Minimizing Age of Information for an Energy Harvesting Source with Updating Failures

Abstract

Consider an energy harvesting (EH) sensor that continuously monitors a system and sends time-stamped status update to a destination. The sensor harvests energy from nature and uses it to power its updating operations. The destination keeps track of the system status through the successfully received updates. With the recently introduced information freshness metric "Age of Information" (AoI), our objective is to design optimal online status updating policy to minimize the long-term average AoI at the destination, subject to the energy causality constraint at the sensor. Due to the noisy channel between the sensor and the destination, each transmitted update may be erased with a fixed probability, and the AoI at the destination will be reset to zero only when an update is successfully received. We first consider status updating without feedback available to the sensor and show that the Best-effort Uniform updating (BU) policy is optimal in a broadly defined class of online policies. We then investigate status updating with perfect feedback to the sensor and prove similar optimality of the Best-effort Uniform updating with Retransmission (BUR) policy. In order to prove the optimality of the proposed policies, for each case, we first identify a lower bound on the long-term average AoI among a broad class of online policies, and then construct a sequence of virtual policies to approach the lower bound asymptotically. Since those virtual policies are sub-optimal to the original policy, the original policy is thus optimal.

Optimal status updating with a finite-battery energy harvesting source

“…where Pr(E = 0) = 1, E X 2 | E = 0 = τ 2 1 + ( 2 µ 2 H + 2 µH τ 1 )e −µH τ1 and E [X | E = 0] = τ 1 + 1 µH e −µH τ1 . Accordingly,∆ is given by (13). By Theorem 3, τ * 1 =∆ π * and combining this with (13)…”

Using Erasure Feedback for Online Timely Updating with an Energy Harvesting Sensor

“…4, we plot the long term average AoI λ * versus the erasure probability q. We also plot the optimal threshold λ * − q 1−q , and compare the results with that of the infinite battery case, derived in [25] to be 1 2 (1−q) . We see that the AoI increases with q, which is quite expected.…”

“…Of particular interest, are those pertaining to energy harvesting communications [15]- [26], in which age-minimal energy management schemes are designed. The most closely related works to this one are [25], [26], in which updates are transmitted through an erasure channel, with [25] focusing on infinite battery sensors with and without erasure status feedback, and [26] focusing on unit-sized battery sensors without feedback. We note that [16] also considers the problem without feedback, cast as an MDP, yet in a discrete time setting.…”

Optimal Transmission Policies for Energy Harvesting Age of Information Systems with Battery Recovery

“…On the other hand, between t ∈ [8,9], both the harvested and recovered units of energy are stored in the battery. Finally, recovery opportunities are missed between t ∈ [5,7], [9,10] because of the probabilistic recovery model.…”

“…Energy harvesting information update systems has been studied in the AoI literature for various scenarios [4]- [10]. References [7]- [9] investigate the optimal scheduling policies to minimize average AoI under transmission errors whereas the same metric is used in [4], [6], [10] for error-free channel. The study in [5] aims to identify the achievable average message rate and AoI for an energy harvesting AoI system.…”