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Power consumption is an essentially important issue and an interesting challenge to prolong the lifetime of wireless sensor network (WSN). Sensors closer to a sink node have a larger forwarding traffic burden and consume more energy than nodes further away from the sink. The whole operational lifetime of WSN is deteriorated because of such an uneven node power consumption patterns, leading to what is known as an energy hole problem (EHP) around the sink node. In this article, we propose a novel power-saving scheme to alleviate the EHP based on the Min(N, T) policy M/G/1 queuing model. With little management cost, the proposed queue-based power-saving technique can be applied to prolong the lifetime of sensor network economically and effectively. For the proposed queue-based model, mathematical framework on performance measures have been formulated. And also we analyze the average traffic load per node for concentric sensor network. Focusing on the nodes located in the innermost shell of WSN, numerical and NS2 network simulation results validate that the proposed approach indeed provides a feasibly cost-effective approach for lifetime elongation of sensor networks.