Power efficiency is a crucially important issue in the IEEE 802.15.4/ZigBee sensor networks (ZSNs) for majority of sensor nodes equipped with non-rechargeable batteries. To increase the lifetime of sensor networks, each node must optimize power consumption as possible. Among open literatures, much research works have focused on how to optimally increase the probability of sleeping states using multifarious wake-up strategies. Making things different, in this article, we propose a novel optimization framework for alleviating power consumption of sensor node with the D-policy M/G/1 queuing approach. Toward green sensor field, the proposed power-saving technique can be applied to prolong the lifetime of ZSN economically and effectively. For the proposed data aggregation model, mathematical framework on performance measures has been formulated. Data simulation using MATLAB tool has been conducted for exploring the feasibility of the proposed approach. And also we analyze the average traffic load per node for tree-based ZSN. Focusing on ZigBee routers deployed at the innermost shell of ZSN, network simulation results validate that the proposed approach indeed provides a feasibly cost-effective approach for prolonging lifetime of ZSNs.