Sentences to ponder

Jason Kottke reports:

The collective optimization of individual driving routes by drivers using realtime traffic maps slows everyone down.
That is, everyone picking the "fastest" route on the map results in
overall slowdowns. Interestingly, the solution to this problem may be
to remove some roads so that drivers have fewer options for route
optimization.

Here is more.  To how many other problems can this point be applied?

Comments

Isn't this just a complex, multi-user form of nash equilibrium?

1) Braess's paradox is well-known in computer networks. A key, though, is that it's really an existence proof that adding capacity can *sometimes* decrease througput.

From an economics perspective, think market failure.

Markets almost always work real well and in the way that's expected (well at least to me). However, market failures do exist.

Recognizing that they exist can be useful, but assuming that every market will be a market failure is a bad bad idea.

2) It's also a known problem in computer networks that if routers are building maps based on stale information, you can get really bad results.

Not reading the actual paper, but knowing that most in-car traffic units can have data that's up to 30 minutes old, I suspect that this is what actually drove the empirical results, not Braess's paradox.

3) For another analogy, closing roads is a "Nudge".

4) The price of anarchy (illustrated in the post) is the impetus for central planning. Hayek would note that there's also a significant cost in gathering enough information to make the right decisions, which increases rapidly when the information is time sensitive.

Often, the cost of gathering the information outweighs the cost of anarchy. This is why mobile ad-hoc networks are distributed.

"Imagine two routes to a destination, a short but narrow bridge and a longer but wider highway. Let’s also imagine that the combined travel times of all the drivers is shortest if half take the bridge and half take the highway... Eventually, the traffic flow settles into what’s called the Nash equilibrium..., in which each route takes the same amount of time. But in this equilibrium the travel time is actually longer than the average time it would take if half of the drivers took each route."

The argument hinges on a claim that one route, the bridge here, responds worse to congestion. It's faster with low congestion but worsens rapidly. A marginal car moving from highway to bridge worsens congestion more on the bridge than it relieves the highway. Apparently some short cuts really do need to remain somewhat secret.

In a two route case, you never get the counter-intuitive result that removing one route would make things better. Indeed, without that result the point is interesting, but not as much. Removing the route works in some cases because it removes a way for people to get to the roads that need to be less used.

There are of course other solutions; notably among them one could use road pricing to solve the problem. If the socially optimal result is that one route is faster than another, simply introduce road pricing on the bridge and the problem is solved. The paper notes this, though it also notes that if the fees are not returned to the people than this still imposes a societal cost. (However, I think that they're missing that collecting it as a tax is more efficient than loss due to congestion, which helps nobody.)

There's a question in Rasmusen's book on Information and game theory that is basically this exact problem.

Drive in Denver then drive in Fairfax and then tell me with a straight face that reducing the number of routes is a good solution to gridlock. The idea is ludicrous.

Basketball! http://gravityandlevity.wordpress.com/2009/05/28/braesss-paradox-and-the-ewing-theory/

It's only slightly relevant, but whenever I'm slogging through traffic on the highway I always think about how it's a decent market analogy... no one has to direct traffic to the fastest lane, but if a lane's moving faster (i.e. more profits/return) than more cars will switch to that lane (i.e. reallocating resources) until the return comes back down to the same as the other lanes. And you even have people that keep switching too late and just get burned even worse (think bubbles, maybe?)

I have a Tom Tom with "realtime" traffic updates. It is a lifesaver in Los Angeles, where we have a large number of long secondary roads paralleling almost every freeway (with a few "pinch points" over the mountains).

On the other hand, in DC because there are only a few bridges across the Potomac, when they all get clogged, there is nothing you can do!

That's a stupid theory when applied to, say, the LA freeway system. Realtime traffic maps help me avoid major traffic jams caused by accidents.

I agree with M. Thacker, people are missing the point a little. Check out the example in the wiki http://en.wikipedia.org/wiki/Braess's_paradox

To imagine the way that traffic dieting (lower capacity roads) could speed up travel time, remove the extra capacity (lanes) from the 45min sections in order to make the travel time there a function of traffic as well.

It's a little difficult to see, but actually the bid-ask spread on a stock corresponds to congestion in the flow of stock from lower to higher valuing owners. So the parallel point would be that a tendency for every buyer and seller to go to the market maker with the narrowest spread would tend to widen the spread overall.

But the points by Steve Sailer and John Thacker make a lot of sense to me. The congestion externality (of "intelligent redirection of flow"?) seems much smaller when there are rapid changes in the relative congestion of different routes.

To imagine the way that traffic dieting (lower capacity roads) could speed up travel time, remove the extra capacity (lanes) from the 45min sections in order to make the travel time there a function of traffic as well.

Right, and it can work on normal days in several locations. However, after reading Steve Sailer's comment, it occurs to me that the importance of alternate routes in providing insurance when the delay function and capacity suddenly changes due to accident, construction, or road maintenance may be more important than the occasional problems with Braess's paradox.

Braess's paradox should be considered when deciding how to add new roads, or where to upgrade roads most effectively, but robustness of the system to changing conditions is important too, not just optimal behavior when all roads are fully open.

I'm reminded of monopolistic competition - It stops just short of a perfectly competitive optimum because people appreciate the value of choice.

"Having lived in a city that built traffic circles in a busy industrial area without bothering to figure out if said circles were navigable by an 18-wheeler...."

Me too. Ours also have large mounds on top so you can't see who's coming.

But hey, traffic circles are good. Those sophisticated Europeans use them.

Note that this all becomes moot with circa 2013 GPS systems, which feed back your intended route to a central server, learn about other drivers plans thereby, and can guesstimate the paths of non-GPS-enabled drivers by the movement their cellphones in an out of given cell tower zones.

Reading the original and then the responses, I'm reminded of the seminar I took with Kleinrock, the original "god" of queuing theory and the one who made the case for building the internet protocols on packet switching.

He used lots of readily observable examples to illustrate different problems in handling congestion in packet switch networks, and in modeling these networks, nearly everyone involving cars in traffic.

Here are two that I can easily explain and that I think you will readily grasp from your own experience. For all who have been in a city at night, and been in a room high enough at night, say eating dinner at the top of a hotel, you have watch the wave of red lights sweep back through traffic as a random car on the road hits the brakes, and then cars following hit their brakes and the red brake light sweep back up the road for miles.

That explains why you hit the brakes and then creep along for a mile or two, and then the traffic suddenly speeds up for no reason. 10 minutes earlier someone hit the brake around where you speeded up, and that caused a congestion block to sweep back up the road, and that is what slowed you down.

If you think about that effect, then imagine a tunnel under a river where the traffic entering races downhill simply pulled by gravity, and then as they start heading uphill out of the tunnel, they slow down as they don't push down on their accelerator. In other words, the cars leaving the tunnel are going slower than those entering, so those going down need to slow down, they hit the brakes, and the following cars hit their brakes, and the wave of braking cars sweeps up to the entrance to the tunnel, causing a back up at the entrance to the tunnel. So, at this point this is the same as the example above.

The solution that a traffic engineer in conjunction with queuing theorist came up with was to put a stop light at the entrance to the tunnel. They really did. The light goes green for long enough for the down section of the tunnel to fill up, and then the light stays red long enough for the last of the cars to start climbing up and out, then it turns green and fills the down tunnel again. The lead cars rush down, climb out slower, but often faster than the last cars in the last bunch, so the cars come out the other end without a break in traffic.

But the one of the final points he made was that solving lots of queuing theory problems required solving laplace transforms, or other likewise unsolved problems, so this was a great field to find problems for getting a math phd and probably a Nobel prize or one of the other awards and medals.

I think this posting is an example of the lack of reality checking rampant among freakonomists who attempt to blithely apply academic theories to real world situations without stopping and thinking.

The issue is that for somebody driving, say, LA's freeways (the #1 application for real time traffic technology), there's little point in choosing an alternate route due to minor differences in traffic speeds. The majority of trips have one route that is much shorter than any other possible route, so choosing an alternate route because the average speed on the alternate is 60 mph versus 55 on the primary route isn't worth it. What is definitely worth it is taking the alternate route because the average speed on your primary route is 15 mph due to a jack-knifed semi.

Radio stations have been broadcasting traffic information for a half century because of these considerations.

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