Optimal Update Policy for the Monitoring of Distributed Sources

TL;DR

The paper analyzes optimal update strategies for monitoring multiple binary-state remote sources under a constraint on update signaling. By bounding the error probability with a tractable surrogate and reformulating the problem, it reveals that the optimal policy has a structured three-stage update pattern and derives explicit per-source transition points. The approach combines dynamic-programming simplifications, tail-error analysis, and a KKT-based optimization to yield practical transition times for each source. This work advances efficient distributed monitoring by clarifying how to allocate limited update resources to preserve correct top-K decisions.

Abstract

When making decisions in a network, it is important to have up-to-date knowledge of the current state of the system. Obtaining this information, however, comes at a cost. In this paper, we determine the optimal finite-time update policy for monitoring the binary states of remote sources with a reporting rate constraint. We first prove an upper and lower bound of the minimal probability of error before solving the problem analytically. The error probability is defined as the probability that the system performs differently than it would with full system knowledge. More specifically, an error occurs when the destination node incorrectly determines which top-K priority sources are in the ``free'' state. We find that the optimal policy follows a specific ordered 3-stage update pattern. We then provide the optimal transition points for each stage for each source.

Figures (3)

• Figure 1: Network Model
• Figure 2: An example of the summation terms approximating the error probability, with rows being unique to each remote source and columns representing time.
• Figure 3: An example of the summation terms approximating the error probability after Theorem \ref{['thm:simp_form']}. Here, orange boxes are ones where the source updates in either error state, while all other boxes the remote source only ever updates in one particular error state, determined by the values of $\mu_n$ and $\lambda_n$.

Theorems & Definitions (12)

• Theorem 3
• Remark 4
• Theorem 5
• Theorem 6
• Lemma 7
• Lemma 8
• Lemma 10
• Lemma 11
• Lemma 12
• Lemma 13