Dynamic marginal cost, access control, and pollution charge: A comparison of bottleneck and whole link models

In this paper, we investigate theoretical constructions and properties of three interrelated travel demand management measures including marginal cost pricing, access control, and pollution charge under dynamic traffic assignment framework. For congested traffic networks modeled by the two vertical queue models, that is, the whole link model and the deterministic queuing model, on which flows are controlled, we derive dynamic marginal costs for paths and users' external costs for controlled links. As a strategy to implement the access control, the access pricing is formulated as a dynamic system optimal assignment with access (e.g., traffic volume, queue) control problem, wherein the access constraints represent the restrictions on the traffic volumes and/or environmental constraints. For the whole link model case, an optimal control problem formulation is adopted to investigate the dynamic traffic equilibrium. We derive and discuss the necessary condition for operating the transportation system with capacity/environmental constraints optimally. For the deterministic queuing model case, the inflow to a bottleneck is saturated such that no queue would be formed. The dynamic externalities of the two models are compared. It is found that different externality structures of the two models result in different tolling structures to achieve dynamic system optimal assignment. On the basis of this access pricing analysis and an "equivalent" environmental capacity that converts the environmental constraint into traffic volume restriction, we investigate the traffic-induced air pollution pricing scheme.