By eliminating redundant data flows, data aggregation capabilities in wireless sensor networks could transmit less data to reduce the total energy consumption. However, additional data collisions incur extra data retransmissions. These data retransmissions not only increase the system energy consumption, but also increase link transmission delays. The decision of when and where to aggregate data depends on the trade-off between data aggregation and data retransmission. The challenges of this problem need to address the routing (layer 3) and the MAC layer retransmissions (layer 2) at the same time to identify energy-efficient data-aggregation routing assignments, and in the meantime to meet the delay QoS. In this paper, for the first time, we study this cross-layer design problem by using optimization-based heuristics. We first model this problem as a non-convex mathematical programming problem where the objective is to minimize the total energy consumption subject to the data aggregation tree and the delay QoS constraints. The objective function includes the energy in the transmission mode (data transmissions and data retransmissions) and the energy in the idle mode (to wait for data from downstream nodes in the data aggregation tree). The proposed solution approach is based on Lagrangean relaxation in conjunction with a number of optimization-based heuristics. From the computational experiments, it is shown that the proposed algorithm outperforms existing heuristics that do not take MAC layer retransmissions and the energy consumption in the idle mode into account.
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