Maximum lifetime convergecast tree in wireless sensor networks

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.