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Flexible Polymers Show How To Improve Daily Commute

Flexible Polymers Show How To Improve Daily Commute

November 7th, 2013 | by Petti FongTechnologist

Next time you’re stuck on the commuter train, consider this: Do you attract or do you repulse? It could make all the difference in how quickly you reach your destination.

Physicists at the Hong Kong University of Science and Technology (HKUST) and Aston University in the United Kingdom have figured out how to apply polymer physics to figure out the best routes for individual commuters to improve a metro’s performance.

Polymers are big natural or synthetic molecules that create a long list of everyday objects, from textiles to plastics and proteins. You’ll find them in everything from credit cards to airplane bodies. Each polymer molecule is a flexible chain of particles, like a string with two ends.

Fixed points, flexible routes

Now think of mass transit commuters as polymers. The two ends are each commuter’s fixed points of departure and destination while the rest of the path—polymer’s structure—is flexible.

Depending on their structures and composition, polymers can either attract or repel each other. Find the optimal alignment of polymers and that, according to the researchers, could lead to the optimal alignment of commuter paths.

During rush hour, the scientists say, it’s best to introduce a repulsive force between polymers to discourage overlapping.

In off-peak hours, do the opposite: introduce an attractive force to encourage path-sharing.

“Many of us may think that the shortest path is always the best choice. However, it is not the case and the usual choice of going through the shortest path is a bad one when everyone does that,” study coauthor and HKUST physicist Chi-ho Yeung tells Txchnologist. “During peak hours, some popular routes which lie on the shortest path of many commuters may be overloaded, causing delays which make it slower on these paths than a slightly longer one.”

The simulations devised by the scientists were applied to the London Underground metro system. Telling commuters to take certain well-coordinated paths and not necessarily the shortest route resulted in only a five percent longer trip over the shortest one. Meanwhile, congestion was reduced by 24 percent.

“Since the travellers have a tendency to avoid crowding, we can imagine that there is a repulsive force between polymers,” says study coauthor Michael Wong, also from HKUST. “On the other hand, during off-peak when we need to consolidate the traffic, the travellers have the tendency to stay together during their journeys. So we can imagine that there is an attractive force between the polymers.”

Flexible paths decrease congestion

What surprised the researchers was the discovery of the opposite of what was expected. The accepted hypothesis was that the shortest path is always the best choice. Not so, they say. The usual choice of going through the shortest path is a bad one when everyone makes the same choice. During peak hours, some popular routes that lie on the shortest path of many commuters may be overloaded, causing delays that make it slower on those paths than a slightly longer one.

Yet, although congestion does not occur during off-peak hours, the shortest path is still a bad choice, say the researchers, because the whole network has to remain active even for the few number of commuters on the less popular routes. That’s why they concluded that off-peak commuters should be encouraged to travel on some common routes so less popular bus routes or train lines could be cut when moving a small volume of people.

The challenge the researchers faced was how to coordinate individual paths of multiple commuters. Decisions have to be made for the whole system simultaneously while GPS navigation and trip planners on smartphones consider each user independently. Such apps show individuals only the shortest path. Due to the computational costs involved, most existing routing algorithms are static and based on selfish decisions, with nonadaptive routing tables indicating the shortest path to destinations regardless of local traffic

That’s why the researchers came up with using polymers as models. Physics tools that have been developed to study polymers can be applied to study transportation networks.

“The analogy is actually easy to understand,” says Wong. “Suppose I represent my travel path by a polymer. The two ends of the polymer will be fixed representing my starting point and destination. The body of the polymer will be flexible depending on my path choice. Now everyone represents their path by a polymer. We then obtain a collection of polymers on a transportation network.”

The researchers are working to develop an app that will recommend routes based on their algorithm that will tell users what is the optimal path, not just the shortest one. But they note that no matter how sound and scientific their optimal route recommendations may be, commuters will often take the road most travelled.

From the study’s abstract, which has been submitted to the journal Proceedings of the National Academy of Sciences:

“Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing sub-optimal solutions. We employ the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path-optimization problems and derive a simple, principled, generic and distributed routing algorithm capable of considering simultaneously all individual path choices.”

Top Image: Michael Wong (left) and Chi-ho Yeung demonstrate the results of the path optimization tool they developed by applying polymer physics to route-planning. Courtesy Hong Kong Institute of Science and Technology.

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