In this paper, the optimal data aggregation routing for maximizing the network lifetime in wireless sensor
networks(WSNs) is investigated. By analyzing network traffic and power consumption, a network flow model is proposed
for data aggregated WSNs. Maximum lifetime and network flow model are combined to design a group of mixed integer
programming cost function. The approximate optimal relay transmission rate and data aggregation routing are obtained by
utilizing the dual decomposition method. The simulation results show that the proposed algorithm can reduce data traffic,
balance energy consumption, and prolong the network lifetime effectively.