Traffic network equilibrium problems with capacity constraints of arcs and linear scalarization methods (Q1952898)

Summary: Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of \textit{Zh. Lin} [Nonlinear Anal., Real World Appl. 11, No. 4, 2280--2284 (2010; Zbl 1198.90085)], and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.