Structural Analysis of Specific Environmental Traffic Assignment Problems

The goal of this article is to develop a framework for Environmental Traffic Assignment (E-TAP); that is a methodology for allocating traffic flows on a road network with the objective of minimizing objective functions related to energy such as fuel consumption or traffic pollutants. We investigate the underlying minimization problem in E-TAP which we characterize and study for uniqueness. This study is accomplished by exploiting convexity properties of the developed environmental objective functions and obtaining parameter sets for which the objective functions are strictly convex. The considered minimization problem is framed along the well-known Wardrop principles to develop two cases: 1) a User Equilibrium (UE) case that assumes selfish-routing of individuals and 2) a Social Optimal (SO) case that obtains the minimized solution for the entire system. In case of the UE we show uniqueness of solutions. In case of SO numerical studies indicate convexity and thus uniqueness, however a rigorous proof is not developed. We present a case study application of E-TAP for the greater Los Angeles area and compare these results with time-based traffic assignment.