Transportation network policy modeling with goal targets and generalized penalty functions

In this paper the authors develop a transportation network policy model that determines the equilibrium flow pattern and the transportation link tolls or taxes/subsidies in the presence of imposed transportation goals on the links of the network. The penalties (and subsidies) are functions of the deviations from the targets. The governing equilibrium conditions are shown to satisfy a variational inequality problem and existence and uniqueness results are presented using this methodology. A decomposition algorithm is proposed that resolves the problem into series of traffic network equilibrium problems and two simpler subproblems. Convergence results are also given. Finally, the algorithm is applied to numerical examples that illustrate how the model can be utilized for transportation pricing policy, as well as the numerical performance of the algorithm. This work extends recent research in spatial market policy modeling with goal targets on bipartite networks and with fixed penalties.