Computation of multicommodity affine network equilibrium problem using iterative methods

Abstract

This paper concerns with solution schemes of a multi-commodity affine network equilibrium. Assuming existence of affine excess supply function for each node and affine shipping cost function for each link, this multicommodity affine network equilibrium problem (MANEP) is converted into a linear complementarity problem (LCP). This ICP can be solved by known complementary pivoting algorithms such as Lemke``s. Since it is likely that a MANEP be of large scale and special structure, however, iterative methods may be preferred. Iterative method for MANEPs are investigated with special emphasis on the block Gauss-Seidel iterative method which is based on the decomposition concept. Convergence properties including a sufficiency condition are also investigated. The potential application areas of these iterative methods are discussed and an illustrative example is given.