Closing Roads to Help Traffic Flow

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.1598v4.pdf

In class the other day, we played a game where each student had to pick a path to take from point A to point B, given two separate game scenarios. In Game 2, a super-fast high was built in order to facilitate traffic better. However, if everyone chose that path thinking it would be the shortest, it would become the longest. As the results showed, most people chose the path that used that super-fast highway, resulting in a bigger delay and lower payoff.

In relation to this game we played, the study above, done by three sceintists, looked at the congestion of Boston, London, and New York City. They found that when drivers seek out the shortest route, they end up making travel longer. The solution to this was to close a few of the roads, thus dropping the price of anarchy, because now drivers would not be able to "selfishly optimize their routes". This ties into the Braess Paradox, which discusses how if a new road is available that appears to make travel time shorter, everyone would take it, hence making the trip longer. So, by not opening up new roads, and instead, closing some roads, travel time/congestion could improve. The study showed that travel time overall was longer, but traffic was "smoother".

This poses the question....is it possible for us here in the US to close down roads in order to manage traffic?

While it is likely that such an action could alleviate in-city congestion, closing congested stretches of road would probably cause more trouble than it is worth. In the US at least, most highways that travel through cities are extend far from the city in both directions, meaning there is a portion of travellers who are really just passing through (Think of the highway as having a very high betweeness value). Closing the highway might make the local commuters have faster routes, but it would cripple the long-range commuters path by making them take sidestreets.

The problem with closing roads to try to manage congestion is, as you said, the new routes would take longer. Removing roads decrease traffic if the elimination of one roads cause the commuters to spread out on several slower routes that they wouldn't have considered earlier. Therefore, on each of the smaller, slower roads, there would be fewer cars which would keep the traffic running more smoothly. However, we are still selfish and the society as a whole isn't always logical so they may argue against getting rid of the fast road simply because they hate the idea of having to take the slow road even if that decreases traffic and the length of the commute. So the first part of the problem is finding the best way to decrease the amount of traffic and the second part is the politics of getting everyone to agree to that.

Here is a webpage that shows the costs of future road projects in California.
http://www.latimes.com/news/nationworld/nation/la-na-transport-list14-2009apr14,0,1505152.story

Closed roads and changes in infrastructure are not cheap by any means. For over 50 road projects in California, costs will exceed $600 million. Rebuilding roads and making new ones use a lot of resources and mainly require large amounts of man power. Closing roads to maintain sound congestion levels can be good and bad in certain situations. Making people use alternate roads could disperse cars onto various, equal paths to a destination. However, this would also be limiting the number of options people have. Ultimately, there will be a greater delay on alternate roads by closing a common road such as a highway. Clearly, building an infrastructure is very costly, but it is an investment that needs to be made to reduce future construction and provide stable traffic networks.

How many of you eat at Willard?
Ever noticed how a particular dish take longer to prepare on a busy day than a slow day?
I've decided that if everyone's order was motivated by a time criteria, i could model the time it takes for everyone to get a dish like the traffic problem.

For example lets assume that the if more pizzas are cooked in the oven, each pizza is cooked slower. And lets assume that no matter how many salads are ordered, they all take the same amount of time to prepare. thus if we wanted to minimize cumulative delay of orders we could model each dish as a function, multiply each function by how many people are eating them, and sum these values as a new function. Taking the derivative of this new function and finding the values that produce zeros, will then identify the same values that minimize the cumulative food delay