When to pull data from sensors for minimum Distance-based Age of incorrect Information metric

Abstract

The age of Information (AoI) has been introduced to capture the notion of freshness in real-time monitoring applications. However, this metric falls short in many scenarios, especially when quantifying the mismatch between the current and the estimated states. To circumvent this issue, in this paper, we adopt the age of incorrect of information metric (AoII) that considers the quantified mismatch between the source and the knowledge at the destination. We consider for that a problem where a central entity pulls the information from remote sources that evolve according to a Markovian Process. It selects at each time slot which sources should send their updates. As the scheduler does not know the real state of the remote sources, it estimates at each time the value of AoII based on the Markovian sources' parameters. Its goal is to keep the time average of AoII function as small as possible. We develop a scheduling scheme based on Whittle's index policy for that purpose. To that extent, we proceed by using the Lagrangian Relaxation Approach and establish that the dual problem has an optimal threshold policy. Building on that, we compute the expressions of Whittle's indices. Finally, we provide some numerical results to highlight the performance of our derived policy compared to the classical AoI metric.

Coexistence between Task- and Data-Oriented Communications: A Whittle's Index Guided Multi-Agent Reinforcement Learning Approach

“…Particularly, the principal component for the surrogate loss of the conventional MAPPO utilizes both the advantage functions in (20) and the probability ratios in (21). The former ones are directly derived from the value functions, which are estimated based on the generated trajectory in (19). Now, with the modification in (15), the agent action selected at the states satisfying b m (t) > 0 in the generated trajectory is the optimal agent action since no other agent action is allowable at these states.…”

“…There has been growing research interest in designing AoIIbased scheduling policy for monitoring devices [14], [16]- [19]. Specifically, the authors in [16], [17] discussed the scenario where the target process to be predicted simply follows the binary distribution, and the optimal policy for the case with one target process and a low-complexity suboptimal policy for the case with multiple target processes were developed.…”

“…Specifically, the authors in [16], [17] discussed the scenario where the target process to be predicted simply follows the binary distribution, and the optimal policy for the case with one target process and a low-complexity suboptimal policy for the case with multiple target processes were developed. One step further, the authors in [14], [18], [19] discussed a more complex prediction scenarios, where the target processes have more than two states. Specifically, the authors in [18], [19] discussed the scenario where the state transitions of the processes only occur between the adjacent states, and a Whittle's index based suboptimal policies were proposed for the case with multiple target processes.…”

“…One step further, the authors in [14], [18], [19] discussed a more complex prediction scenarios, where the target processes have more than two states. Specifically, the authors in [18], [19] discussed the scenario where the state transitions of the processes only occur between the adjacent states, and a Whittle's index based suboptimal policies were proposed for the case with multiple target processes. The author in [14] considered the scenario where the state transitions between any two states are allowable, and derived the optimal policy for the case with one target process.…”

Query-Age-Optimal Scheduling Under Sampling and Transmission Constraints

“…This could be practically limited due to continuous sampling costs or even impossible due to, e.g., insufficient energy to make sampling at each time, as is often the case in energy harvesting systems. Even though [12] and its extensions [13], [17] do not base the AoII optimization on a fully observable source, there is no sampling cost involved, and it is assumed that the process of interest can be sampled at any given time upon request (from the monitor); thus, each sensor (that senses the underlying source process) needs to always remain active to listen for requests, which can quickly deplete its batteries [14].…”