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

• Published in: IEEE transactions on wireless communications Vol. 21; no. 3; pp. 1751 - 1765
• Main Authors: Gong, Jie, Zhu, Jianhang, Chen, Xiang, Ma, Xiao
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Age; Age-of-information; Batteries; Cost analysis; Energy; Energy consumption; energy-age tradeoff; Internet of Things; Markov chains; Markov decision process; Markov processes; Monitoring; Sensor systems; Sensors; sleep mode; Thresholds; Tradeoffs; Wireless communication
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2021.3106395

Age-of-Information (AoI), or simply age, which measures the data freshness, is essential for real-time Internet-of-Things (IoT) applications. On the other hand, energy saving is urgently required by many energy-constrained IoT devices. This paper studies the energy-age tradeoff for status update from a sensor to a monitor over an error-prone channel. The sensor can sleep, sense and transmit a new update, or retransmit by considering both sensing energy and transmit energy. An infinite-horizon average cost problem is formulated as a Markov decision process (MDP) with the objective of minimizing the weighted sum of average AoI and average energy consumption. By solving the associated discounted cost problem and analyzing the Markov chain under the optimal policy, we prove that there exists a threshold optimal stationary policy with only 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 thresholds can be efficiently found by a line search. Numerical results show the performance of the optimal policies and the tradeoff curves with different parameters. Comparisons with the conventional policies show that considering sensing energy is of significant impact on the policy design, and introducing sleep mode greatly expands the tradeoff range.