38 - A Combined Model of Housing Location and Traffic Equilibrium Problems in a Continuous Transportation System

Abstract

This paper introduces a combined housing location and traffic equilibrium problem in a continuous transportation system. The main objective has been to study the effects of congestion externality and housing rent in the disutility function on the choice of housing location in a city. Two models are formulated to address the problem. The first model is developed for a circular city with angular symmetrical properties, in which the problem is specified as an IVP for a system of ODEs, and specially designed but effective hierarchical line search (HLS) scheme is used to solve the problem. The solution properties of this model are thoroughly investigated, and form the basis of the development of the second model, which is a generalized model for a city of arbitrary shape that does not have symmetrical properties. The formulation of the generalized model is based on the Galerkin method in the weighted residual technique and the finite element method (FEM). The problem is solved by the Newton-Raphson algorithm with a line search. Two numerical examples are used to demonstrate the effectiveness of the methodology. The first example is an angular symmetrical circular city, to which both the HLS and FEM are applied, with identical solutions being obtained. The second example is of arbitrary shape, which shows the effectiveness of the generalized model in addressing the problem of irregular geometry and unsymmetrical propertied in practice. Future research will include the evaluation of the economic aspects of the housing location problem, the formulation of a bi-level problem that maximizes the social benefit of housing distribution, and the investigation of polycentric urban forms.