Regional Air Quality Conformity in Transportation Networks with Stochastic Dependencies: A Theoretical Copula-Based Model

Abstract

The air quality levels in various regions around the world remain a large public concern. Transportation is known to be a major contributor to reduced air quality levels. Until now, the modeling of the regional impact of transportation on air quality has been based on the assumption of determinism. On the other hand, it is well recognized that transportation systems are subject to both demand and supply uncertainties. In this paper, we relax the assumption of determinism and allow for capacity and link flow uncertainty. We introduce a probability measure – coined the conformity probability – to capture the full probabilistic behavior of vehicular emissions. Moreover, stochastic dependencies are modeled using copulas, generalizing other commonly used dependence modeling techniques in the transportation network modeling arena. In a case study we demonstrate that such a generalization is critical as the ranking of capacity expansion projects to improve air quality is shown to be dependent on the hypothesized dependence structure. Finally, we present some preliminary results that suggest that capacity uncertainty is more detrimental to the environment (i.e. leads to lower conformity probabilities) than demand uncertainty.