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.
Everyone initially chooses a short but congestion-prone route. Before the first simulated day, that road is contrasted with a longer, less sensitive alternative. For the next several days, travel times, the difference between them, and the number of switchers are displayed before the allocation updates. Vehicle animation reflects the changing route times. A jump forward reveals the eventual balance: travelers using either route have little reason to move alone. The important point is that equilibrium is not a command issued to drivers. It can emerge from many small day-to-day responses, although the speed and stability of convergence depend on the adjustment rule and the congestion functions.
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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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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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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