Stability of traffic dynamics in the implementation of road pricing

Implementing road pricing disturbs the existing user equilibrium. In response, the traffic evolves in a dynamical way so as to approach a new equilibrium. However, there is no guarantee that the traffic flow dynamics would always arrive at the new equilibrium. In particular, the new equilibrium cannot be attained if it is dynamically unstable. This paper first shows with an example where such instability and unattainability can occur, followed by a systematic examination on the imbalance and resulting flow dynamics introduced by the implementation of road pricing. This paper then shows a possible solution to achieve stability is through sequential implementation of road pricing, shedding light on how road pricing may be implemented.