Emission modeling and pricing on single-destination dynamic traffic networks

•This research studies first-best dynamic emission pricing problem in a traffic network.•The emission pricing framework aims to solve two sub-problems.•The first sub-problem must have a free flow solution, if exists and the emission function is monotonic.•Monotonicity properties of emission functions are crucial for network-wide emission pricing.•Free flow solutions offer new perspectives for network-wide emission pricing.

This paper proposes an emission pricing model for single-destination dynamic traffic networks. The model contains two sub-models derived from the corresponding two sub-problems: a system optimum dynamic traffic assignment problem and a first-best dynamic emission pricing scheme. For the first problem, it proves that under certain conditions, an optimal solution, if exists, must be a free-flow solution to minimize the generalized system cost including the costs of total travel times and total emissions (or fuel consumption). The optimal first-best emission pricing can then be determined by solving an optimal control problem, using the free-flow dynamic system optimal solution as the input. Numerical results are provided to illustrate the proposed models and the solution methods.