Core Concepts
The authors analyze the age of information (AoI) in a scenario where energy-harvesting devices send status updates to a gateway following the slotted ALOHA protocol and receive no feedback. They derive analytical expressions for the average AoI and age-violation probability, and provide accurate and easy-to-compute approximations.
Abstract
The authors investigate the age of information (AoI) in a scenario where energy-harvesting devices send status updates to a gateway following the slotted ALOHA protocol and receive no feedback. They model energy harvesting as an independent Bernoulli process, where each device harvests an energy unit in a slot with a given probability. Upon receiving a new sensor reading, a device with a certain battery level transmits the update using a portion of its available energy with a given probability.
The authors derive analytical expressions for the average AoI and age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold. However, the numerical evaluation of these exact expressions is infeasible due to high complexity. To address this, the authors propose an approximate analysis that ignores the time dependency of the battery profile of the devices whose performance is not tracked. This simplification allows them to derive closed-form approximations of the AoI metrics that are accurate and easy to compute.
The authors conduct numerical experiments where the updates are sent over an additive white Gaussian noise (AWGN) channel. They consider two baseline strategies: transmit a new update whenever possible (BEU) to exploit every opportunity to reduce the AoI, and transmit only with full battery (TFB) to increase the chance of successful decoding. The authors show that an optimized strategy significantly outperforms both baselines in terms of the AoI metrics and throughput, for both decoding-with-capture and decoding-without-capture cases.
Without capture, the benefit of transmitting with high power vanishes as the power grows large because the successful decoding probability becomes limited by collision. Therefore, the devices should put aside some energy for later transmissions. On the contrary, with capture, the devices should transmit with either high or moderate energy, because this facilitates successive interference cancellation (SIC). Decoding with capture outperforms decoding without capture for the optimized strategy.
The authors also show that a high energy harvesting rate can increase the average AoI and AVP. In this case, the devices often have enough energy and transmit regardless of the obtainable AoI reduction, leading to many transmissions that cause collisions and, even if successful, result in a small AoI reduction. This issue can be resolved by progressively increasing the transmission probability after each transmission, which prioritizes updates that reduce the AoI value considerably if successfully delivered.
Stats
The average throughput is given by T = αU ΣE
b=0 νb Σb
bt=0 πb,bt ¯
ωbt.
The average AoI is given by ¯
Δ = 1 + E[Y^2] / (2E[Y]).
The age-violation probability is given by ζ(θ) = 1 - (1/E[Y]) * (Σ^(θ-1)
y=1 y P[Y=y] + (θ-1) P[Y>θ-1]).
Quotes
"The authors derive analytical expressions for the average AoI and age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold."
"The authors show that an optimized strategy significantly outperforms both baselines in terms of the AoI metrics and throughput, for both decoding-with-capture and decoding-without-capture cases."
"The authors also show that a high energy harvesting rate can increase the average AoI and AVP. In this case, the devices often have enough energy and transmit regardless of the obtainable AoI reduction, leading to many transmissions that cause collisions and, even if successful, result in a small AoI reduction."