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To prolong the lifetime of sensor nodes, most research works have focused on how to tune the duty cycling schemes among nodes to save the communication cost using multifarious wake-up strategies. To this aim, we propose a novel design strategy for mitigating average power consumption of sensor node using the Min(N, T) policy M/G/1 queuing theory. There is a heavy overhead for packet collisions and channel contention resulting from restarting the process of medium contention. The basic point of our approach is that Min(N, T) dyadic policy would mitigate the total average times of medium contention by having both a counter (N) and a timer (T) for the control of triggering on a radio server to transmit queued packets, and then power consumption of communication can be alleviated. We show how the improvement level on power consumption can be achieved through analytical and simulated results. To meet the mission requirements in sensor networks, the proposed add-on power saving technique can also provide a design framework for the sensor network manager to optimize relevant system parameters including power consumption and latency delay.