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Coverage is one of the key issues to achieve energy efficiency of a wireless sensor network. Sensor scheduling is one of the most important methods to solve coverage problems. It can ensure the coverage degree of a region and prolong the network lifetime. In this paper, we focus on the k -coverage scheduling problem to guarantee k -coverage sensing and network connectivity. We consider both deterministic and stochastic sensing models of the sensors and adapt the results of deterministic sensing model to solve the sensor scheduling problem under the stochastic sensing model. We use regular pentagons to divide the sensing disks to solve the k -coverage problem. Each sensor node runs a stochastic k -coverage-preserving scheduling algorithm to determine its work modes, and redundant nodes can enter into sleep mode, while active nodes ensure the coverage of the network. Theoretical analysis and simulation results show that our algorithm can reduce the number of active nodes and extend the network lifetime significantly while maintaining a given coverage degree. [ABSTRACT FROM AUTHOR]