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Age-of-Information (AoI), or simply age, which measures the data freshness,is essential for real-time Internet-of-Things (IoT) applications. On the otherhand, energy saving is urgently required by many energy-constrained IoTdevices. This paper studies the energy-age tradeoff for status update from asensor to a monitor over an error-prone channel. The sensor can sleep, senseand transmit a new update, or retransmit by considering both sensing energy andtransmit energy. An infinite-horizon average cost problem is formulated as aMarkov decision process (MDP) with the objective of minimizing the weighted sumof average AoI and average energy consumption. By solving the associateddiscounted cost problem and analyzing the Markov chain under the optimalpolicy, we prove that there exists a threshold optimal stationary policy withonly two thresholds, i.e., one threshold on the AoI at the transmitter (AoIT)and the other on the AoI at the receiver (AoIR). Moreover, the two thresholdscan be efficiently found by a line search. Numerical results show theperformance of the optimal policies and the tradeoff curves with differentparameters. Comparisons with the conventional policies show that consideringsensing energy is of significant impact on the policy design, and introducingsleep mode greatly expands the tradeoff range.

Sleep, Sense or Transmit: Energy-Age Tradeoff for Status Update with Two-Thresholds Optimal Policy