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This paper studies the problem of energy consumption minimization in wireless sensor networks (WSNs) under uncertainty in sensor node generated traffic. It is important to consider traffic uncertainty because WSNs designed for surveillance and monitoring applications typically operate in event-driven and query-driven modes for which the node generated traffic changes from instant to instant. The problem is formulated as a two-stage stochastic linear program with recourse where the objective is to minimize the sum of the energy cost expended on the carried traffic and the average energy cost of blocked traffic, under the constraint of a fixed energy budget at each node. The stochastic programming formulation lends to the consideration of two approaches for handling the randomly generated traffic: a deterministic approach in which all future generated random traffic are constrained by the link flows determined for the nominal traffic, and a stochastic approach where the link flows are adapted as the node generated traffic changes. Numerical results show that, compared to the deterministic approach, the stochastic approach provides up to 10% savings in network-level energy consumption and this is achieved without a loss in received data quality. The network-level energy savings translate to a prolonged network lifetime.