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Recent studies demonstrate the importance of computational precision of user equilibrium traffic assignment so- lutions for scenario comparisons. When traffic assignment is hierarchically embedded in a model for network design and/or road pricing, not only the precision of the solution itself becomes more important, but also the precision of its derivatives with respect to the design parameters should be considered.

The main purpose of this paper is to present a method for precise computations of equilibrium derivatives. Numeri- cal experiments on a small network are used for two evaluations: 1. precision of computed equilibrium derivatives; and 2. the impact of precise derivatives on the quality of network design solutions.