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To boost energy saving for the general delay-tolerant IoT networks, a two-stage, and single-relay queueing communication scheme is investigated. Concretely, a traffic-aware N-threshold and gated-service policy are applied at the relay. As two fundamental and significant performance metrics, the mean waiting time and long-term expected power consumption are explicitly derived and related with the queueing and service parameters, such as packet arrival rate, service threshold and channel statistics. Besides, we take into account the electrical circuit energy consumptions when the relay server and access point (AP) are in different modes and energy costs for mode transitions, whereby the power consumption model is more practical. The expected power minimization problem under the mean waiting time constraint is formulated. Tight closed-form bounds are adopted to obtain tractable analytical formulae with …