On the equivalence between stationary link flow patterns and traffic network equilibria

The paper proposes a conjecture on the equivalence between a day-to-day stationary link flow pattern and traffic network equilibrium. Without imposing any condition on the link travel cost functions, we prove the conjecture in both static and dynamic transportation networks, under three different cost-responsive route choice mechanisms. This equivalence suggests that the monitoring and analysis of traffic patterns can be conducted on the level of the links rather than paths with implications for intelligent transportation systems.