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Age of Information in Random Access Networks with Energy Harvesting

Fangming Zhao, Nikolaos Pappas, Meng Zhang, Howard H. Yang

TL;DR

The findings indicate that the optimal update rate should be set to one in the energy-constrained regime where the energy consumption rate exceeds the energy arrival rate, and if the optimal blocklength of the data packet is pre-configured, an energy buffer size supporting only one transmission is sufficient.

Abstract

We study the age of information (AoI) in a random access network consisting of multiple source-destination pairs, where each source node is empowered by energy harvesting capability. Every source node transmits a sequence of data packets to its destination using only the harvested energy. Each data packet is encoded with finite-length codewords, characterizing the nature of short codeword transmissions in random access networks. By combining tools from bulk-service Markov chains with stochastic geometry, we derive an analytical expression for the network average AoI and obtain closed-form results in two special cases, i.e., the small and large energy buffer size scenarios. Our analysis reveals the trade-off between energy accumulation time and transmission success probability. We then optimize the network average AoI by jointly adjusting the update rate and the blocklength of the data packet. Our findings indicate that the optimal update rate should be set to one in the energy-constrained regime where the energy consumption rate exceeds the energy arrival rate. This also means if the optimal blocklength of the data packet is pre-configured, an energy buffer size supporting only one transmission is sufficient.

Age of Information in Random Access Networks with Energy Harvesting

TL;DR

The findings indicate that the optimal update rate should be set to one in the energy-constrained regime where the energy consumption rate exceeds the energy arrival rate, and if the optimal blocklength of the data packet is pre-configured, an energy buffer size supporting only one transmission is sufficient.

Abstract

We study the age of information (AoI) in a random access network consisting of multiple source-destination pairs, where each source node is empowered by energy harvesting capability. Every source node transmits a sequence of data packets to its destination using only the harvested energy. Each data packet is encoded with finite-length codewords, characterizing the nature of short codeword transmissions in random access networks. By combining tools from bulk-service Markov chains with stochastic geometry, we derive an analytical expression for the network average AoI and obtain closed-form results in two special cases, i.e., the small and large energy buffer size scenarios. Our analysis reveals the trade-off between energy accumulation time and transmission success probability. We then optimize the network average AoI by jointly adjusting the update rate and the blocklength of the data packet. Our findings indicate that the optimal update rate should be set to one in the energy-constrained regime where the energy consumption rate exceeds the energy arrival rate. This also means if the optimal blocklength of the data packet is pre-configured, an energy buffer size supporting only one transmission is sufficient.

Paper Structure

This paper contains 59 sections, 8 theorems, 141 equations, 12 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Contributions
  4. System model
  5. Network Configuration
  6. Transmission Strategy
  7. Performance Metric
  8. Preliminary
  9. Transmission Success Probability under Finite Blocklength
  10. Conditional Network Average AoI
  11. Characterizing the Energy Dynamics
  12. Energy Dynamics under Finite Buffer
  13. Distribution of the Energy Buffer State
  14. Single-EU Consumption with General Energy Buffer Size
  15. Multiple-EU Consumption with Small Energy Buffer Size
  16. ...and 44 more sections

Key Result

lemma 1

Conditioning on the point process $\Phi$, the transmission success probability can be tightly approximated as: where $\kappa_j$ represents the amount of energy stored in source node $j$'s energy buffer and $\theta_{N, \epsilon }$ is given by the solution of the following equationThe quantity $\theta_{N, \epsilon }$ can be regarded as the effective SINR decoding threshold, which decreases as the p

Figures (12)

  • Figure 1: A snapshot of the considered system model: The up-left figure illustrates the basic model of an energy harvesting-enabled link. The up-mid figure depicts the spatial distribution of the network, representing the random locations of transmitter-receiver (square and circle, respectively) pairs. The solid black line is the typical link, the solid red lines represent other active links, and the inactive ones are dashed blue lines. The upright figure shows the aggregate interference effect in the network. The schematic below outlines the energy storage and consumption cycle for data transmission.
  • Figure 2: An illustration of AoI evolution over the typical link.
  • Figure 3: A Markov chain characterizing the dynamics of energy harvesting and consumption.
  • Figure 4: Network average AoI versus energy buffer size. $\xi=0.8$, $\eta=0.3$, $\lambda \in \{0.01,0.04,0.07,0.1\}$, $\frac{P_{ \mathrm{tx}}}{\sigma^2}=13~\text{dB}$, $N=3$, $\epsilon=10^{-6}$.
  • Figure 5: Network average AoI versus update rate. $\lambda = 0.01$, $\xi\in\{0.3,0.8\}$, $N\in\{1,5,10\}$, i.e., $c_N\in\{100,500,1000\}\text{bits}$, $\frac{P_{ \mathrm{tx}}}{\sigma^2}=13~\text{dB}$, $B=100$, $\epsilon=10^{-6}$.
  • ...and 7 more figures

Theorems & Definitions (15)

  • Remark 1
  • lemma 1
  • Remark 2
  • Remark 3
  • lemma 2
  • lemma 3
  • lemma 4
  • Corollary 1
  • Remark 4
  • Theorem 1
  • ...and 5 more