Routes, equilibrium, pricing, and system-wide effects.
Small choices reshape the whole
Building an extra road sounds like an unambiguous improvement. Braess's paradox shows why that intuition can fail when drivers independently choose the route that seems fastest to them. A new link changes everyone's incentives, and the resulting route changes can overload roads that previously worked well.
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Many commuters want to arrive at a similar time, but a bottleneck can admit only a limited number of vehicles per minute. If everyone departs near the preferred time, a long queue forms. If departures are spread out, the queue shrinks, but some people arrive early or late instead.
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Drivers consider the time they personally spend on a road, but each additional driver may slow down many others. That difference between private and collective cost can make the route pattern chosen by individuals less efficient than the pattern that minimizes total travel time.
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Route choice is learned through experience. If one road becomes slower than another, some travelers switch the next day, changing congestion on both roads. Repeating this adjustment can eventually bring the travel times of used routes close together.
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Better travel information can change traffic for the worse when many drivers act on the same message. A route that looks faster to an individual may become crowded after enough other travelers receive the identical signal.
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City roads do not all deteriorate at once. Some still carry traffic near their usual speed while others slow sharply, and the usable network can break into separate connected regions. Percolation analysis asks how that connectivity changes as the standard for a sufficiently fast road is tightened.
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When each traveler chooses the cheapest available route, the result may cost society more than a coordinated assignment would. The price of anarchy measures how large that gap can become under a stated class of congestion rules.
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Traffic signals grant intersections one movement at a time, often making vehicles stop and restart. Rhythmic control proposes a different organizing rule for automated traffic: reserve moving slots that pass through the grid in a coordinated pattern, so vehicles can join a slot and keep progressing.
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