Scenarios where nodes have limited energy and forward messages of different importances (priorities) are frequent in the context of wireless sensor networks.Tailored to those scenarios, this paper relies on stochastic tools to develop selective message forwarding schemes. The schemes will depend on parameters such as the available battery at the node, the energy cost of retransmitting a message, or the importance of messages. The forwarding schemes are designed for three different cases: 1) when sensors maximize the importance of their own transmitted messages; 2) when sensors maximize the importance of messages that have been successfully retransmitted by at least one of its neighbors; and 3) when sensors maximize the importance of messages that successfully arrive to the sink. More sophisticated schemes will achieve better importance performance, but will also require information from other sensors. The results contribute to identify the variables that, when made available to other nodes, have a greater impact on the overall network performance. Suboptimal schemes that rely on local estimation algorithms and entail reduced computational cost are also designed.
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