Update Rate, Accuracy, and Age of Information in a Wireless Sensor Network

TL;DR

This work analyzes a single-sensor wireless monitoring system where a time-varying process is modeled as a 1-D random walk and updates are generated only when the state reaches ±$T$ relative to the last report. It derives closed-form expressions for the update rate $\lambda$, the normalized sum AoI $\text{NSAoI} = \frac{1}{2}\left(1 + \frac{\mathbb{E}[L^2]}{\mathbb{E}[L]}\right)$, and the long-term estimation error EMSE via a shifted random-walk framework and Markov-chain analysis, providing insight into the trade-offs between update rate, AoI, and accuracy. The results show how increasing $T$ lowers the update rate but worsens AoI and accuracy, enabling the determination of a minimum $\lambda$ to meet specified NSAoI and EMSE constraints; these analytic insights are corroborated by numerical simulations. The findings have practical implications for energy-constrained wireless sensor networks where freshness and precision of time-sensitive information must be balanced against communication cost.

Abstract

Age of Information (AoI), namely the time that has elapsed since the most recently delivered packet was generated, is receiving increasing attention with the emergence of many real-time applications that rely on the exchange of time-sensitive information. AoI captures the freshness of the information from the perspective of the destination. The term "accuracy of information" is used to assess how close the estimate at the destination is to the parameter value measured by the sensor. In this paper, the mean square error (MSE) is used to evaluate the accuracy of information. We focus on a single sensor that monitors a time-sensitive physical process, which is modelled as a random walk. Whenever the state of the random walk changes by more than a specified threshold, the sensor generates a status update packet and transmits it to the destination. When no update packet is received, the destination assumes that the state of the process has not changed. We study the problem of finding the minimum update rate under AoI and accuracy of information constraints. More specifically, we derive analytical expressions for the update rate, the AoI, and the MSE.

Figures (7)

• Figure 1: An example of AoI evolution in an update cycle of length $l$.
• Figure 2: An illustration of a shifted update cycle and estimation error with $T=2$, and $p+q \neq 1$.
• Figure 3: Update rate $\lambda$ as a function of the threshold $T$, with $p=q=0.5$, 0.4, 0.3.
• Figure 4: Normalized sum AoI versus the threshold $T$ for $p=q=0.3$, 0.4, 0.5.
• Figure 5: Normalized sum AoI versus update rate $\lambda$ for different sets of $(p,q)$ values.