A reduction method for local sensitivity analyses of network equilibrium arc flows

A reduction method is proposed which allows standard sensitivity techniques for variational inequalities to applied to equilibrium network flow proble ms without additional assumptions on either the underlying network or the n umbers of active paths. In particular it is shown that under mild regularit y conditions, small perturbations of equilibria can be given an explicit ar e-flow representation which is free of path-flow variables. It is also show n that this reduced form allows the differentiability of perturbations to b e studied by standard methods. These results are illustrated by a small num erical example. (C) 1999 Elsevier Science Ltd. All rights reserved.