This study proposes a trial-and-error congestion pricing method to achieve system optimum under day-to-day flow dynamics with unknown demand. Travelers are assumed to adjust their route choice day by day so that the resultant traffic flow under a trial of tolls evolves from one day to another. We rigorously demonstrate that if psychological inertia is considered in travelers' day-to-day route choice behavior, the convergence of the proposed trial-and-error congestion pricing method can be guaranteed without requiring the observed network flows to be in user equilibrium. Furthermore, the proposed method also allows tolls to be updated at irregular time intervals, which greatly relaxes the implementation requirements of existing congestion pricing schemes in the literature. This study is very significant from a practical point of view because it provides a flexibility approach that greatly reduces the implementation time of the traditional trial-and-error congestion pricing method. Numerical experiments are conducted to validate our theoretical findings.
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