A regional economy, land use, and transportation model (relu-tran©):: Formulation, algorithm design, and testing

RELU is a dynamic general equilibrium model of a metropolitan economy and its land use, derived by unifying in a theoretically valid way, models developed by one of the authors [Anas (1982), Anas-Arnott (1991, 1997), Anas-Kim (1996), Anas-Xu (1999)]. RELU equilibrates floor space, land and labor markets, and the market for the products of industries, treating development (construction and demolition), spatial interindustry linkages, commuting, and discretionary travel. Mode choices and equilibrium congestion on the highway network are treated by unifying RELU with the TRAN algorithm of stochastic user equilibrium [Anas-Kim (1990)]. The RELU-TRAN algorithm's performance for a stationary state is demonstrated for a prototype consisting of 4-building, 4-industry, 4-labor-type, 15-land-use-zone, 68-link-highway-network version of the Chicago MSA. The algorithm solves 656 equations in a special block-recursive convergent procedure by iterations nested within loops and loops within cycles. Runs show excellent and smooth convergence from different starting points, so that the number of loops within successive cycles continually decreases. The tests also imply a numerically ascertained unique stationary equilibrium solution of the unified model for the calibrated parameters.