Traffic network equilibrium problems with demands uncertainty and capacity constraints of arcs by scalarization approaches

This paper focuses on the vector traffic network equilibrium problem with demands uncertainty and capacity constraints of arcs, in which, the demands are not exactly known and assumed as a discrete set that contains finite scenarios. For different scenario, the demand may be changed, which seems much more reasonable in practical programming. By using the linear scalarization method, we introduce several definitions of parametric equilibrium flows and reveal their mutual relations. Meanwhile, the relationships between the scalar variational inequality as well as the (weak) vector equilibrium flows are explored, meanwhile, some necessary and sufficient conditions that ensure the (weak) vector equilibrium flows are also considered. Additionally, by means of nonlinear scalarization functionals, two kinds of equilibrium principles are derived. All of the derived conclusions contain the demands uncertainty and capacity constraints of arcs, thus the results proposed in this paper improved some existing works. Finally, some numerical examples are employed to show the merits of the improved conclusions.