Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Abstract

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

Semantics- and Task-Oriented Scheduling for Networked Control Systems in Practice

“…Fig. 14 shows the evolution of nMSE with increasing AoI together with the MSE for IP without the normalization step from (22). It illustrates the different growth speed of the nMSE for our considered application classes.…”

“…FIGURE 14.The normalized mean squared error plotted against AoI, ∆ for different control sub-systems used in this work, i.e., inverted pendulum (IP), Ieasy, I mid , I hard as before. In addition, we present the raw for IP before the normalization step from(22) to illustrate its necessity.…”