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We consider the problem of activity scheduling and area coverage in sensor networks, and especially focus on problems that arise when using a more realistic physical layer. Indeed, most of the previous work in this area has been studied within an ideal environment, where messages are always correctly received. In this paper, we argue that protocols developed with such an assumption can hardly provide satisfying results in a more realistic world. To show this, we replace the classic unit disk graph model by the lognormal shadowing one. The results show that either the resulting area coverage is not sufficient or the percentage of active nodes is very high. We thus present an original method, where a node decides to turn off when there exists in its vicinity a sufficiently reliable covering set of neighbors. We show that our solution is very efficient as it preserves area coverage while minimizing the quantity of active nodes.