Risk-neutral second best toll pricing

We propose a risk-neutral second best toll pricing (SBTP) scheme to account for the possible nonuniqueness of user equilibrium solutions. The scheme is designed to optimize for the expected objective value as the UE solution varies within the solution set. We show that such a risk-neutral scheme can be formulated as a stochastic program, which complements the traditional risk-prone SBTP approach and the risk-averse SBTP approach we developed recently. The proposed model can be solved by a simulation-based optimization algorithm that contains three major steps: characterization of the UE solution set, random sampling over the solution set, and a two-phase simulation optimization step. Numerical results illustrate that the proposed risk-neutral design scheme is less aggressive than the risk-prone scheme and less conservative than the risk-averse scheme, and may thus be more preferable from a toll designer’s point of view.

► User equilibrium problem may have nonunique solutions under certain conditions.
► Toll designers’ risk-taking behavior needs to be considered when multiple solutions exist.
► A stochastic program can be developed when the toll designer is risk-neutral.
► The stochastic program can be solved via a three-step algorithm.
► The risk-neutral scheme can be applied to both link-based and path-based formulations.