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In wireless sensor networks, the sensors collect data and deliver it to a sink node. Most of the existing proposals deal with the traffic flow problem to deliver data to the sink node in an energy-efficient manner. In this paper, we extend this problem into a multi-sink case. To maximize network lifetime and to ensure fairness, we propose (i) how to position multiple sink nodes in a sensor network and (ii) how to route traffic flow from all of the sensors to these multiple sink nodes. Both of the problems are formulated by the linear programming model to find optimal locations of the multiple sink nodes and the optimal traffic flow rate of routing paths in wireless sensor networks. The improved lifetime and fairness of our scheme are compared with those of the multi-sink aware minimum depth tree scheme.