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.
Highlights
We derive the upper and lower bounds of the average value of information (VoI), which are tractable and useful for the design and optimisation of freshness-aware applications. Through all of these results, we provide a clear statistical framework linking the VoI to the age of information (AoI) and a formal justification for the selection of non-linear age functions
In the high signal-to-noise ratio (SNR) regime resulting from high correlation, the VoI can be approximated as a logarithmic function of the AoI, which is given by the following: V ( a) ≈ − log(2κγa + 1) + log(1 + γ)
We explore the VoI in a specific FCFS M/M/1 queue system and derive its statistical properties
Summary
There are more and more real-time monitoring and control applications, such as industrial control, Internet of Things, autonomous driving and so on. The basic notion of the AoI grows linearly with a unit slope as time goes by, and it is independent of the context and the inherent characterisation of the targeted random process (e.g., the correlation property of the underlying source data). We obtained the closed-form expression of the VoI, which relates to the correlation of the process under observation at the source and the noise in the transmission environment, but we did not investigate its relationship to the AoI and its statistical characterisations in more depth. We derive the upper and lower bounds of the average VoI, which are tractable and useful for the design and optimisation of freshness-aware applications Through all of these results, we provide a clear statistical framework linking the VoI to the AoI and a formal justification for the selection of non-linear age functions.
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