We study the problem of building a maximum lifetime data collection tree for periodic convergecast applications in wireless sensor networks. We experimentally observe that if two nodes transmit the same number of data packets, the amount of energy consumption of the nodes is approximately the same even if the payload lengths of the transmitted packets are different. This is because the major energy consumption during a packet transmission arises from radio start-up and medium access control overhead. Our formulated lifetime maximization problem captures the energy expenditure due to message transmissions/ receptions in terms of the number of data packets transmitted/ received, in contrast to prior works, which consider the number of data units (amount of sensor data generated by a node) transmitted/ received. Variable transmission power levels of the radio and accounting for the sensor energy consumption are other factors that make our problem formulation different from those in prior work. We prove that this problem is NP-complete by reducing the set cover problem to it and propose an algorithm to solve it. The performance of the proposed algorithm is experimentally evaluated using Jain’s fairness index as a metric by implementing it on an actual testbed consisting of 20 sensor nodes and compared with those of the widely used shortest path tree and random data collection tree algorithms. The energy consumption of different nodes under the proposed algorithm are shown to be more balanced than under the shortest path tree and random data collection tree algorithms. Also, the performance of the proposed algorithm in large networks is studied through simulations and is compared with those of the state-of-the-art RaSMaLai algorithm, directed acyclic graph algorithm and clustering based OPTIC algorithm, and the shortest path tree, minimum spanning tree, and random tree based data collection schemes. Our simulations show that the proposed algorithm provides a significantly higher network lifetime compared to all the other considered data collection approaches.

我们研究了为无线传感器网络中的周期性聚合广播应用构建最大生命周期数据收集树的问题。我们通过实验观察到，如果两个节点传输相同数量的数据包，即使传输的数据包的有效载荷长度不同，节点的能量消耗量也大致相同。这是因为数据包传输期间的主要能量消耗来自无线电启动和媒体访问控制开销。我们制定的生命周期最大化问题根据发送/接收的数据包的数量来捕获由于消息发送/接收引起的能量消耗，与考虑数据单元数量的先前工作相反（节点生成的传感器数据量）传输/接收。无线电的可变传输功率水平和考虑传感器能耗是使我们的问题表述与先前工作不同的其他因素。我们通过将集合覆盖问题归约来证明这个问题是 NP 完全的，并提出了一种算法来解决它。通过在由 20 个传感器节点组成的实际测试平台上实现该算法，并与广泛使用的最短路径树和随机数据收集树算法的性能进行比较，使用 Jain 的公平性指数作为度量对该算法的性能进行了实验评估。与最短路径树和随机数据收集树算法相比，所提出算法下不同节点的能量消耗更加均衡。还，通过仿真研究了该算法在大型网络中的性能，并与最先进的 RaSMaLai 算法、有向无环图算法和基于聚类的 OPTIC 算法以及最短路径树、最小生成树、和基于随机树的数据收集方案。我们的模拟表明，与所有其他考虑的数据收集方法相比，所提出的算法提供了明显更高的网络寿命。