Variational inequality formulation of the system-optimal travel choice problem and efficient congestion tolls for a general transportation network with multiple time periods

This paper examines the problem of optimal congestion pricing for a general transportation network with multiple time periods. Traditional optimization formulations of a system-optimal travel choice problem are reviewed and their limitations are discussed. A variational inequality formulation of the system-optimal problem is presented and efficient congestion tolls are calculated. This formulation is a generalization of the traditional optimization formulation with the symmetry condition. A numerical example is provided to interpret further the relationship between the variational inequality and the optimization formulations.