中文摘要：

传感器网络由大量能量有限的微型传感器节点组成．因此，如何保证在足够覆盖监测区域的同时延长网络的寿命，是一个需要解决的重要问题．为了达到这一目标，一种广泛采用的策略是选出部分能够足够覆盖监测区域的节点作为工作节点，同时关闭其他冗余节点．提出了一个数学模型，使得只要已知监测范围扣节点感知半径的比值，就可以计算出达到服务质量期望所需要的节点数量．需要指出的是：与大部分研究覆盖的文献不同，该研究不基于节点的位置信息，因此可以极大地降低硬件成本，并且减少节点获得和维护位置信息的开销．模拟实验结果表明：在随机部署条件下。服务质量期望与实验所得到的实际覆盖度的误差不大于服务质量期望的2％；而对于相同的服务质量期望和实际覆盖度，计算所得的工作节点数量与实验所得的工作节点数量的误差小于计算数量的5％，这表明推导出的节点数量与服务质量期望之间的关系与模拟实验的结果相吻合．该结果可以广泛应用于传感器网络的节点部署、拓扑控制等领域中．

英文摘要：

Since wireless sensor networks consist of a large number of tiny sensors with limited power supply, it becomes a major concern that how to extend sensor network lifetime and maintain sufficient sensing area at the same time. To achieve this goal, a broadly used strategy is to select some sensor nodes as working nodes to cover the deployment area and at the same time turn off redundant nodes. This paper proposes a mathematical model in which only if the proportion of the sensing range of nodes to the range of the deployment area is known, the number of the nodes needed to reach the expected coverage fraction can be calculated. This work is different from the most literature studying the coverage problem because it is not based on location information of sensor nodes, and thus the cost of hardware and the energy consumption on sensor nodes for deriving and maintaining location information can be considerably reduced. The simulated experiment suggests that in random deployment strategy, the error between the expected coverage fraction and the coverage fraction derived from the simulated experiment is no larger than 2% of the expected coverage fraction; when the expected coverage fraction and the coverage fraction derived from the simulated experiment is the same, the error between the number of working nodes derived from the calculation and the number of working nodes derived from the simulated experiment is less than 5% of the number derived from the calculation. It suggests that the results are identical to the experimental results. The analytical results in this paper can be widely adopted in handling sensor deployment, topology control, and other issues.