Cordon-based congestion pricing in a continuum traffic equilibrium system

This paper presents an application of the continuum traffic equilibrium model for the cordon-based congestion pricing problem. The traffic equilibrium model treats densely spaced roads as a continuum over which commuters are continuously dispersed. Suppose in the morning peak-hour, all commuters travel to the central business district (CBD) by taking their individual shortest routes. Their user-optimal route choice behavior, with or without toll pricing, can be formulated as a calculus of variations problem and solved efficiently by the modern finite element method. By plotting the numerical results in a two-dimensional space in the form of contour lines of travel cost to the CBD, one can intuitively identify the level of congestion and the external cost anywhere in the city. Hence, the continuum model and two-dimensional numerical representation allow a traffic planner to select easily one or multiple toll cordon(s) in the city and evaluate the impact of cordon toll charges on the resultant social welfare and user benefits.