Optimal Update Policy for the Monitoring of Distributed Sources

TL;DR

This paper derives the optimal finite-time update policy for monitoring distributed binary sources under reporting constraints, minimizing error probability by following a specific 3-stage update pattern with analytically determined transition points.

Contribution

It introduces a novel analytical solution for the optimal update policy in distributed source monitoring with constraints, including bounds and a structured 3-stage pattern.

Findings

Optimal policy follows a specific ordered 3-stage pattern.

Analytical transition points for each stage are provided.

Bounds on the minimal probability of error are established.

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.