sim
City minimized intersections just as much as -- if not more than -- throughput
and mean travel distance.

------
cvigoe
If anyone is interested in topics like this and wants to delve some more into
the mathematics, I’d highly recommend Tim Roughgarden’s lecture series on
Algortihmic Game Theory:

[https://www.youtube.com/playlist?list=PLEGCF-
WLh2RJBqmxvZ0_i...](https://www.youtube.com/playlist?list=PLEGCF-
WLh2RJBqmxvZ0_ie-mleCFhi2N4)

------
jl2718
Palo Alto Central Express. Cut off side streets. Traffic will improve, and
kids will be safe in the street.

------
gpderetta
At the limit, if you remove all capacity (or leave a nominal capacity for a
single commuter that works beside their home to remove infinites), the
individual transit time goes to zero! It follows we should remove all roads!!!

It seems to me that the average transit time is the wrong metric to optimize
for.

~~~
algorias
No. In Braess' paradox both the situation with and without the extra road have
the exact same total flow from A to B. Removing flow capacity is not allowed.

------
mcguire
" _In 1983, Steinberg and Zangwill provided, under reasonable assumptions, the
necessary and sufficient conditions for Braess ' paradox to occur in a general
transportation network when a new route is added._"

Anyone know what those conditions are, offhand?

~~~
saosebastiao
The biggest is that the drivers have adequate information about road capacity
and traffic conditions and are acting rationally on that information.

I actually believe that Waze has contributed to a lot of urban traffic
problems as of late, because it ensures that more people contribute to braess'
paradox instances that might have gone unrealized in the past.

------
ruskerdax
While I don't have an in-depth technical understanding of exactly why this
happens in every instance, I have definitely observed this while playing
Cities: Skylines, a SimCity-like game which emulates traffic flow.

~~~
Sharlin
However, note that the traffic flow simulation in C:S is rather simplistic for
performance reasons: specifically the pathfinder doesn't take dynamic traffic
conditions into account at all! A traveler never chooses an alternative route
even if the primary one is congested. But yeah, adding routes usually means
also adding choke points (that is, intersections) which naturally slows down
traffic.

------
rundigen12
Whoa, I was just reading about this yesterday! Did I consent to tracking when
I created an account here? ;-)

