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A trafficless traffic jam?

Carmageddon Dos. Los Angeles. 405 freeway. Starting Friday night (September 28th) all the way till tomorrow morning (October 1st), engineers have been working 53 straight hours to ensure everything goes well for the closing of a 10-mile section on the 405 (nation’s busiest freeway). The northern half of Mulholland Drive is being demolished as a part of a $1 billion project to add a carpool lane. What to expect after one of the most used sections on the 405 is closed down? Traffic jams elsewhere are created (say on the 10 freeway). People want to find the fastest possible way to get to their final destination. However by finding a best alternative path, no traffic actually gets built up.

It is common knowledge that there is the potential for extreme congestion, thus measures are taken to prevent a traffic jam catastrophe. For example, for the trucking community, the delivery services alter their work schedule not to make deliveries or to travel far outside the area. The traffic model we’ve described is really a game in which the drivers are players and each player’s possible strategies consist of the possible routes from their starting point to their destination.

In the traffic game, there is generally not a dominant strategy: either route has the potential to be the best choice for a player if all the other players are using the other route. The paradox of there being no traffic buildups (Braess’s paradox) is actually not at all paradoxical. If some particular driver could do better by taking an alternative path (a best response), the energy of the traffic pattern would decrease. If no driver has a best response, the traffic pattern is at equilibrium. Until the traffic pattern reaches equilibrium, the driver will keep taking a different path, constantly modifying the traffic pattern.




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September 2012