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This paper describes a robust optimization approach for a network design problem explicitly incorporating traffic dynamics and demand uncertainty. In particular, we consider a cell transmission model based network design problem of the linear programming type and use box uncertainty sets to characterize the demand uncertainty. The major contribution of this paper is to formulate such a robust network design problem as a tractable linear programming model and demonstrate the model robustness by comparing its solution performance with the nominal solution from the corresponding deterministic model. The results of the numerical experiments justify the modeling advantage of the robust optimization approach and provide useful managerial insights for enacting capacity expansion policies under demand uncertainty.