Statistical Age of Information: A Risk-Aware Metric and Its Applications in Status Updates

TL;DR

This work introduces Statistical AoI, an EVaR-based tail-aware metric Δ(ρ) for peak AoI, enabling risk-sensitive evaluation of status updates. It develops a two-step optimization framework to minimize Δ(ρ) over wireless fading channels, deriving a channel-threshold, threshold-Lambert-W-based optimal sampling policy that transitions from a step function to a constant as ρ varies. It then extends the framework to a TDMA MAC setting with multiple sources, providing an efficient time-allocation scheme that equalizes the per-source statistical AoI under frame constraints. Numerical results show that Statistical AoI-based designs yield tighter tail performance and better risk satisfaction than conventional average or maximum AoI-based schemes, highlighting practical benefits for time-sensitive, risk-aware systems.

Abstract

Age of information (AoI) is an effective measure to quantify the information freshness in wireless status update systems. It has been further validated that the peak AoI has the potential to capture the core characteristics of the aging process, and thus the average peak AoI is widely used to evaluate the long-term performance of information freshness. However, the average peak AoI is a risk-insensitive metric and therefore may not be well suited for evaluating critical status update services. Motivated by this concern, and following the spirit of entropic value-at-risk (EVaR) in the field of risk analysis, in this paper we present a concept, termed Statistical AoI, for providing a unified framework to guarantee various requirements of risk-sensitive status-update services with the demand on the violation probability of the peak age. In particular, as the constraint on the violation probability of the peak age varies from loose to strict, the statistical AoI evolves from the average peak AoI to the maximum peak AoI. We then investigate the statistical AoI minimization problem for status updates over wireless fading channels. It is interesting to note that the corresponding optimal sampling scheme varies from step to constant functions of the channel power gain with the peak age violation probability from one to zero. We also address the maximum statistical AoI minimization problem for multi-status updates with time division multiple access (TDMA), where longer transmission time can improve reliability but may also cause the larger age. By solving this problem, we derive the optimal transmission time allocation scheme. Numerical results show that our proposals can better satisfy the diverse requirements of various risk-sensitive status update services, and demonstrate the great potential of improving information freshness compared to baseline approaches.

Figures (14)

• Figure 1: A typical status updating process in monitoring systems.
• Figure 2: (a) The AoI process at the side of destination, where $A^{(i)}$ represents the $i$th peak age and $A_{\rm th}$ denotes the lower bound of peak age satisfying ${\rm Pr}(A \geq A_{\rm th}) \leq \rho$, and (b) the relationships among VaR, CVaR, and EVaR in terms of peak age.
• Figure 3: AoI processes at the sides of source and destination.
• Figure 4: Optimal sampling rate with respect to AoI exponent and channel power gain.
• Figure 5: The tendencies of $(1/\theta)\log M_A(\theta)$, $(1/\theta)\log(1/\rho)$, and $(1/\theta)\log((1/\rho)M_A(\theta))$ with respect to $\theta$.