A multimodal traffic network equilibrium model with emission pollution permits: Compliance vs noncompliance

In this paper, we develop a multimodal traffic network equilibrium model with vehicular emission pollution permits using the theory of variational inequalities. We consider both the case of compliance in which travelers emit pollutants no more than that mandated by their license holdings and that of non-compliance. In the former case, we prove that environmental standards imposed by the authorities are met provided that the initial license allocation meets the environmental target. For the latter model, we establish a penalty scheme that guarantees that there will be no nonconcompliant behavior. Qualitative analysis of the model is conducted and existence and uniqueness results of the solution are obtained. An algorithm is proposed, with convergence results, to compute the multimodal equilibrium link load, travel demand, marginal cost of emission abatement, emission underflow, overflow, license, and license price pattern. The algorithm is then applied to several numerical examples.