A multi-class congestion-pricing problem in a continuum transportation system

Abstract

Consider a city of an arbitrary shape where difference classes of users are distributed continuously over the city region. Within this region, the road network is dense and can be represented as a continuum and users patronize a two-dimensional continuum transportation system to the central business district. In this paper, two different congestion-pricing models for this continuum transportation system with multiple user classes are studied. The first model is concerned about the social welfare maximization, which determines the optimal toll rates that maximize the total benefit of the whole system, and the second model is cordon-based congestion-pricing, which offers a sub-optimal but more practical tolling strategy. Both of these models are solved by the finite element method and a promising Newtonian-based solution algorithm. Finally, a numerical example is adopted for giving an idea on the impact of cordon toll charges on the resultant social welfare.