A congestion-pricing problem with a polycentric region and multi-class users: a continuum modelling approach

Consider a region of arbitrary shape with multiple cities competing for multi-class users that are distributed continuously over the region. Within this region, the road network is represented as a continuum and users patronise in a two-dimensional continuum transportation system to their chosen city. A logit-type distribution function is specified to model the probabilistic destination choices made by the different classes of users. In this article, two different congestion-pricing models for this multi-class and multi-city continuum transportation system are studied. The first model focused on utility maximisation, which determines the optimal toll rates that maximise the total utility of the system, while the second model is a cordon-based congestion-pricing model that offers a sub-optimal but more practical tolling strategy. Both models are solved by finite element method and a promising Newtonian-based solution algorithm. A numerical example is given to show the effectiveness of the mathematical program and solution algorithm.

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