On Binary Mode Choice/Assignment Models

We consider the two mode equilibrium road and transit assignment model which incorporates a zonal aggregate mode choice model. We reformulate this special structure network equilibrium model as a variational inequality and demonstrate that the origin to destination demands and travel costs, link flows and link travel costs are unique when appropriate sufficient conditions are satisfied. Then we demonstrate the existence of equivalent optimization formulations of special versions of this problem and study sufficient conditions for the convergence of diagonalization methods that are used to obtain solutions for this model.