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An optimum selective transmission scheme for energy-limited sensor networks where sensors send or forward messages of different importance (priority) is developed. Considering the energy costs, the available battery, the message importance's and their statistical distribution, sensors decide whether to transmit or discard a message so that the importance sum of the effectively transmitted messages is maximized. It turns out that the optimal decision is made comparing the message importance with a time-variant threshold. Moreover, the gain of the selective transmission scheme, compared to a non-selective one, critically depends on the energy expenses, among other factors.
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