Stanková, K., Bliemer, M.C.J., and Olsder, G.J. Dynamic road pricing with traffic-flow dependent tolling, pp. 1-17. In Proceedings of the 87th Annual Meeting of the Transportation Research Board, January 13-17. At: Washington, D.C., USA, 2008.
In this paper the dynamic optimal toll design problem as a game of the Stackelberg type is investigated, with the road authority as a leader and drivers of the road network as followers. The road authority sets tolls on some links in the network such as to minimize total travel time of the system, while in each time instance the travelers choose their routes so as to minimize their own perceived travel costs. We assume that only a proper subset of the set of links can be tolled (second-best tolling). Two types of problems are studied: The ``classical'' Stackelberg game with the road authority imposing a constant or time-varying toll and, as a true extension, the so-called ``inverse Stackelberg game'' with the road authority setting toll as a function of traffic flows in the network. In both situations the drivers are assumed to choose their routes in accordance with the dynamic logit-based stochastic user equilibrium. We formulate the dynamic optimal toll design problem with flow-dependent second-best tolling and present a solution algorithm. This algorithm will be applied in a small case study, where the tolls are affine functions of link traffic densities on tolled links. Even with this rather simple tolling one can improve the system performance remarkably. The results of flow-dependent tolling (Inverse Stackelberg) can never be worse than those of the tolling independent of traffic flow (Stackelberg). In some situations the optimal second-best flow-dependent toll can be decreasing with traffic flow. This phenomena will be discussed as well.