A convex approach to traffic assignment problem under air quality constraints for planning purposes

This paper presents a convex optimization approach to the traffic assignment problem under air quality constraints for planning purposes. First, an optimization problem is formulated. The total travel time is used to represent the travel cost, and CO concentration is selected to evaluate the air quality. A coefficient is developed to describe the geometric characteristic from the emission source to the dispersion target. The regression analysis is conducted to model the emission rate with respect to the traffic volume, so that emission concentration consideration could be formulated as a linear function of volume. The case study is conducted on an abstraction from the network in College Station, Texas, involving 14 links and 30 Origin-Destination (O-D) pairs. In this case study, the optimization problem with 74 decision variables can be solved within a few seconds. The short computation time indicates the feasibility of applying the proposed approach to a large scale network for planning purposes. In addition, the tradeoff between travel cost and air quality is examined. The results demonstrate that with this traffic assignment approach air quality can be improved without causing much worsening of conventional operation performance measures: a 16.7% reduction of the emission concentration only leads to a 1.5% increase of total travel time.