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The continuous network design problem that occurs when the origindestination time-dependent demands are random variables with known probability distributions is described. A chance-constraint and two-stage linear programming formulation are introduced based on a system optimum dynamic traffic assignment model that propagates traffic according to the cell transmission model. The introduced approaches are limited to continuous link improvements and do not provide for new link additions. The chance-constrained model is tested on an example network that resembles a freeway corridor to demonstrate the simplicity and applicability of the approach. Initial results suggest that planning for an inflated demand may produce benefits in terms of system performance and reduced variance.