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Comment by saosebastiao | Hacker News Reader

Exactly. In other words, in order to globally optimize for throughput, you would have to deoptimize some people's routes.

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In the toy example given in the linked page, with the A->B link in place the global optimum (in terms of total minutes spent travelling) is for 1750 cars to travel Start->A->End for 67.5 minutes of travel, 500 cars to travel Start->A->B->End for 45 minutes of travel and 1750 cars to travel Start->B->End for 67.5 minutes of travel. This gives a total of 258750 minutes spent travelling.

If you imagine that one of the Start->A->End travellers switches to Start->A->B->End, we now have 1749 cars travelling Start->A->End for 67.5 minutes, 501 cars travelling Start->A->B->End for 45.01 minutes and 1750 cars travelling Start->B->End for 67.51 minutes. The car that switched improved its own travel time from 67.5 minutes to 45.01 minutes, but the total time spent travelling increased to 258750.01 minutes (one driver saved themselves 22.49 minutes, but cost 2250 other drivers 0.01 minutes each).

So yes, if you found yourself in that second state, to improve the global optimum you would have to move to the first state by de-optimising the route of one of those 501 Start->A->B->End drivers.

Normally you would do this through prices, but most roads don't work that way.

Hwy 635 in Dallas has a variable-toll expressway lower level.

There are definitely many variable-tolled roads. The trouble is that frequently they are embedded in a system of non-tolled (or, really, not-allowed-to-be-tolled) roads, and that the tolling is not well-focused on congestion. Basically, the Braess "paradox" emerges if you try to make a road network that's optimal for travel patterns over an entire day, without using pricing to ration scarce space.

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