Maximizing Lifetime of Data-Gathering Trees with Different Aggregation Modes in WSNs

We study the problem of maximizing the network lifetime of a data-gathering tree in a wireless sensor network (WSN). Both data routing and data aggregation are considered at the same time to improve the energy efficiency for data collection in WSNs. With different data-aggregation methods, three aggregation modes are studied: full aggregation, non-aggregation, and a hybrid partial-aggregation using compressive sensing. The full aggregation means that an intermediate sensor node will aggregate all the received data from its children and its own generated data into one data unit and then send it to its parent. If no aggregation is used, an intermediate sensor node will forward all the received data units plus its own data separately. For the hybrid partial-aggregation, once the number of incoming data units is bigger than a compression threshold, they will be compressed into a constant size for transmission. For each mode, an exact solution based on mixed-integer linear programming (MIP) is proposed to find the optimal data-gathering tree with the maximum network lifetime. Although non-linear relations exist between the lifetime of a sensor node and the number of data units received or transmitted, we succeed to express it by a set of linear equations. The correctness of the MIP models is proven formally. Simulation results demonstrate that the network lifetime can be increased tenfold by changing the compression threshold from five to one, which is, however, at the expense of bigger end-to-end delay and lower data accuracy. Thus, this compression threshold should be properly chosen for real applications.