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One of the major sources of energy waste in wireless sensor networks (WSNs) is idle listening, that is, the cost of actively listening for potential packets. This article focuses on reducing idle-listening time via a dynamic duty-cycling technique which aims at optimizing the sleep interval between consecutive wake-ups. We considered a receiver-initiated MAC method for WSNs in which the sender waits for a beacon signal from the receiver before starting to transmit. Since each sender receives beacon signals from several nodes, the data are routed on multiple paths in a data collection network. In this context, we propose an optimization framework for minimizing the energy waste of the most power-hungry node of the network. To this aim, we first derive an analytic model that predicts nodes' energy consumption. Then, we use the model to derive a distributed optimization technique. Simulation results via NS-2 simulator are included to illustrate the accuracy of the model, and numerical results assess the validity of the proposed scheme.