Bilevel dynamic continuum model for housing allocation and transportation emission problems in an urban city

In this study, we examine housing allocation and transportation emission problems in an urban city. Housing development patterns have a significant influence on travel behavior and related transportation emissions. We consider a hypothetical city with one central business district in which the road network is assumed to be sufficiently dense to be viewed as a continuum. We establish a bilevel dynamic continuum model to describe the relationships among housing provision, the transportation system, and traffic-related emissions. In the lower-level subprogram, housing allocation is considered in a simultaneous departure time and route-choice dynamic traffic user equilibrium model, in which travelers choose routes and departure times that satisfy dynamic user-optimal principles. In the upper-level subprogram, the total emissions are minimized by optimizing the housing allocation. The finite-volume method, the projection method, the method of successive averages, and the Frank-Wolfe method are applied to solve the presented model based on unstructured meshes. A numerical experiment for an urban area with one central business district is given to demonstrate the effectiveness of the model and the numerical algorithm.