Traffic shortcut paradox

Can adding a road make everyone slower?

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At this demand, does the shortcut improve travel time?

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How it works & assumptions

Routes have one fixed 45-minute segment and one segment taking flow/100 minutes. A zero-time link creates an equilibrium time D/50 for D≤4500, else 90 for D≤9000. Without it, time=45+D/200.

Ideal nonatomic selfish routing with fixed demand and directed roads. Equilibrium is solved analytically, not a traffic forecast.

References: Networks, Crowds, and Markets, Chapter 8: Modeling Network Traffic Using Game Theory (2010)

This is an ideal mathematical model, not a measurement or a forecast.

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