A continuous traffic equilibrium model with multiple user classes

Abstract

We consider a city with several facilities that compete with each other for customers of different classes. The transportation system of the city is a highly dense road network. The customers are distributed continuously in the city, and each chooses a facility based on his or her transportation cost to the facility and the in-situ cost at the facility. We assume that different classes of users perceive costs differently, and hence are subject to different transportation cost functions and market externalities. An equivalent mathematical model is formulated and proved to satisfy the user equilibrium conditions. The resultant problem is solved by the finite element method. Numerical examples for both cases of fixed and elastic demand are given to illustrate the effectiveness of the proposed methodology.