Analysis of Age-Energy Trade-off in IoT Networks Using Stochastic Geometry

TL;DR

The paper addresses the trade-off between energy harvesting and data transmission in IoT networks by introducing a slotted frame where a fraction $\xi$ of each slot is devoted to energy harvesting and the remainder to data decoding. It formulates Joint Success Probability $\mu_{\phi}$ as the probability that harvested energy exceeds $E_{th}$ and the downlink SIR exceeds $\beta$, and it analyzes Peak AoI (PAoI) under both non-preemptive and preemptive queueing, using stochastic geometry to model transmitter locations as a Poisson point process. The authors derive upper and lower bounds on JSP and an upper bound on PAoI, revealing that there exists a unique optimal slot partitioning factor $\xi^{*}$ that maximizes JSP and minimizes PAoI for a given deployment and transmit power; the preemptive queue consistently yields lower PAoI than the non-preemptive one. The NL EH model, which includes minimum and saturation thresholds, is shown to significantly influence JSP and PAoI, particularly at low power, and guides practical design decisions. Overall, the work provides design insights for tuning $\xi$ and queueing policies to balance energy harvesting and timely data decoding in energy-constrained IoT networks, with implications for deployment density and power budgeting.

Abstract

We study an internet of things (IoT) network where devices harvest energy from transmitter power. IoT devices use this harvested energy to operate and decode data packets. We propose a slot division scheme based on a parameter $ξ$, where the first phase is for energy harvesting (EH) and the second phase is for data transmission. We define the joint success probability (JSP) metric as the probability of the event that both the harvested energy and the received signal-to-interference ratio (SIR) exceed their respective thresholds. We provide lower and upper bounds of (JSP), as obtaining an exact JSP expression is challenging. Then, the peak age-of-information (PAoI) of data packets is determined using this framework. Higher slot intervals for EH reduce data transmission time, requiring higher link rates. In contrast, a lower EH slot interval will leave IoT devices without enough energy to decode the packets. We demonstrate that both non-preemptive and preemptive queuing disciplines may have the same optimal slot partitioning factor for maximizing the JSP and minimizing the PAoI. For different transmit powers and deployment areas, we recommend the optimal slot partitioning factor for the above two metrics under both queuing disciplines.

Figures (10)

• Figure 1: Illustration of sample path of AoI under non-preemptive queue discipline.
• Figure 2: Illustration of sample path of AoI under preemptive queue discipline.
• Figure 3: Illustration of the process $\hat{W_{i}}$ under preemptive queue discipline.
• Figure 4: The accuracy of the UB, AC and LB of the JSP, $\mu _{\phi }$ for both L EH and NL EH models with respect to the transmit power.
• Figure 5: Lower and upper bounds of joint success probability, $\mu _{\phi}$ with respect to the radius, R compared with the actual simulation when received power $P_{r}$ lies in between $P_{r,min}$ and $P_{r,max}$.

Theorems & Definitions (13)

• Definition 1
• Definition 2
• lemma 1
• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4