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We present a stochastic traffic engineering framework for optimizing bandwidth provisioning and route selection in networks. The objective is to maximize revenue from serving demands, which are uncertain and specified by probability distributions. We consider heterogenous demands with different unit revenues and uncertainties. Based on mean-risk analysis, the optimization model enables a carrier to maximize mean revenue and contain the risk that the revenue falls below an acceptable level. Our framework is intended for off-line traffic engineering design, which takes a centralized view of network topology, link capacity, and demand. We obtain conditions under which the optimization problem is an instance of convex programming and therefore efficiently solvable. We also study the properties of the solution and show that it asymptotically meets the stochastic efficiency criterion. We derive properties of the optimal solution for the special case of Gaussian distributions of demands. We focus on the impact of demand uncertainty on various aspects of traffic engineering, such as link utilization, bandwidth provisioning and total revenue. The carrier's tolerance to risk is shown to have a strong influence on traffic engineering and revenue management decisions. We develop the efficient frontier, which is the entire set of Pareto optimal pairs of mean revenue and revenue risk, to aid the carrier in selecting an appropriate operating point.