In this paper, first, the traffic problem is studied from the Finsler geometric point of view and it is shown that the related metric is a Finsler metric of Randers type. Therefore, the time optimal paths of traffic problem are geodesics of this Randers metric. A real example is given by using the Maple program. Then a nonlinear complementary problem for traffic equilibrium problem is studied and it is shown that a Randers metric can be considered as a gap function in the nonlinear complementarity problem. Next, we extend the nonlinear complementarity problem of traffic equilibrium for a dynamical network. These results may be used in the different equilibrium problems.