Optimized network equilibrium models of combined travel and residential location choices

Abstract

This dissertation derives two network equilibrium models of combined travel and residential location choices. The first combined model is formulated based on the user-optimized network equilibrium principle. The second combined model is derived based on the stochastic user equilibrium principle. The study starts with the review of research work related to the combined urban transportation and location modeling and moves on to analyze the network equilibrium principles, the modeling theories, and formulation approaches for solving the user-optimized network equilibrium assignment problem. Given this background information, a combined travel and residential location choice model (CTRLUE) is developed based on a disaggregated residential allocation model (DRAM) together with the user-optimized trip assignment model so that the choices of both travel and residential location can be predicted simultaneously. Then the emphasis is placed on analysis of the functions and characteristics of the combined model. We establish the theorem of equivalence to demonstrate that the CTRLUE model which is represented by the system equations can be formulated as an equivalent convex programming problem with linear constraints. We also prove the equilibrium solution to the problem is unique and at an optimal solution point the Karush-Kuhn-Tucker conditions exist. Furthermore, the theorem of sensitivity is proved based on in depth analysis of the properties of the programming problem. After establishing a set of theorems, in accordance with a more realistic travel behavior assumption, another combined travel and residential location model (CTRLSUE) incorporating the stochastic network equilibrium route choice function is proposed and its equivalent mathematical programming problem is derived. The corollaries of convexity, existence, uniqueness, positivity, equivalence, and sensitivity are established. The maximum likelihood method and the gradient search algorithm are utilized to estimate model parameters. The computation procedures based on either the convex combinations algorithm or the Evans algorithm are presented. In addition, the model specification and the iterative computation processes for implementation of the combined models are discussed. Finally, the suggestions for further research are proposed.