Timely Status Updates in Slotted ALOHA Networks With Energy Harvesting

TL;DR

This work tackles AoI in a dense slotted ALOHA network where $U$ energy-harvesting devices with battery capacity $E$ transmit updates with no gateway feedback. It develops a Markovian framework to obtain the exact average AoI and introduces accurate, low-complexity approximations for AoI and AVP, alongside throughput analysis. The study evaluates baseline strategies (transmit-on-update vs energy-aware transmission), and demonstrates that an optimized, energy-and-time-aware policy, especially when decoding with capture, significantly improves AoI metrics and throughput. It also shows that decoding multiple packets via successive interference cancellation and adapting transmission probability to both battery level and time since last transmission yields substantial gains, particularly in high-load and energy-harvesting regimes.

Abstract

We 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. We let the devices adjust the transmission probabilities based on their current battery level. Using a Markovian analysis, we derive analytically the average AoI. We further provide an approximate analysis for accurate and easy-to-compute approximations of both the average AoI and the age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold. We also analyze the average throughput. Via numerical results, we investigate two baseline strategies: transmit a new update whenever possible to exploit every opportunity to reduce the AoI, and transmit only when sufficient energy is available to increase the chance of successful decoding. The two strategies are beneficial for low and high update-generation rates, respectively. We show that an optimized policy that balances the two strategies outperforms them significantly in terms of both AoI metrics and throughput. Finally, we show the benefit of decoding multiple packets in a slot using successive interference cancellation and adapting the transmission probability based on both the current battery level and the time elapsed since the last transmission.

Figures (13)

• Figure 1: Example of the AoI process. Here, $Y$ is the time elapsed between two refreshes, and $\theta$ is an threshold.
• Figure 2: Markov chain $M_1$ describing the slot-wise evolution of the battery level of a device.
• Figure 3: An example of the chain $(X^{(s)},B^{(s)})$ for $E = 2$. This chain describes the slot-wise evolution of the AoI refresh status and battery level of a device. The transitions that lead to an refresh are depicted by red dashed lines.
• Figure 4: An example of the chain $M_2$ for $\mathrm{E}=2$. This chain describes the slot-wise evolution of the battery level of a device from an refresh (state $({\mathrm{S}}',0)$, $({\mathrm{S}}',1)$, or $({\mathrm{S}}',2)$) to the next refresh (state ${\mathrm{S}}"$). This chain is obtained from $(X^{(s)},B^{(s)})$ in Fig. \ref{['fig:markov_XB']} by redirecting all transitions that lead to an refresh into a new state ${\mathrm{S}}"$.
• Figure 5: The Markov chains describing the AoI refresh of a generic device in the case of always-full battery.

Theorems & Definitions (11)

• Lemma 1: Battery profile evolution of $\mathrm{U}-1$ devices
• proof
• Theorem 1: metrics in terms of the inter-refresh time distribution
• Remark 1: Complexity Issue
• Lemma 2: Distribution of the inter-refresh time $Y$
• Theorem 2: Approximate AoI metrics
• Theorem 3: metrics with always-full battery
• Theorem 4: Multi-threshold slotted ALOHA
• proof
• Lemma 3: Discrete phase-type distribution