Obtaining Network Cost(s) from One Link's Output

Consider user-optimization on a directed network whose link costs remain unevaluated, but are assumed to be positive affine symmetric functions of link flows. We focus instead on the equilibrium output variations, locally, of one arbitrary link resulting from variations in either its intrinsic cost or in the demand of the Origin/Destination pair under consideration. With only this local information as output, our algorithm generates, for that particular O/D-pair, the user equilibrium cost as a complete (piecewise-linear) function of O/D-demand, from any one initiating segment: such a segment may be obtained by an independent decomposition procedure.