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Network lifetime is one of the most critical issues for wireless sensor networks (WSNs) since most sensors are equipped with non-rechargeable batteries with limited energy. To prolong the lifetime of a WSN, one common approach is to dynamically schedule sensors' active/sleep cycles (i.e., duty cycles) with sleep scheduling algorithm. In this paper, we propose a new sleep scheduling algorithm, named EC-CKN (Energy Consumed uniformly-Connected K-Neighborhood) algorithm, to prolong the network lifetime. The algorithm EC-CKN, which takes the nodes' residual energy information as the parameter to decide whether a node to be active or sleep, not only can achieve the k-connected neighborhoods problem, but also can assure the k awake neighbor nodes have more residual energy than other neighbor nodes at the current epoch. Based on the algorithm EC-CKN, we can obtain the state transition probability at the n'th epoch, and upper bound and lower bound of the network lifetime by Markov chain and Markov decision chain.