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

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 lin (2010),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. © 2012 x. q. tian and y. d. xu.