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Uncertainties are unavoidable in engineering applications. A new model is proposed for designing networks under uncertainty of future demands. The objective is to minimize the total travel time budget required to satisfy the total travel time reliability constraint while considering the route choice behavior of network users. The model adopts the value-at-risk risk measure instead of the utility function to model planner risk preferences. It allows the planners to specify their risk preferences by using a confidence level of alpha on the total travel time reliability. This alpha reliable network design model is formulated as a stochastic bilevel optimization problem. The upper-level subprogram is a variant of the chance-constrained model that minimizes the total travel time budget subject to a chance constraint with a user-specified confidence level, a budget constraint, and design variable constraints; the lower-level subprogram …