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

TL;DR

This paper investigates the energy-age tradeoff in IoT status updates, proposing a two-threshold optimal policy that balances data freshness and energy consumption, with significant improvements over conventional policies.

Contribution

It introduces a novel two-threshold policy for minimizing a weighted sum of AoI and energy, considering sensing and sleep modes in IoT devices.

Findings

Optimal policy is a two-threshold stationary policy.

Sleep mode significantly expands the energy-age tradeoff range.

Considering sensing energy impacts policy design and performance.

Abstract

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.