One important indicator of traffic network resilience is rapidity, which measures the speed at which a system returns to its normal state after a disruption. In this paper, we propose a day-to-day tolling scheme to increase the rapidity of road traffic systems after disturbances caused by natural or man-made events such as accidents, flooding, earthquake, and infrastructure damage. The theory of projected dynamical systems is applied to model the transient behaviour of traffic when faced with network disruptions. We further provide three computationally tractable solution methods for designing the toll under various assumptions on the information availability. The effectiveness of the proposed tolling scheme is guaranteed by theoretically established estimates. Numerical experiments on several test networks demonstrate the effectiveness of the dynamic tolling mechanisms in improving the rapidity and the potential cost efficiency of the traffic systems.
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