An Integrated Behavioral Model of Land Use and Transport System: A Hyper-network Equilibrium Approach

The interaction between the land use and transport in the urban context is a relevant issue in policy making. The connection between both systems arises since the former is causal of urban development while the latter is a consequence of it and significant contributor at the same time. One difficulty to unmask such interactions is to understand and determine the global system equilibrium, which is the matter of this paper. The households’ decisions, from their residential location to their travel and route choices, are described as a process of interdependent discrete choices that reflect the long term equilibrium. Consumers are assumed to optimize their combined residence and transport options, which are represented as a set of paths in an extended network that includes the transport system together with fictitious additional links that represents land use and location market. At equilibrium no household is better off by choosing a different option for residential location or by choosing a different set of trips’ destinations and routes. We study several alternative models starting from a simple case with fixed real estate supply and exogenous travel demand, to more complex situations with a real estate market, trip destination choices and variable trip frequencies. The equilibrium is characterized by an equivalent optimization problem which is strictly convex coercive and unconstrained. The optimality conditions for this optimization problem reproduce the transport equilibrium conditions as much as the land use equilibrium conditions. The approach provides a comprehensive characterization of the solution regarding existence and uniqueness, together with an algorithm to obtain the solution with well-defined convergence properties. The model is applicable to real size problems, with heterogeneous population and locations, as well as multiple trip purposes.