Modeling equilibria in integrated transportation-land use models
This research focuses on equilibrium modeling of integrated transportation-land use models (ITLUMs) based on spatial input-output (SIO) theory. First, it analyzes equilibria in the SIO model by studying sales prices“ and trade volumes“ solution existence and uniqueness. A fixed-point formulation is proposed for the uncongestible, random-utility-based multiregional input-output (RUBMRIO) model, which consists of a set of model equations. Under weak conditions regarding sales prices, the set of price solutions is shown to exist. And these are unique under sufficiently small dispersion parameters. Price solutions uniqueness is also discussed under more general conditions which permit much larger dispersion parameter values. Once prices are known, commodity flows are found to be unique. The fixed-point formulation established here verifies that the common/original RUBMRIO iterative algorithm converges almost surely, regardless of the initial values. However, a modified algorithm is demonstrated to be more efficient. Second, the dissertation examines two methods to approach the overall equilibria of a full, congestible ITLUM based on the RUBMRIO model. First, a combined model is constructed which synthesizes all the ITLUM components including location choices, travel frequencies choices, mode choices, and route choices. The optimization conditions are derived, and they can be assembled to show the equivalence of the combined model to these component choice models. The uniqueness of equilibrium solution is also discussed. Evans“ algorithm is proposed to solve this combined model. Second, a ”linked„ model is assembled using two feedback strategies: the first uses a single loop; the second implements an additional internal loop. A numerical example for the Dallas-Fort Worth network suggests that both feedback methods converge to the unique solution; but the second one, with double loops, converges more efficiently. In summary, the two methods developed here are of theoretical interest and practical application.