Counterintuitive physics may help everyone drive home quicker

October 2, 2008 By Lisa Zyga feature
Network of the main roads in Boston-Cambridge. Road colors indicate the amount of delay caused in the Nash flow if the road is removed (red indicating the greatest delay, blue indicating no delay). Black dotted roads are those whose removal reduces the travel time, a counterintuitive effect known as Braess’s paradox. Image credit: Hyejin Youn, et al.

If you're trying to drive to a destination as quickly as possible, you might think that knowing the traffic conditions would help you choose the quickest route for yourself. Traffic reports and new GPS technologies that provide traffic data are based on this assumption – but scientists have found that knowing this information may do more harm than good.

A recent study has investigated just how much time is lost due to individuals opting for strategies that maximize their own personal utility rather than the social optimum, which often aren’t the same. Physicists Hyejin Youn and Hawoong Jeong from the Korea Advanced Institute of Science and Technology in Daejeon, Korea, and computer scientist Michael Gastner from the Santa Fe Institute and the University of New Mexico in the US, call this lost time “the price of anarchy” (POA) that society must pay for the lack of individual coordination.

Defined as the ratio of the total travel time of an individual’s optimal route to the total travel time of society’s optimal routes, a high POA means that individuals pursuing the best route for themselves are slowing down the overall traffic flow. When analyzing the traffic in three major cities – Boston, London, and New York City – the researchers found that individuals waste up to 30%, 24%, and 28% of their travel time, respectively, due to choosing a personally optimal route instead of a socially optimal one. The team also calculated the POA for four simulated traffic networks, and found similar results.

“People usually believe that inefficiency can be lessened by providing more information,” the scientists told PhysOrg.com. “On the contrary, our model assumes the full information of traffic and shortest paths in a given traffic condition for every player; that is, all the traffic conditions are known to every player. As GPS and computer-modeling-based devices are developed more and more, we believe the drivers follow [an individually optimal] flow more and more.”

At the core of the price of anarchy are two related concepts: Waldrop’s principle and the Nash equilibrium. Waldrop’s principle, which is fairly obvious, says that humans approach the problem of finding routes in a network from the self-interested perspective of finding the quickest route for themselves.

The second concept, the Nash equilibrium, occurs when an individual cannot choose a better strategy for himself if other individuals keep their strategies unchanged (i.e. an individual can not improve his situation by changing unilaterally). In the traffic situation, say you know which routes the other drivers take, maybe because you’ve tried different routes to find out which is the fastest way to get home from work. After trying different routes, you choose the route that is fastest for yourself. Then you cannot find a faster route as long as the other drivers stick to their same routes (which they do, because they cannot find faster routes, either).

But if many drivers could change their routes simultaneously, then the effect might be a decrease in everyone’s travel time, and society would come closer to the social optimum rather than languishing in the Nash equilibrium. The scientists found that modifying the network structure can sometimes lead to faster overall travel times, since network changes affect everyone. Surprisingly, they found that closing certain roads can sometimes increase efficiency and allow drivers to travel faster.

This counterintuitive result, that adding extra capacity to a network can sometimes reduce its overall efficiency, is called Braess’s paradox. The paradox exists because the Nash equilibrium and the social optimum react in different ways to changes in the network. Specifically, closing a road cannot improve the socially optimal travel time, but it could potentially improve the Nash travel time. This is because individuals seeking their own fastest times may get further away from the social optimum by taking the individually-optimal roads, and closing those roads forces them to take the socially optimal path. In the same way, adding new roads in an attempt to decrease congestion might even create more delay in the Nash equilibrium, but not necessarily decrease congestion in the social optimum strategy.

“Braess’s paradox is interesting and counterintuitive,” the authors explained. “It is still controversial to say that closing a road is the best way to deal with a complex traffic network. Instead, we would rather emphasize that opening a new road without careful consideration can worsen the system contrary to the original intention.”

The scientists noted that studying traffic flow could not only help planners design better road networks, but could also have applications in other areas of science, such as electronics and economics. For example, physicists know that removing wires in an electric circuit can sometimes counterintuitively increase the conductance, similar to how removing roads can sometimes increase traffic flow. Understanding the agents’ behaviors in a network can also be useful for designing networks such as the Internet and peer-to-peer file sharing, as well as optimizing (or minimizing) flow in many different kinds of networks.

“It was surprising and delighting at first: similar principles also emerge in physics without having a direct connection to game theory,” the authors said.

More information: Youn, Hyejin; Gastner, Michael T.; and Jeong, Hawoong. “Price of Anarchy in Transportation Networks: Efficiency and Optimality Control.” Physical Review Letters 101, 128701 (2008).

Copyright 2008 PhysOrg.com.
All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com.

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20 comments

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zbarlici
3.4 / 5 (14) Oct 02, 2008
Social optimum?......... in case you havent noticed this stupid N. American (and probably most of the world`s) society operates on an "I AM #1" mentality... and you know what that means? it means most people think "screw you, you, AND you all of you".. just so he can gain a little. I`m not a bitter guy i just wanted to point this out. Good day to all
tkjtkj
3.5 / 5 (4) Oct 02, 2008
zbarlici : i dont see where any
'socially optimum' is equated
to be the sum of all 'personal'
ones. They most certainly are
different animals, no?
jscroft
2.4 / 5 (18) Oct 02, 2008
There's a fallacy here. The individual optimum IS the social optimum... so long as the individual can correctly assume that other individuals are also implementing the social optimum. Within the context of this piece, "individual optimum" only applies to those individuals who haven't read this piece. :)

One could envision a recursive scenario where my GPS calculates the optimal path based on the assumption that X% of other GPS users are calculating the socially vs. individually optimal path... based on the assumption that X% of other GPS users are calculating the socially vs. individually optimal path... ad infinitim.

Presumably X would rise over time as more devices adopted the method.

The key here is that the individual's goal is still to optimize his OWN path. It just so happens that the best route to this goal proceeds via a global-optimization routine.

Lazarus Long said it best: "Beware of altruism. It is based on self-deception, the root of all evil."

Self-interest is a much more reliable quality than altruism in us monkeys... and, as is so often the case, we see here that enlightened self-interest produces precisely the same effect.
holmstar
4.3 / 5 (7) Oct 02, 2008
"Social optimum" basically means the minimal average travel time for all people who are traveling. When moving to a social optimum type system, some people will certainly end up with longer travel times than what they had as individuals, while most end up saving time. So, social optimum is definitely not the same as individual optimum for that minority. Not a fallacy at all.
Minnaloushe
3 / 5 (7) Oct 02, 2008
Here is Wisdom:

"Small change can often be found under seat cushions."

Lazarus Long (thanks js!);
frajo
1.3 / 5 (3) Oct 02, 2008
I'm sceptical about this assumption: "... humans approach the problem of finding routes in a network from the self-interested perspective of finding the quickest route for themselves."
Because, personally, I prefer the easier route, which is not necessarily the same as the quicker route. With "easier" I associate less stress, fewer risks, fewer traffic lights, fewer corners and so on. Of course, the delay has to be acceptable.
Jarry
1 / 5 (1) Oct 02, 2008
Shouldn't it be "drive home more quickly"?
vlam67
3.7 / 5 (6) Oct 02, 2008
This study does not take into account hopeless drivers who hesitates when they should go, drivers who start up so slowly as if all the time in the world is theirs alone while they are at the front of the queue...
...jumping to the side lanes dotted with parked cars and then hope and appeal to the generosity of others to blend back in to the main flow, no signaling when changing lanes, stop and signal too late when turning across traffic...
...taxis cruising slowing conserving their gas waiting for fares,drug dealers late on deliveries and drive accordingly...
... and the stupid tendency of most drivers to slow down when there is more vehicles around them, no matter the traffic flow situations or perceived danger levels, which they SHOULD be able to critically access...but, honestly, they are just glorified Homo Erectus in mobile machinery... may be they are on the phone, looking for a parking spot, or just being obstructive for the joy of it as many young d**ckheads on the cruise while have nothing to do...or just loafing along to show they are such employed and have much free time that they don't need to show consideration and promptness in cut-and-thrust traffic of the common foul-smelling rabble...I could go on and on. The list of selfishness and inconsideration is endless.
Roach
1 / 5 (1) Oct 03, 2008
Well a quick question about the GPS units stearing prople onto train tracks and into lakes. Are these GPS units working towards a "social optimum"? Pretty sneeky.
Bazz
4 / 5 (4) Oct 03, 2008
It also doesnt account for accidents, thunderstorms and meteorite impacts.It merely suggests there are possible ways of improving traffic conditions.
deatopmg
2 / 5 (4) Oct 03, 2008
Social optimum?......... in case you havent noticed this stupid N. American (and probably most of the world`s) society operates on an "I AM #1" mentality... and you know what that means? it means most people think "screw you, you, AND you all of you".. just so he can gain a little. I`m not a bitter guy i just wanted to point this out. Good day to all


Especially in Cambridge Massachusetts and 617 environs - note the way they drive. me, me, me, ME!
Noumenon
1.8 / 5 (5) Oct 03, 2008
Social optimum?......... in case you havent noticed this stupid N. American (and probably most of the world`s) society operates on an "I AM #1" mentality... and you know what that means? it means most people think "screw you, you, AND you all of you".. just so he can gain a little. I`m not a bitter guy i just wanted to point this out. Good day to all


Your naive. Individualistic self preservation is a natural force which results in competition in a free capitalistic society, which in turn results in sophisticated countries like America that can afford to give billions in money and aid and fight for civil rights through out the world, ....hardly selfish. Oh, and we're polite too.
Flakk
1 / 5 (1) Oct 04, 2008
This study does not take into account hopeless drivers who hesitates when they should go, drivers who start up so slowly as if all the time in the world is theirs alone while they are at the front of the queue...
...jumping to the side lanes dotted with parked cars and then hope and appeal to the generosity of others to blend back in to the main flow, no signaling when changing lanes, stop and signal too late when turning across traffic...
...taxis cruising slowing conserving their gas waiting for fares,drug dealers late on deliveries and drive accordingly...
... and the stupid tendency of most drivers to slow down when there is more vehicles around them, no matter the traffic flow situations or perceived danger levels, which they SHOULD be able to critically access...but, honestly, they are just glorified Homo Erectus in mobile machinery... may be they are on the phone, looking for a parking spot, or just being obstructive for the joy of it as many young d**ckheads on the cruise while have nothing to do...or just loafing along to show they are such employed and have much free time that they don't need to show consideration and promptness in cut-and-thrust traffic of the common foul-smelling rabble...I could go on and on. The list of selfishness and inconsideration is endless.


ROFL, You must drive through Dallas or Houston a lot!
Crossrip
1 / 5 (1) Oct 05, 2008
I propose an ultra fast lane. 85 MPH.
Crossrip
1 / 5 (1) Oct 05, 2008
85mph being the minimum speed.
nilbud
1 / 5 (4) Oct 05, 2008
Drug dealers who are late on deliveries continue to drive at normal speeds. There's no point in getting busted for speeding or careless driving with a carload of drugs.

As for noumenon, it's always hilarious to come across truly gullible types who believe all propaganda. Here in the EU they've all died out over the years but it's fascinating to see the sub-species still grazing away in the US. It's sad though that they all seem to be stuck in 1976, thinking the ISS is Skylab and drinking tang.
jscroft
3 / 5 (6) Oct 05, 2008
Er... am I understanding you correctly, nilbud? You assert that Americans generally believe propaganda, but Europeans DON'T?

Hmm. Let's see... in just the last century, we wide-eyed dreamers saved your hard-bitten, pragmatic asses at Belleau Wood. Then we did it again on the beaches of Normandy. We spent all our play money and brought those nice Soviets down before they could annex the REST of Europe, and now we bleed into the sands of Iraq and Afghanistan because you wisely chose to ignore Islam's 14-century vendetta against the West.

Europe's cemeteries are filled with Americans who saw clearly what your parents and grandparents weren't willing to see. Shame on us, who thought our blood might purchase wisdom for their children.

Instead, you parrot the words of men who swear to exterminate you, and have the audacity to sneer at OUR gullibility.

Nilbud, I wouldn't sit in your house, eat your food, and call you a fool. Most of us here are Americans. If you haven't the discipline to confine your comments to the scientific questions raised here, you might at least display a little class and refrain from insulting your hosts.
Noumenon
1 / 5 (3) Oct 05, 2008
nilbud must be young, he confuses history with propaganda.
jscroft
2 / 5 (4) Oct 05, 2008
Young, and a troll to boot. It's annoying... if you can't have a conversation on the basis of fact HERE, where in the world can you?
shem
1 / 5 (1) Feb 09, 2009
Expanding on Vlam67's comment,

I recently began to wonder if increased cell phone usage is contributing to the decline in fuel economy in the US over the past few years. Increased following distances, characteristic of cell phone users, and delayed reaction times decreased the effective capacity of roads. The delayed reaction times decrease throughput at bottlenecks, particularly traffic signals. This slows people down to less efficient speeds (below 55mph, faster is fuel efficient) and creates more stop-and-go traffic.

Personally, I think the fuel economy decline has more to do with bad information and price pressure from sky-rocketing gasoline prices. Accelerating quickly, but smoothly, is generally more efficient than slow. Higher cruising speeds are more efficient below 55mph, provided the cruising time is long enough to make up for the cost of the additional acceleration. This is contrary to popular belief.

In addition, I can think of other economic factors. The CBO estimates vehicle fleet turnover to be about 14 years, perhaps efficient early-mid 90%u2019s vehicles are retiring and our fleet is beginning to reflect the late 90 and early 2000 preference for SUV%u2019s as commuter vehicles.

Giffen Behavior, people driving more during congested times to maintain their income, and driving less for consumption.

Then there are instances where good behavior becomes bad. Avoiding brakes is a very economical behavior, provided there is no congestion. But idling along because of expecting a to hit a traffic signal a second time prevents other queues from clearing and prevents people from reaching destinations that might be before the bottleneck.

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