  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 less computational complexity. The optimal energy-saving service threshold
that can flexibly adjust to packet arrival rate is determined. In addition,
numerical results reveal that: 1) sacrificing the mean waiting time not
necessarily facilitates power savings; 2) a higher arrival rate leads to a
greater optimal service threshold; and 3) our policy performs better than the
current state-of-the-art.
